G. Papadopoulos
We find that the structure constants 4-form of a metric 3-Lie algebra is the sum of the volume forms of orthogonal 4-planes proving a conjecture in math/0211170. In particular, there is no metric 3-Lie algebra associated to a $\mathfrak{u}(N)$ Lie algebra for $N>2$. We examine the implication of this result on the existence of a multiple M2-brane theory based on metric 3-Lie algebras.
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The present paper describes the $W$--geometry of the Abelian finite non-periodic (conformal) Toda systems associated with the $B,C$ and $D$ series of the simple Lie algebras endowed with the canonical gradation. The principal tool here is a generalization of the classical Plücker embedding of the $A$-case to the flag manifolds associated with the fundamental representations of $B_n$, $C_n$ and $D_n$, and a direct proof that the corresponding Kähler potentials satisfy the system of two--dimensional finite non-periodic (conformal) Toda equations. It is shown that the $W$--geometry of the type me…
A family of Majumdar-Papapetrou type solutions in sigma-model of p-brane origin is obtained for all direct sums of finite-dimensional simple Lie algebras. Several examples of p-brane dyonic configurations in D=10 (IIA) and D=11 supergravities corresponding to the Lie algebra sl(3,C) are considered.
We consider a low-energy effective action for the gauge field on Wess-Zumino-Witten D-branes in a compact simple Lie group, in the limit of large k. We prove that the effective action is bounded from below, and study stability of various D-brane configurations, including some class of non-maximally symmetric ones. We show that for Lie groups of rank higher than one, the D-brane ground state breaks the Kac-Moody symmetry of the boundary theory. We then give arguments hinting that the "fuzzy sphere" D2-brane which is known to be the stable brane configuration in the case of SU(2), may also corre…
We derive the super Yang-Mills action of Dp-branes on a torus T^{p-4} from the nonabelian (2,0) theory with Lie 3-algebra. Our realization is based on Lie 3-algebra with pairs of Lorentzian metric generators. The resultant theory then has negative norm modes, but it results in a unitary theory by setting VEV's of these modes. This procedure corresponds to the torus compactification, therefore by taking a transformation which is equivalent to T-duality, the Dp-brane action is obtained. We also study type IIA/IIB NS5-brane and Kaluza-Klein monopole systems by taking other VEV assignments. Such v…
We review various generalizations of the notion of Lie algebras, in particular those appearing in the recently proposed Bagger-Lambert-Gustavsson model, and study their interrelations. We find that Filippov's n-Lie algebras are a special case of strong homotopy Lie algebras. Furthermore, we define a class of homotopy Maurer-Cartan equations, which contains both the Nahm and the Basu-Harvey equations as special cases. Finally, we show how the super Yang-Mills equations describing a Dp-brane and the Bagger-Lambert-Gustavsson equations supposedly describing M2-branes can be rewritten as homotopy …
We consider the realization of affine ADE Lie algebras as string junctions on mutually non-local 7-branes in Type IIB string theory. The existence of the affine algebra is signaled by the presence of the imaginary root junction ``delta'', which is realized as a string encircling the 7-brane configuration. The level k of an affine representation partially constrains the asymptotic (p,q) charges of string junctions departing the configuration. The junction intersection form reproduces the full affine inner product, plus terms in the asymptotic charges.
Using the concept of 3-Lie bialgebra, which has recently been defined in arXiv:1604.04475, we construct Bagger-Lambert-Gustavson (BLG) model for M2-brane on Manin triple of a special 3-Lie bialgebra. Then by using the correspondence and relation between those 3-Lie bialgebra with Lie bialgebra, we reduce this model to an $N=(4,4)$ WZW model (D2-brane), such that, its algebraic structure is a Lie bialgebra with one 2-cocycle. In this manner by using correspondence of 3-Lie bialgebra and Lie bialgebra (for this special 3-Lie algebra) one can construct M2-brane from a D2-brane and vice versa.
