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 and the Bagger-Lambert model.
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 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.
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 …
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 …
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, $\hat{b}_μ$.
The Newton-Hooke algebras in d dimensions are constructed as contractions of dS(AdS) algebras. Non-relativistic brane actions are WZ terms of these Newton-Hooke algebras. The NH algebras appear also as subalgebras of multi-temporal relativistic conformal algebras, SO(d+1, p+2). We construct generalizations of pp-wave metrics from these algebras.
The known extended algebras associated with p-branes are shown to be generated as topological charge algebras of the standard p-brane actions. A representation of the charges in terms of superspace forms is constructed. The charges are shown to be the same in standard/extended superspace formulations of the action.
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 further develop the correspondence between representations of Ding-Iohara-Miki (DIM) algebra and Type IIB branes. In particular we explicitly compute the Hanany-Witten type 5-brane crossing operator which plays the role of the $R$-matrix and has interesting combinatorial properties. We explore the corresponding lattice integrable models and notice a possible connection with statistics of plane partitions.
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…
In string theory, nilpotence of the BRS operator $\d$ for the string functional relates the Chern-Simons term in the gauge-invariant antisymmetric tensor field strength to the central term in the Kac-Moody algebra. We generalize these ideas to p-branes with odd p and find that the Kac-Moody algebra for the string becomes the Mickelsson-Faddeev algebra for the p-brane.
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…
We postulate a new type of operator algebra with a non-abelian extension. This algebra generalizes the Kac--Moody algebra in string theory and the Mickelsson--Faddeev algebra in three dimensions to higher-dimensional extended objects ($p$-branes). We then construct new BRST operators, covariant derivatives and curvature tensors in the higher-dimensional generalization of loop space.
We construct a new classical solution in the ABJM theory corresponding to M5-branes with a non-zero self-dual three form flux. This is an M-theory lift of the D4-brane solution expressed as a non-commutative plane in the three dimensional super Yang-Mills theory. We discuss that our solution is closely related with the three-algebra. We show that the corresponding configuration of the M5-brane satisfies the equations of motion in the single M5-brane action. We find the agreement between the tension of the M5-brane solution in the ABJM action and the one computed from the single M5-brane action…
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…
It is shown that the generalized (with nonpolynomial Lagrangian) Chern-Simons membranes and in general $p$-branes moving in $D$-dimensional target space admit an infinite set of secondary constraints. With respect to the Poisson bracket these constraints satisfy closed algebra containing $p$-dimensional classical $W$ algebra as a subalgebra. In the case when the target space dimension $D$ is finite the theory is topological.
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 show that questions concerning the topological B-model on a Calabi-Yau manifold in the Landau-Ginzburg phase can be rephrased in the language of commutative algebra. This yields interesting and very practical methods for analyzing the model. We demonstrate how the relevant "Ext" groups and superpotentials can be computed efficiently by computer algebra packages such as Macaulay. This picture leads us to conjecture a general description of D-branes in linear sigma models in terms of triangulated categories. Each phase of the linear sigma model is associated with a different presentation of t…
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.
We study the current algebras of the NS5-branes, the Kaluza-Klein (KK) five-branes and the exotic $5^2_2$-branes in type IIA/IIB superstring theories. Their worldvolume theories are governed by the six-dimensional $\mathcal{N}= (2,0)$ tensor and the $\mathcal{N} = (1,1)$ vector multiplets. We show that the current algebras are determined through the S- and T-dualities. The algebras of the $\mathcal{N} = (2,0)$ theories are characterized by the Dirac bracket caused by the self-dual gauge field in the five-brane worldvolumes, while those of the $\mathcal{N} = (1,1)$ theories are given by the Poi…
We express the covariant actions of a super p-brane and the corresponding equations of motion, in the flat and curved superspaces, in terms of the Nambu (p+1)-brackets. These brackets make the (p+1)-algebra structure of super p-brane manifest. For the flat superspace, this reconstruction of the action also allows reformulating it in terms of two sets of differential forms.
Equations of motion for M2- and M5-branes are written down in the $E_{11}$ current algebra formulation of M-theory. These branes correspond to currents of the second and the fifth rank antisymmetric tensors in the $E_{11}$ representation, whereas the electric and magnetic fields (coupled to M2- and M5-branes) correspond to currents of the third and the sixth rank antisymmetric tensors, respectively. We show that these equations of motion have solutions in terms of the coordinates on M2- and M5-branes. We also discuss the geometric equations, and show that there are static solutions when M2- or…
We investigate the algebra generated by the topological Wilson loop operators in WZW models. Wilson loops describe the nontrivial fixed points of the boundary renormalization group flows triggered by Kondo perturbations. Their enveloping algebra therefore encodes all the fixed points which can be reached by sequences of Kondo flows. This algebra is easily described in the case of SU(2), but displays a very rich structure for higher rank groups. In the latter case, its action on known D-branes creates a profusion of new and generically non-rational D-branes. We describe their symmetries and the…
The Noether charge algebras of D-brane actions contain two anomalous terms which modify the standard supertranslation algebra. We use a cocycle approach to derive associated spectra of topological charge algebras. The formalism is applied to $(p,q)$-strings and the D-membrane. The resulting spectra contain known algebras which allow the construction of extended superspace actions.
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.
