This thesis consists of two parts. In the first part we investigate the worldvolume supersymmetry algebra of multiple membrane theories. We begin with a description of M-theory branes and their intersections from the perspective of spacetime and worldvolume supersymmetry algebras. We then provide an overview of the recent work on multiple M2-branes focusing on the Bagger-Lambert theory and its relation to the Nambu-Poisson M5-brane and the ABJM theory. The worldvolume supersymmetry algebras of these theories are explicitly calculated and the charges interpreted in terms of spacetime intersections of M-branes. The second part of the thesis looks at $l_p^3$ corrections to the supersymmetry transformations of the Bagger-Lambert theory. We begin with a review of the dNS duality transformation which allows a gauge field to be dualised to a scalar field in 2+1 dimensions. Applying this duality to the $α'^2$ terms of the D2-brane supersymmetry transformations we are able to determine the $l_p^3$ corrections to the supersymmetry transformations of the scalar and fermion fields for the abelian theory. Generalising to the `non-abelian' Bagger-Lambert theory we are able to determine the $l_p^3$ correction to the supersymmetry transformation of the fermion field. Along the way make a number of observations relating to the implementation of the dNS duality transformation at the level of supersymmetry transformations.
We consider superconformal field theories in three and six dimensions with eight supercharges which can be realized on the world-volume of M-theory branes sitting at orbifold singularities. We find that they should admit a N=4 and N=2 supergravity dual in AdS_4 and AdS_7, respectively. We discuss the characteristics of the corresponding gauged supergravities.
We calculate the potential between various configurations of membranes and gravitons in M(atrix) theory. The computed potentials agree with the short distance potentials between corresponding 2-branes and 0-brane configurations in Type IIA string theory, bound to a large number of 0-branes to account for the boost to the infinite momentum frame. We show that, due to the large boost, these type IIA configurations are almost supersymmetric, so that the short and long distance potentials actually agree. Thus the M(atrix) theory is able to reproduce correct long distance behavior in these cases.
A review of the construction of a Weyl-invariant spinning-membrane action that is $polynomial$ in the fields, without a cosmological constant term, comprised of quadratic and quartic-derivative terms, and where supersymmetry is linearly realized, is presented. The action is invariant under a $modified$ supersymmetry transformation law which is derived from a new $ Q + K + S $ sum-rule based on the 3D-superconformal algebra .
A new local world volume supersymmetric Lagrangian for the bosonic membrane is presented. The starting Lagrangian is the one constructed by Dolan and Tchrakian with vanishing cosmological constant, with quadratic and quartic derivative terms. Our Lagrangian differs from the one constructed by Lindstrom and Rocek in the fact that it is polynomial in the fields facilitating the quantization process. It is argued, rigorously, that if one wishes to construct polynomial actions without a curvature scalar term and, where supersymmetry is linearly realized in the space of physical fields, after the e…
We perform a heat kernel asymptotics analysis of the nonperturbative superpotential obtained from wrapping of an M2-brane around a supersymmetric noncompact three-fold embedded in a (noncompact) G_2-manifold as obtained in [1], the three-fold being the one relevant to domain walls in Witten's MQCD [2], in the limit of small "zeta", a complex constant that appears in the Riemann surfaces relevant to defining the boundary conditions for the domain wall in MQCD. The MQCD-like configuration is interpretable, for small but non-zero zeta as a noncompact/"large" open membrane instanton, and for vanis…
It has been recently argued by some authors that is impossible to construct a Weyl invariant spinning membrane action, where the $S$-supersymmetry associated with the 3D superconformal algebra, is relinquished without gauge fixing. Contrary to those assertions, we show why it is possible to construct a Weyl-invariant spinning polynomial membrane action, without curvature terms,where $both$ the conformal boost symmetry and $S$-supersymmetry are explicitly broken by the action. It is shown that the gauge algebra $closes$ despite that the two latter symmetries are broken . For this to happen, a m…
We investigate supersymmetric boundary conditions in both the Bagger-Lambert and the ABJM theories of interacting membranes. We find boundary conditions associated to the fivebrane, the ninebrane and the M-theory wave. For the ABJM theory we are able to understand the enhancement of supersymmetry to produce the (4,4) supersymmetry of the self-dual string. We also include supersymmetric boundary conditions on the gauge fields that cancel the classical gauge anomaly of the Chern-Simons terms.
We investigate space-time supersymmetry of the model of multiple M2-branes proposed by Bagger-Lambert and Gustavsson. When there is a central element in Lie 3-algebra, the model possesses an extra symmetry shifting the fermions in the central element. Together with the original worldvolume supersymmetry transformation, we construct major part of the eleven dimensional space-time super-Poincaré algebra with central extensions. Implications to transverse five-branes in the matrix model for M-theory are also discussed.