We show that the WZW model on the Heisenberg Lie group $H_4$ has Poisson-Lie symmetry only when the dual Lie group is ${ A}_2 \oplus 2{ A}_1$. In this way, we construct the mutual T-dual sigma models on Drinfel'd double generated by the Heisenberg Lie group $H_4$ and its dual pair, ${ A}_2 \oplus 2{ A}_1$, as the target space in such a way that the original model is the same as the $H_4$ WZW model. Furthermore, we show that the dual model is conformal up to two loops order. Finally, we discuss $D$-branes and the worldsheet boundary conditions defined by a gluing matrix on the $H_4$ WZW model. …
We propose a generalization of the Bagger-Lambert-Gustavsson action as a candidate for the description of an arbitrary number of M2-branes. The action is formulated in terms of N=2 superfields in three dimensions and corresponds to an extension of the usual superfield formulation of Chern-Simons matter theories. Demanding gauge invariance of the resulting theory does not imply the total antisymmetry of the underlying 3-Lie algebra structure constants. We relax this condition and propose a class of examples for these generalized 3-Lie algebras. We also discuss how to associate various ordinary …
Motivated by the recent proposal of an N=8 supersymmetric action for multiple M2-branes, we study the Lie 3-algebra in detail. In particular, we focus on the fundamental identity and the relation with Nambu-Poisson bracket. Some new algebras not known in the literature are found. Next we consider cubic matrix representations of Lie 3-algebras. We show how to obtain higher dimensional representations by tensor products for a generic 3-algebra. A criterion of reducibility is presented. We also discuss the application of Lie 3-algebra to the membrane physics, including the Basu-Harvey equation an…
Global issues of the Poisson-Lie T-duality are addressed. It is shown that oriented open strings propagating on a group manifold $G$ are dual to $D$-brane - anti-$D$-brane pairs propagating on the dual group manifold $\ti G$. The $D$-branes coincide with the symplectic leaves of the standard Poisson structure induced on the dual group $\ti G$ by the dressing action of the group $G$. T-duality maps the momentum of the open string into the mutual distance of the $D$-branes in the pair. The whole picture is then extended to the full modular space $M(D)$ of the Poisson-Lie equivalent $\si$-models …
We write the conditions for open strings with charged endpoints in the language of gluing matrices. We identify constraints imposed on the gluing matrices that are essential in this setup and investigate the question of their invariance under the Poisson-Lie T-plurality transformations. We show that the chosen set of constraints is equivalent to the statement that the lifts of D-branes into the Drinfel'd double are right cosets with respect to a maximally isotropic subgroup and therefore it is invariant under the Poisson-Lie T-plurality transformations.
In this note we analyze the geometry of maximally symmetric boundary conditions in Lie supergroup Wess-Zumino-Novikov-Witten models. We find that generically the worldvolume of a brane is a twisted superconjugacy class, very much like in the Lie group case. Whenever the brane is not completely delocalized in the fermionic directions a new atypical class of branes arises. We give an example of these new branes and show for type I supergroups and trivial gluing conditions that they can be naturally associated with atypical representations of the affine Lie superalgebra.
Using quiver gauge theories in (1+2)-dimensions, we give brane realizations of a class of Quantum Hall Solitons (QHS) embedded in Type IIA superstring on the ALE spaces with exotic singularities. These systems are obtained by considering two sets of wrapped D4-branes on 2-spheres. The space-time on which the QHS live is identified with the world-volume of D4-branes wrapped on a collection of intersecting 2-spheres arranged as extended Dynkin diagrams of Kac-Moody Lie algebras. The magnetic source is given by an extra orthogonal D4-brane wrapping a generic 2-cycle in the ALE spaces. It is shown…
Electric S-brane solutions with two non-composite electric branes and a set of l scalar fields are considered. The intersection rules for branes correspond to Lie algebras A_2, C_2 and G_2. The solutions contain five factor spaces. One of them, M_0, is interpreted as our 3-dimensional space. It is shown that there exists a time interval where accelerated expansion of our 3-dimensional space is compatible with a small enough variation of the effective gravitational constant G(τ). This interval contains τ_0, a point of minimum of the function G(τ). A special solution with two phantom scalar fiel…
We give a systematic account of symmetric D-branes in the Lie group SU(3). We determine both the classical and quantum moduli space of (twisted) conjugacy classes in terms of the (twisted) Stiefel diagram of the Lie group. We show that the allowed (twisted) conjugacy classes are in one-to-one correspondence with the integrable highest weight representations of the (twisted) affine Lie algebra. In particular, we show how the charges of these D-branes fit in the twisted K-theory groups.