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…
We study non-relativistic limits of the N=6 Chern-Simons-Matter theory that arises as a low-energy limit of the M2-brane gauge theory with background flux. The model admits several different non-relativistic limits and we find that the maximal supersymmetry we construct has 14 components of supercharges, which is a novel example of non-relativistic superconformal algebra in (1+2) dimension. We also investigate the other limits that realize less supersymmetries.
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.
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.
F theory and M theory are formulated as gauge theories of area preserving diffeomorphism algebra. Our M theory is shown to be 1-brane formulation rather than 0-brane formulation of M theory of Banks, Fischler, Shenker and Susskind and the F theory is shown to be 1-brane formulation rather than -1-brane formulation of type IIB matrix theory of Ishibashi, Kawai, Kitazawa and Tsuchiya.
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.
We derive the fully extended supersymmetry algebra carried by D-branes in a massless type IIA superspace vacuum. We find that the extended algebra contains not only topological charges that probe the presence of compact spacetime dimensions but also pieces that measure non-trivial configurations of the gauge field on the worldvolume of the brane. Furthermore there are terms that measure the coupling of the non-triviality of the worldvolume regarded as a U(1)-bundle of the gauge field to possible compact spacetime dimensions. In particular, the extended algebra carried by the D-2-brane can cont…
The algebra of Noether supercharges of the M-5-brane effective action is shown to include both 2-form and 5-form central charges. Surprisingly, only the 5-form charge is entirely due to the Wess-Zumino term because the `naive' algebra is the M-2-brane supertranslation algebra. The full structure of central charges is shown to be directly related to the projector arising in the proof of $κ$-symmetry of the M-5-brane action. It is also shown to allow `mixed' M-brane configurations preserving 1/2 supersymmetry that include the (non-marginal) M-2-brane/M-5-brane `bound state' as a special case.
We review recent studies of branes in AdS x S and pp-wave spaces using effective action methods (probe branes and supergravity). We also summarise results on an algebraic study of D-branes in these spaces, using extensions of the superisometry algebras which include brane charges.
It is shown that the previously noticed internal dynamical $SO(D-1)$ symmetry arXiv:1003.5189 for relativistic M-branes moving in $D$-dimensional space-time is naturally realized in the (extended by powers of $\frac{1}{p_+}$) enveloping algebra of the Poincaré algebra.
It is known that the M-branes of M-theory correspond to p-form charges in the D=11 spacetime supersymmetry algebra. Here we show that their intersections are encoded in the p-form charges of their worldvolume supersymmetry algebras. Triple intersections are encoded in double intersection worldvolume algebras with eight supercharges.
We begin a classification of the symmetry algebras arising on configurations of type IIB [p,q] 7-branes. These include not just the Kodaira symmetries that occur when branes coalesce into a singularity, but also algebras associated to other physically interesting brane configurations that cannot be collapsed. We demonstrate how the monodromy around the 7-branes essentially determines the algebra, and thus 7-brane gauge symmetries are classified by conjugacy classes of the modular group SL(2,Z). Through a classic map between the modular group and binary quadratic forms, the monodromy fixes the …
The physical meaning of the Reflection Equation Algebras of hep-th/0107265 and hep-th/0203110 is elucidated in the context of Wess--Zumino--Witten D-brane geometry, as determined by couplings of closed-string modes to the D-brane. Particular emphasis is laid on the role of algebraic fusion of the matrix generators of the Reflection Equation Algebras. The fusion is shown to induce transitions among D-brane configurations admitting an interpretation in terms of RG-driven condensation phenomena.
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…
It has long been appreciated that superalgebras with bosonic and fermionic generators additional to those in the super-Poincare algebra underlie p-brane and D-brane actions in superstring theory. These algebras have been revealed via "bottom up" approaches, involving consideration of Noether charges, and by "top down" approaches, involving the construction of manifestly supersymmetry invariant Wess-Zumino actions. In this paper, we give an alternative derivation of these algebras based on integrability of supersymmetry transformations assigned to fields in order to solve a cohomology problem r…
We consider a 3-brane of positive cosmological constant (de Sitter) in D-dimensional Minkowski space. We show that the Poincare algebra in the bulk yields a SO(4,2) algebra when restricted to the brane. In the limit of zero cosmological constant (flat brane), this algebra turns into the conformal algebra on the brane. We derive a correspondence principle for Minkowski space analogous to the AdS/CFT correspondence. We discuss explicitly the cases of scalar and gravitational fields. For a 3-brane of finite thickness in the transverse directions, we obtain a spectrum for vector gravitational pert…
Two superalgebras associated with $p$-branes are the constraint algebra and the Noether charge algebra. Both contain anomalous terms which modify the standard supertranslation algebra. These anomalous terms have a natural description in terms of double complex cohomology of generalized forms. By retaining fermionic charges and allowing for gauge freedom in the double complex, it is shown that the algebra of conserved charges forms a spectrum with free parameters. The spectrum associated with the Green-Schwarz superstring is shown to contain and generalize the known superalgebras associated wit…
By turning on antisymmetric background fluxes, we study how multiple M2-branes are coupled to them. Our investigation concentrates on the gauge invariance conditions for the Myers-Chern-Simons action. Furthermore, the dimensional reduction of M2-branes to D2-branes introduces more constraints on the newly introduced tensors. Particularly, for the theory based on A_4 algebra, we are able to fix all components of them up to an overall normalization constant. These results can not be simply obtained from the previously proposed cubic matrix representation for this algebra. We also comment on cubi…
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…