A local world volume Q-supersymmetric Weyl invariant Lagrangian for the membrane is presented. An analysis is provided which solves the problems raised by some authors in the past concerning the algebraic elimination of the auxiliary fields belonging to the coupling function supermultiplet. The starting bosonic action is the one given by Dolan and Tchrakian with vanishing cosmological constant and with quadratic, quartic derivative terms. Our Lagrangian differs from the one of Lindstrom and Rocek in the fact that is polynomial in the fields facilitating the quantization process. It is argued, …
We perform a systematic study, in eleven dimensional supergravity, of the geometry of wrapped brane configurations admitting $AdS_2$ limits. Membranes wrapping holomorphic curves in Calabi-Yau manifolds are found to exhibit some novel features; in particular, for fourfolds or threefolds, the gravitational effect of the branes on the overall transverse space is only weakly restricted by the kinematics of the Killing spinor equation. We also study the $AdS_2$ limits of the wrapped brane supergravity descriptions. For membranes wrapped in a two-fold, we derive a set of $AdS_2$ supersymmetry condi…
This paper examines various aspects of the recently proposed theory of coincident membranes by Bagger and Lambert. These include the properties of open membranes and the resulting boundary theory with an interpretation in terms of the fivebrane and marginal supersymmetric deformations of the interactions with the relation to the holographic dual.
In this note we investigate quantum aspects of the newly proposed theory of multiple membranes put forward by Bagger and Lambert. In particular we analyse the possibility of a finite renormalisation of the coupling at one loop.
We derive the BPS equations satisfied by lump solitons in $(2+1)$-dimensional sigma models with toric 8-dimensional hyper-Kähler (${HK}_8$) target spaces and check they preserve 1/2 of the supersymmetry. We show how these solitons are realised in M theory as M2-branes wrapping holomorphic 2-cycles in the $\bE^{1,2}\times {HK}_8$ background. Using the $κ$-symmetry of a probe M2-brane in this background we determine the supersymmetry they preserve, and note that there is a discrepancy in the fraction of supersymmetry preserved by these solitons as viewed from the low energy effective sigma model…
By analysing supersymmetry transformations we derive new BPS equations for the D=11 fivebrane propagating in flat space that involve the world-volume three-form. The equations generalise those of 2,3,4 and 5 dimensional special Lagrangian submanifolds and are relevant for describing membranes ending on these submanifolds.
Partition functions for M2-brane theories in various backgrounds are computed. We consider in particular configurations of membranes at orbifold singularities preserving N=5 or N=6 supersymmetry. The worldvolume membrane theory for some of these configurations has been recently constructed in terms of N=6 Chern-Simons theories. The detailed structure of the partition functions as well as their transformation rules under the R-symmetry are explicitly computed using the Plethystic Programme.
We generalize the supermembrane solution of D=11 supergravity by permitting the 4-form $G$ to be either self-dual or anti-self-dual in the eight dimensions transverse to the membrane. After analyzing the supergravity field equations directly, and also discussing necessary conditions for unbroken supersymmetry, we focus on two specific, related solutions. The self-dual solution is not asymptotically flat. The anti-self-dual solution is asymptotically flat, has finite mass per unit area and saturates the same mass=charge Bogomolnyi bound as the usual supermembrane. Nevertheless, neither solution…
Starting from gauged N=8 supergravity in three dimensions we construct actions for multiple membranes by taking the limit to global supersymmetry for different choices of the embedding tensor. This provides a general framework that reproduces many recent results on multiple membrane actions as well as generalisations thereof. As examples we discuss conformal (non-conformal) gaugings leading to multiple M2-branes (D2-branes) and massive deformations of these systems.
The exact quantum integrability aspects of a sector of the membrane is investigated. It is found that spherical membranes moving in flat target spacetime backgrounds admit a class of integrable solutions linked to SU(infty) SDYM equations (dimensionally reduced to one temporal dimension). After a suitable ansatz, the SDYM equations can be recast in the form of the continuous Toda molecule equations whose symmetry algebra is the dimensional reduction of the W (infty} plus {\bar W}(infty} algebra. The latter algebra is explicitly constructed. Highest weight representations are built directly fro…
There exist extremal p-brane solutions of $D\!=\!11$ supergravity for p=2~and~5. In this paper we investigate the zero modes of the membrane and the five-brane solutions as a first step toward understanding the full quantum theory of these objects. It is found that both solutions possess the correct number of normalizable zero modes dictated by supersymmetry.