We show that the Bagger-Lambert-Gustavsson (BLG) theory with two pairs of negative norm generators is derived from the scaling limit of an orbifolded Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. The BLG theory with many Lorentzian pairs is known to be reduced to the Dp-brane theory via Higgs mechanism, so our scaling procedure can be used to derive Dp-branes directly from M2-branes in the field theory language. In this paper, we focus on the D3-brane case and investigate the scaling limits of various quiver Chern-Simons theories obtained from different orbifolding actions. Remarkably, in …
Lorentzian signature D-branes of all dimensions for the Nappi-Witten string are constructed. This is done by rewriting the gluing condition $J_+=FJ_-$ for the model chiral currents on the brane as a well posed first order differential problem and by solving it for Lie algebra isometries $F$ other than Lie algebra automorphisms. By construction, these D-branes are not twined conjugacy classes. Metrically degenerate D-branes are also obtained.
Constructing M2-brane and its boundary conditions from D2-brane and the related boundary conditions and vice versa has been possible in our recent work by using 3-Lie bialgebra for BLG model with N = 8 supersymmetry. This could be generalized for BL model with N = 6 by the concept of the 3-Leibniz bialgebra. The 3-Lie bialgebra is an especial case of 3-Leibniz bialgebra, then more comprehensive information will be obtained in this work. Consequently, according to the correspondence of these 3-Leibniz bialgebras with Lie bialgebras, we reduce to D2-brane such that with some restrictions on the …
The geometric description of D-branes in WZW models is pushed forward. Our starting point is a gluing condition\, $J_{+}=FJ_-$ that matches the model's chiral currents at the worldsheet boundary through a linear map $F$ acting on the WZW Lie algebra. The equivalence of boundary and gluing conditions of this type is studied in detail. The analysis involves a thorough discussion of Frobenius integrability, shows that $F$ must be an isometry, and applies to both metrically degenerate and nondegenerate D-branes. The isometry $F$ need not be a Lie algebra automorphism nor constantly defined over th…
We complete the study of the Poisson-Sigma model over Poisson-Lie groups. Firstly, we solve the models with targets $G$ and $G^*$ (the dual group of the Poisson-Lie group $G$) corresponding to a triangular $r$-matrix and show that the model over $G^*$ is always equivalent to BF-theory. Then, given an arbitrary $r$-matrix, we address the problem of finding D-branes preserving the duality between the models. We identify a broad class of dual branes which are subgroups of $G$ and $G^*$, but not necessarily Poisson-Lie subgroups. In particular, they are not coisotropic submanifolds in the general …
We reformulate the bosonic action of unstable M3-brane to manifest its algebraic representation. It is seen that in contrast with string and M2-brane actions that are represented only in terms of two and three dimensional Lie-algebras respectively, the algebraic form of M3-brane action is a combination of four, three and two dimensional Lie-algebras. Corresponding brackets appear as mixtures of tachyon field, space-time coordinates, $X$, two-form field, $\hatω^{(2)}$, and Born-Infeld one-form, $\hat{b}_μ$.
Departing from the observation that the Penrose limit of AdS_3 x S^3 is a group contraction in the sense of Inonu and Wigner, we explore the relation between the symmetric D-branes of AdS_3 x S^3 and those of its Penrose limit, a six-dimensional symmetric plane wave analogous to the four-dimensional Nappi--Witten spacetime. Both backgrounds are Lie groups admitting bi-invariant lorentzian metrics and symmetric D-branes wrap their (twisted) conjugacy classes. We determine the (twisted and untwisted) symmetric D-branes in the plane wave background and we prove the existence of a space-filling D5…
The Higgs sector of the low-energy physics of n of coincident D-branes contains the necessary elements for constructing noncommutative manifolds. The coordinates orthogonal to the coincident branes, as well as their conjugate momenta, take values in the Lie algebra of the gauge group living inside the brane stack. In the limit when n=\infty (and in the absence of orientifolds), this is the unitary Lie algebra u(\infty). Placing a smooth manifold K orthogonally to the stack of coincident D-branes one can construct a noncommutative C*-algebra that provides a natural definition of a noncommutativ…
An abundance of the Poisson-Lie symmetries of the WZNW models is uncovered. They give rise, via the Poisson-Lie $T$-duality, to a rich structure of the dual pairs of $D$-branes configurations in group manifolds. The $D$-branes are characterized by their shapes and certain two-forms living on them. The WZNW path integral for the interacting $D$-branes diagrams is unambiguously defined if the two-form on the $D$-brane and the WZNW three-form on the group form an integer-valued cocycle in the relative singular cohomology of the group manifold with respect to its $D$-brane submanifold. An example …
We apply the Lie algebra expansion method to the $\mathcal{N}=1$ super-Poincaré algerba in four dimensions. We define a set of p-brane projectors that induce a decomposition of the super-Poincaré algebra preparatory for the expansion. We show that starting from the $\mathcal{N}=1$ supergravity action in four dimensions it is possible to obtain two non-relativistic supersymmetric theories, one describing strings, the other membranes.
Superimposed D-branes have matrix-valued functions as their transverse coordinates, since the latter take values in the Lie algebra of the gauge group inside the stack of coincident branes. This leads to considering a classical dynamics where the multiplication law for coordinates and/or momenta, being given by matrix multiplication, is nonabelian. Quantisation further introduces noncommutativity as a deformation in powers of Planck's constant. Given an arbitrary simple Lie algebra and an arbitrary Poisson manifold, both finite-dimensional, we define a corresponding C*-algebra that can be rega…
A family of composite black brane solutions in the model with scalar fields and fields of forms is presented. The metric of any solution is defined on a manifold which contains a product of several Ricci-flat "internal" spaces. The solutions are governed by moduli functions H_s (s = 1, ..., m) obeying non-linear differential equations with certain boundary conditions imposed. These master equations are equivalent to Toda-like equations and depend upon the non-degenerate (m x m) matrix A. It was conjectured earlier that the functions H_s should be polynomials if A is a Cartan matrix for some se…
We consider string junctions with endpoints on a set of branes of IIB string theory defining an ADE-type gauge Lie algebra. We show how to characterize uniquely equivalence classes of junctions related by string/brane crossing through invariant charges that count the effective number of prongs ending on each brane. Each equivalence class defines a point on a lattice of junctions. We define a metric on this lattice arising from the intersection pairing of junctions, and use self-intersection to identify junctions in the adjoint and fundamental representations of all ADE algebras. This informati…
We formalize higher dimensional and higher gauge WZW-type sigma-model local prequantum field theory, and discuss its rationalized/perturbative description in (super-)Lie n-algebra homotopy theory (the true home of the "FDA"-language used in the supergravity literature). We show generally how the intersection laws for such higher WZW-type sigma-model branes (open brane ending on background brane) are encoded precisely in (super-) L-infinity-extension theory and how the resulting "extended (super-)spacetimes" formalize spacetimes containing sigma model brane condensates. As an application we pro…
We construct a class of Lie 3-algebras with an arbitrary number of pairs of generators with Lorentzian signature metric. Some examples are given and corresponding BLG models are studied. We show that such a system in general describes a supersymmetric massive vector multiplets after the ghost fields are Higgsed. Simple systems with nontrivial interaction are realized by infinite dimensional Lie 3-algebras associated with the loop algebras. The massive fields are then naturally identified with the Kaluza-Klein modes by the toroidal compactification triggered by the ghost fields. For example, Dp…
In a previous paper we explored how conjugacy classes of the modular group classify the symmetry algebras that arise on type IIB [p,q] 7-branes. The Kodaira list of finite Lie algebras completely fills the elliptic classes as well as some parabolic classes. Loop algebras of E_N fill additional parabolic classes, and exotic finite algebras, hyperbolic extensions of E_N and more general indefinite Lie algebras fill the hyperbolic classes. Since they correspond to brane configurations that cannot be made into strict singularities, these non-Kodaira algebras are spectrum generating and organize to…
We apply canonical Poisson-Lie T-duality transformations to bosonic open string worldsheet boundary conditions, showing that the form of these conditions is invariant at the classical level, and therefore they are compatible with Poisson-Lie T-duality. In particular the conditions for conformal invariance are automatically preserved, rendering also the dual model conformal. The boundary conditions are defined in terms of a gluing matrix which encodes the properties of D-branes, and we derive the duality map for this matrix. We demonstrate explicitly the implications of this map for D-branes in…
The algebra of the generators of translations in superspace is unstable, in the sense that infinitesimal perturbations of its structure constants lead to non-isomorphic algebras. We show how superspace extensions remedy this situation (after arguing that remedy is indeed needed) and review the benefits reaped in the description of branes of all kinds in the presence of the extra dimensions.