In this note we study M5-branes in the multiple membrane action which is recently proposed by Aharony-Bergman-Jafferis-Maldacena. We write down the N=6 supersymmetry transformation of the action and obtain 1/2 BPS equations and their solutions. They are expected to represent membranes ending on a M5-brane. We also consider the M5-M2 bound state in the action.
Certain perturbative aspects of two-dimensional sigma models with (0,2) supersymmetry are investigated. The main goal is to understand in physical terms how the mathematical theory of ``chiral differential operators'' is related to sigma models. In the process, we obtain, for example, an understanding of the one-loop beta function in terms of holomorphic data. A companion paper will study nonperturbative behavior of these theories.
A first-order `BPS' equation is obtained for 1/8 supersymmetric intersections of soliton-membranes (lumps) of supersymmetric (4+1)-dimensional massless sigma models, and a special non-singular solution is found that preserves 1/4 supersymmetry. For 4-dimensional hyper-Kähler target spaces ($HK_4$) the BPS equation is shown to be the low-energy limit of the equation for a Cayley-calibrated 4-surface in $\bE^4\times HK_4$. Similar first-order equations are found for stationary intersections of Q-lump-membranes of the massive sigma model, but now generic solutions preserve either 1/8 supersymmetr…
This work is based on an earlier proposal \cite{hs} that the membrane B-F theory consists of matter fields alongwith Chern-Simons fields as well as the auxiliary pairs of scalar and tensor fields. We especially discuss the supersymmetry aspects of such a membrane theory. It is concluded that the theory possesses maximal supersymmetry and it is related to the L-BLG theory via a field map. We obtain fuzzy-sphere solution and corresponding tensor field configuration is given.
We study classical field theories that do not admit an action principle, implying that their formulation is entirely in terms of equations of motion. In the theories that we consider, supersymmetry is realized on the mass-shell. We will show that the supersymmetry algebras previously studied in the literature, allow for a broader class of potentials and for new target space manifolds. We discuss extensively theories with eight supercharges as well as a massive ten dimensional maximal supergravity.
We study certain aspects of noncommutativity in field theory, strings and membranes. We analyse the dynamics of an open membrane whose boundary is attached to p-branes. Noncommutative features of the boundary string coordinates are revealed by algebraic consistency arguments. Next, we derive Seiberg-Witten-type maps relating currents and their divergences in nonabelian U(N) noncommutative gauge theory with the corresponding expressions in the ordinary (commutative) description. We then exploit these maps to obtain the O(θ) structure of the commutator anomalies in noncommutative electrodynamics…
Among the solutions of string theory and supergravity which preserve some fraction of supersymmetry, the best known are those that leave one half of the supersymmetry unbroken, and there is a large number of field theory models with this pattern of supersymmetry breaking. However, a lot of brane configurations exist which preserve only $1/4$, $1/8$ or more exotic fractions of supersymmetry, and field theory side of these systems remains largely unexplored. To find whether the formalism of nonlinear realizations is useful in construction of models of this type, we consider the systems of some $…
The off-shell description of N=(2,2) supersymmetric non-linear sigma-models is reviewed. The conditions for ultra-violet finiteness are derived and T-duality is discussed in detail.
M2-branes can blow up into BPS funnels that end on calibrated intersections of M5-branes. In this quick note, we make the observation that the constraints required for the consistency of these solutions are automatic in Bagger-Lambert-Gustavsson (BLG) theory, thanks to the fundamental identity and the supersymmetry of the calibration. We use this to explain how the previous ad hoc fuzzy funnel constructions emerge in this picture, and make some comments about the role of the 3-algebra trace form in the derivation.
The first part of this thesis is a general introduction to the bosonic and fermionic string theory, to the concept of D brane and to string dualities. A discussion of anomalies cancellation closes the chapter. The second part of the thesis reviews the basics of orientifold and orbifold constructions and the Scherk-Schwarz mechanism of supersymmetry breaking. The last part starts with an introduction to standard cosmology and inflation. Alternatives to inflation inspired from string theory and time dependent orbifolds are discussed. Finally time dependent solutions of non-supersymmetric strings…
We study the constraints of supersymmetry on flavour in recently proposed models of F-theory GUTs. We relate the topologically twisted theory to the canonical presentation of eight-dimensional super Yang-Mills and provide a dictionary between the two. We describe the constraints on Yukawa couplings implied by holomorphy of the superpotential in the effective 4-dimensional supergravity theory, including the scaling with α_{GUT}. Taking D-terms into account we solve explicitly to second order for wavefunctions and Yukawas due to metric and flux perturbations and find a rank-one Yukawa matrix wit…
We consider the maximal central extension of the supertranslation algebra in d=4 and 3, which includes tensor central charges associated to topological defects such as domain walls (membranes) and strings. We show that for all N-extended superalgebras these charges are related to nontrivial configurations on the scalar moduli space. For N=2 theories obtained from compactification on Calabi-Yau threefolds, we give an explicit realization of the moduli-dependent charges in terms of wrapped branes.