Three-dimensional conformal theories with six supersymmetries and SU(4) R-symmetry describing stacks of M2-branes are here proposed to be related to generalized Jordan triple systems. Writing the four-index structure constants in an appropriate form, the Chern-Simons part of the action immediately suggests a connection to such triple systems. In contrast to the previously considered three-algebras, the additional structure of a generalized Jordan triple system is associated to a graded Lie algebra, which corresponds to an extension of the gauge group. In this note we show that the whole theory…
We consider the graded space $R$ of syzygies for the coordinate algebra $A$ of projective variety $X=G/P$ embedded into projective space as an orbit of the highest weight vector of an irreducible representation of semisimple complex Lie group $G$. We show that $R$ is isomorphic to the Lie algebra cohomology $H=H^\bdot(\Lt,\CC)$, where $\Lt$ is graded Lie subalgebra of the graded Lie s-algebra $L=L_1\oplus\Lt$ Koszul dual to $A$. We prove that the isomorphism identifies the natural associative algebra structures on $R$ and $H$ coming from their Koszul and Chevalley DGA resolutions respectively.…
We show that untwisted respectively twisted conjugacy classes of a compact and simply connected Lie group which satisfy a certain integrality condition correspond naturally to irreducible highest weight representations of the corresponding affine Lie algebra. Along the way, review the classification of twisted conjugacy classes of a simply connected compact Lie group $G$ and give a description of their stabilizers in terms of the Dynkin diagram of the corresponding twisted affine Lie algebra.
We uncover higher algebraic structures on Noether currents and BPS charges. It is known that equivalence classes of conserved currents form a Lie algebra. We show that at least for target space symmetries of higher parameterized WZW-type sigma-models this naturally lifts to a Lie (p+1)-algebra structure on the Noether currents themselves. Applied to the Green-Schwarz-type action functionals for super p-brane sigma-models this yields super Lie (p+1)-algebra refinements of the traditional BPS brane charge extensions of supersymmetry algebras. We discuss this in the generality of higher different…
Recently an action based on Lie 3-algebras was proposed to describe M2-branes. We study the case of infinite dimensional Lie 3-algebras based on the Nambu-Poisson structure of three dimensional manifolds. We show that the model contains self-dual 2-form gauge fields in 6 dimensions, and the result may be interpreted as the M5-brane world-volume action.
We present two derivations of the multiple D2 action from the multiple M2-brane model proposed by Bagger-Lambert and Gustavsson. The first one is to start from Lie 3-algebra associated with given (arbitrary) Lie algebra. The Lie 3-algebra metric is not positive definite but the zero-norm generators merely correspond to Lagrange multipliers. Following the work of Mukhi and Papageorgakis, we derive D2-brane action from the model by giving a variable a vacuum expectation value. The second derivation is based on the correspondence between M2 and M5. We compactify one dimension and wind M5 brane al…
Based on recent developments, in this letter we find 2+1 dimensional gauge theories with scale invariance and N=8 supersymmetry. The gauge theories are defined by a Lagrangian and are based on an infinite set of 3-algebras, constructed as an extension of ordinary Lie algebras. Recent no-go theorems on the existence of 3-algebras are circumvented by relaxing the assumption that the invariant metric is positive definite. The gauge group is non compact, and its maximally compact subgroup can be chosen to be any ordinary Lie group, under which the matter fields are adjoints or singlets. The theori…
Black p-brane solutions for a wide class of intersection rules and Ricci-flat ``internal'' spaces are considered. They are defined up to moduli functions H_s obeying non-linear differential equations with certain boundary conditions imposed. A new solution with intersections corresponding to the Lie algebra C_2 is obtained. The functions H_1 and H_2 for this solution are polynomials of degree 3 and 4.
In this paper, we propose a new model in Lie-N-algebra that removes big bang singularity and produces the world with all it's objects and dimensions from nothing. We name this theory as G-theory. In this model, first, two types of energies with opposite signs are produced from nothing such as the sum over them be zero. They create two types of branes with opposite quantum numbers which interact with each other by exchanging bosonic tensor fields like graviton and compact. By compacting branes, fermionic tensor fields are emerged which some of them play the role of the gravitinos. Also, some di…
The target space M for the sigma-model appearing in theories with p-branes is considered. It is proved that M is a homogeneous space G/H. It is symmetric if and only if the U-vectors governing the sigma-model metric are either coinciding or mutually orthogonal. For nonzero noncoinciding U-vectors the Killing equations are solved. Using a block-orthogonal decomposition of the set of the U-vectors it is shown that under rather general assumptions the algebra of Killing vectors is a direct sum of several copies of sl(2,R) algebras (corresponding to 1-vector blocks), several solvable Lie algebras …
A supersymmetric non-Abelian self-dual gauge theory with the explicit introduction of Kaluza-Klein modes is proposed to give a classical description of multiple M5-branes on $R^5 \times S^1$. The gauge symmetry is parametrized by Lie-algebra valued 1-forms with the redundancy of a 0-form, and the supersymmetry transformations without gauge-fixing are given. We study BPS configurations involving KK modes, including M-waves and M2-branes with non-trivial distributions around the circle. Finally, this supersymmetric gauge theory of two-forms can be equipped with more general non-Abelian gerbes in…
We study the classification of D-branes in all compact Lie groups including non-simply-laced ones. We also discuss the global structure of the quantum moduli space of the D-branes. D-branes are classified according to their positions in the maximal torus. We describe rank 2 cases, namely $B_2$, $C_2$, $G_2$, explicitly and construct all the D-branes in $B_r$, $C_r$, $F_4$ by the method of iterative deletion in the Dynkin diagram. The discussion of moduli space involves global issues that can be treated in terms of the exact homotopy sequence and various lattices. We also show that singular D-b…
Black p-brane solutions for a wide class of intersection rules and Ricci-flat ``internal'' spaces are considered. They are defined up to moduli functions H_s obeying non-linear differential equations with certain boundary conditions imposed. A new solution with intersections corresponding to the Lie algebra A_3 is obtained. The functions H_1, H_2 and H_3 for this solution are polynomials of degree 3, 4 and 3, correspondingly. An example of A_3-solution with three 3-branes in 12-dimensional model (suggested by N. Khviengia et al) is presented.
We show that the geometric interpretation of D-branes in WZW models as twisted conjugacy classes persists in the $λ$--deformed theory. We obtain such configurations by demanding that a monodromy matrix constructed from the Lax connection of the $λ$--deformed theory continues to produce conserved charges in the presence of boundaries. In this way the D-brane configurations obtained correspond to `integrable' boundary configurations. We illustrate this with examples based on $SU(2)$ and $SL(2,\mathbb{R})$, and comment on the relation of these D-branes to both non-Abelian T-duality and Poisson-Li…
Moduli spaces of a large set of $3d$ $\mathcal{N}=4$ effective gauge theories are known to be closures of nilpotent orbits. This set of theories has recently acquired a special status, due to Namikawa's theorem. As a consequence of this theorem, closures of nilpotent orbits are the simplest non-trivial moduli spaces that can be found in three dimensional theories with eight supercharges. In the early 80's mathematicians Hanspeter Kraft and Claudio Procesi characterized an inclusion relation between nilpotent orbit closures of the same classical Lie algebra. We recently showed a physical realiz…
We compute holographic entanglement entropy for subregions of a BCFT thermal state living on a nongravitating black hole background. The system we consider is doubly holographic and dual to an eternal black string with an embedded Karch-Randall brane that is parameterized by its angle. Entanglement islands are conventionally expected to emerge at late times to preserve unitarity at finite temperature, but recent calculations at zero temperature have shown such islands do not exist when the brane lies below a critical angle. When working at finite temperature in the context of a black string, w…
Composite fluxbrane and S-brane solutions for a wide class of intersection rules are considered. These solutions are defined on a product manifold R_{*} x M_1 x ... x M_n which contains n Ricci-flat spaces M_1, ..., M_n with 1-dimensional factor spaces R_{*} and M_1. They are determined up to a set of functions obeying non-linear differential equations equivalent to Toda-type equations with certain boundary conditions imposed. Exact solutions corresponding to configurations with two branes and intersections related to simple Lie algebras C_2 and G_2 are obtained. In these cases, the functions …
We classify canonical metric 3-algebra structures on matrix algebras and find novel three-dimensional conformally invariant actions in N=4 projective superspace based on them. These can be viewed as Chern-Simons theories with special matter content and couplings. We explore the relations of these actions with the N=2 actions based on generalized 3-Lie algebras found earlier and relate them to the original Bagger-Lambert-Gustavsson action.