There are two different methods to describe membrane (string) fluids, which use different field content. The relation between the methods is clarified by construction of combined method. Dirac membrane field appears naturally in new approach. It provides a possibility to consider new aspects of electrodynamics-type theories with electric and magnetic sources. The membrane fluid models automatically prohibit simulatenos existence of electric and magnetic currents. Possible applications to the dark energy problem are mentioned.
Aspects of strings without spacetime supersymmetry
Scuola Normale Superiore（高等师范学校）；INFN（意大利国家核物理研究所）；Instituto de Física Teórica IFT-UAM/CSIC（理论物理研究所 IFT-UAM/CSIC）；Universidad Autónoma de Madrid（马德里自治大学）
Through a nonperturbative analysis on a sextic triple-well potential, we reveal novel aspects of the dynamical property of the system in connection with N-fold supersymmetry and quasi-solvability.
We consider partial spontaneous breaking of N=1 AdS4 supersymmetry OSp(1|4) down to N=1, d=3 Poincare supersymmetry in the nonlinear realizations framework. We construct the corresponding worldvolume Goldstone superfield action and show that it describes the N=1 AdS4 supermembrane. It enjoys OSp(1|4) supersymmetry realized as a field-dependent modification of N=1, d=3 superconformal symmetry and goes into the superfield action of ordinary N=1, D=4 supermembrane in the flat limit. Its bosonic core is the Maldacena-type conformally invariant action of the AdS4 membrane. We show how to reproduce …
Based on the recently proposed action for Matrix theory describing the DLCQ M theory in the maximally supersymmetric pp-wave background, we obtain the supersymmetry algebra of supercharge density. Using supersymmetry transformation rules for fermions, we identify BPS states with the central charges in the supersymmetry algebra, which can be activated only in the large N limit. They preserve some fraction of supersymmetries and correspond to rotating transverse membranes and longitudinal five branes.
The simplest supersymmetry (SUSY) algebra in four dimensional Euclidean space ($4dE$) has been shown to closely resemble the $N = 2$ SUSY algebra in four dimensional Minkowski space ($4dM$). The structure of the former algebra is examined in greater detail in this paper. We first present its Clifford algebra structure. This algebra shows that the momentum Casimir invariant of physical states has an upper bound which is fixed by the central charges. Secondly, we use reduction of the $N = 1$ SUSY algebra in six dimensional Minkowski space ($6dM$) to $4dE$; this reproduces our SUSY algebra in $4d…
We construct the N=2, D=9 supergravity theory up to the quartic fermionic terms and derive the supersymmetry transformation rules for the fields modulo cubic fermions. We consider a class of p-brane solutions of this theory, the stainless p-branes, which cannot be isotropically oxidized into higher dimensions. The new stainless elementary membrane and elementary particle solutions are found. It is explicitly verified that these solutions preserve half of the supersymmetry.
In this thesis, we study the details of some fundamental cosmological problems of the gauge mediated supersymmetry breakdown and we probe the supersymmetry breaking sector by cosmological arguments. We manifest that problems like the metastable vacuum selection and the gravitino overproduction in the reheated early universe are naturally absent in the most general class of gauge mediation models without including additional ingredients or assumptions. We also find that the gravitino can generically account for the bulk dark matter of the universe. Cosmological implications of a stringy UV-comp…
A brief description of some salient aspects of four-dimensional supersymmetry: early history, supermanifolds, the MSSM, cold dark matter, the cosmological constant and the string landscape.
We present an overview of the intimate relationship between string and D-brane dynamics, and the dynamics of gauge and gravitational fields in three spacetime dimensions. The successes, prospects and open problems in describing both perturbative and nonperturbative aspects of string theory in terms of three-dimensional quantum field theory are highlighted.
The supersymmetry algebra for supermembranes, quantized in the light-cone gauge, exhibits central charges induced by wrapping the membrane around compact dimensions. These central charges are manifestly consistent with Lorentz symmetry. While the central charges raise the mass of the membrane states, they still leave the mass spectrum continuous, at least generically. The lower bound on the mass spectrum is set by the winding number and corresponds to a BPS state.