A general form for the boundary coupling of a Lie algebroid Poisson sigma model is proposed. The approach involves using the Batalin-Vilkovisky formalism in the AKSZ geometrical version, to write a BRST-invariant coupling for a representation up to homotopy of the target Lie algebroid or its subalgebroids. These considerations lead to a conjectural description of topological D-branes on generalized complex manifolds, which includes A-branes and B-branes as special cases.
A study of the relation between topology change, energy and Lie algebra representations for fuzzy geometry in connection to $M$-theory is presented. We encounter two different types of topology change, related to the different features of the Lie algebra representations appearing in the matrix models of $M$-theory. From these studies, we propose a new method of obtaining non-commutative solutions for the non-Abelian $D$-brane action found by Myers. This mechanism excludes one of the two topology changing processes previously found in other non-commutative solutions of many matrix-based models …
Brane mechanics and gapped Lie n-algebroids
本文为高维哈密顿力学的BV/BRST形式与Lie n-代数胚上的高阶挠率概念建立对应，通过定义多挠率和多曲率张量将拓扑n-膜模型与微分几何联系起来。
A subclass of recently discovered class of solutions in multidimensional gravity with intersecting p-branes related to Lie algebras and governed by a set of harmonic functions is considered. This subclass in case of three Euclidean p-branes (one electric and two magnetic) contains a cosmological-type solution (in 11-dimensional model with two 4-forms) related to hyperbolic Kac-Moody algebra ${\cal F}_3$ (of rank 3). This solution describes the non-Kasner power-law inflation.
We compute the $L_\infty$-theoretic dimensional reduction of the F1/D$p$-brane super $L_\infty$-cocycles with coefficients in rationalized twisted K-theory from the 10d type IIA and type IIB super Lie algebras down to 9d. We show that the two resulting coefficient $L_\infty$-algebras are naturally related by an $L_\infty$-isomorphism which we find to act on the super $p$-brane cocycles by the infinitesimal version of the rules of topological T-duality and inducing an isomorphism between $K^0$ and $K^1$, rationally. In particular this is a derivation of the Buscher rules for RR-fields (Hori's f…
The Bagger--Lambert construction of N = 8 superconformal field theories (SCFT) in three dimensions is based on 3-algebras. Three groups of researchers recently realized that an arbitrary semisimple Lie algebra can be incorporated by using a suitable Lorentzian signature 3-algebra. The SU(N) case is a candidate for the SCFT describing coincident M2-branes. However, these theories contain ghost degrees of freedom, which is unsatisfactory. We modify them by gauging certain global symmetries. This eliminates the ghosts from these theories while preserving all of their desirable properties. The res…
We find the analogue of the Boillat metric of Born-Infeld theory for the M5-brane. We show that it provides the propagation cone of {\sl all} 5-brane degrees. In an arbitrary background field, this cone never lies outside the Einstein cone. An energy momentum tensor for the three-form is defined and shown to satisfy the Dominant Energy Condition. The theory is shown to be well defined for all values of the magnetic field but there is a limiting electric field strength. We consider the strong coupling limit of the M5-brane and show that the corresponding theory is conformally invariant and admi…
Due to the difficulties of finding superconformal Lagrangian theories for multiple M2-branes, we will in this paper instead focus on the field equations. By relaxing the requirement of a Lagrangian formulation we can explore the possibility of having structure constants $f^{ABC}{}_D$ satisfying the fundamental identity but which are not totally antisymmetric. We exemplify this discussion by making use of an explicit choice of a non-antisymmetric $f^{ABC}{}_D$ constructed from the Lie algebra structure constants $f^{ab}{}_c$ of an arbitrary gauge group. Although this choice of $f^{ABC}{}_D$ doe…
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