Some general aspects of supersymmetry and supergravity are briefly reviewed with emphasis on Noether supercurrents and their role in the discussion of supersymmetry breaking.
The application and extension of well-known BRST cohomological methods to supersymmetric field theories are discussed. The focus is on the emergence and particular features of supersymmetry algebra cohomology in this context. In particular it is discussed and demonstrated that supersymmetry algebra cohomology emerges within the cohomological analysis of standard supersymmetric field theories whether or not the commutator algebra of the symmetry transformations closes off-shell.
In the first half of this note, after briefly motivating and reviewing membrane field theories, we consider their BPS funnel solutions. We discuss some aspects of embedding M-theory fuzzy funnels in these theories. In the second half, we focus on ABJM theory and explain a test of AdS4/CFT3 based on integrability. We discuss a numerical mismatch at one loop in worldsheet perturbation theory and its possible resolutions.
We review developments in the theory of multiple, parallel membranes in M-theory. After discussing the inherent difficulties pertaining to a maximally supersymmetric lagrangian formulation with the appropriate field content and symmetries, we discuss how introducing the concept of 3-algebras allows for such a description. Different choices of 3-algebras lead to distinct classes of 2+1 dimensional theories with varying degrees of supersymmetry. We then describe how these are equivalent to a type of conventional superconformal Chern-Simons gauge theories at level k, coupled to bifundamental matt…
We review aspects of Poisson-Lie T-duality which we explicitly formulate as a canonical transformation on the world-sheet. Extensions of previous work on T-duality in relation to supersymmetry are also discussed. (Contribution to the proceedings of the 30th International Symposium Ahrenshoop on the Theory of Elementary Particles, Buckow, Germany, 26-31 August 1996)
Some field theory aspects can be addressed holographically by introducing D-branes in the string theory duals. In this work, we study this issue in the framework of a dual of N=1 YM, the so-called Maldacena-Nunez model. Some supersymmetric embeddings for D5-brane probes are found and they are interpreted as the addition of fundamental flavors to the gauge theory. This allows to give a dual description of some known aspects of N=1 SQCD and to compute a mass spectrum of mesons.
We clarify certain aspects of instanton operators in five-dimensional supersymmetric gauge theories. In particular, we show how, in the pointlike limit, they become supersymmetric and provide the natural bridge with the instantonic states contributing to the index as well as with the zero mode counting leading to broken current multiplets.
At the core of nonperturbative theories of quantum gravity lies the holographic encoding of bulk data in large matrices. At present this mapping is poorly understood. The plane wave matrix model provides a laboratory for isolating aspects of this problem in a controlled setting. At large boosts, configurations of concentric membranes become superselection sectors, whose exact spectra are known. From the bulk point of view one expects product states of individual membranes to be contained within the full spectrum. However, for non-BPS states this inclusion relation is obscured by Gauss law cons…
Some aspects of finite quantum field theories in 3+1 dimensions are discussed. A model with non--supersymmetric particle content and vanishing one-- and two--loop beta functions for the gauge coupling and one--loop beta functions for Yukawa--couplings is presented.
Generalized membrane solutions of D=11 supergravity, for which the transverse space is a toric hyper-K{\" a}hler manifold, are shown to have IIB duals representing the intersection of parallel 3-branes with 5-branes whose orientations are determined by their $Sl(2;\bZ)$ charge vectors. These IIB solutions, which generically preserve 3/16 of the supersymmetry, can be further mapped to solutions of D=11 supergravity representing the intersection of parallel membranes with any number of fivebranes at arbitrary angles. Alternatively, a subclass (corresponding to non-singular D=11 solutions) can be…
We present an exact analytic class of solutions for a system of two membranes in eleven-dimensional supergravity. One brane in the system is completely localized along the overall and relative transverse coordinates while the other brane in the system is localized only along the overall transverse coordinates. The membrane configuration preserves four supersymmetries. Moreover we find some approximate solutions for the system of two membranes with a Bianchi space as the overall transverse space to both membranes. All supergravity solutions preserve 1/8 of the supersymmetry. Upon dimensional re…
We discuss supersymmetry in twelve dimensions and present a covariant supersymmetric action for a brane with worldsheet signature (2,2), called a super (2+2)-brane, propagating in the osp(64,12) superspace. This superspace is explicitly constructed, and is trivial in the sense that the spinorial part is a trivial bundle over spacetime, unlike the twisted superspace of usual Poincare supersymmetry. For consistency, it is necessary to take a projection of the superspace. This is the same as the projection required for worldvolume supersymmetry. Upon compactification of this superspace, a torsion…
We conjecture the existence of two new non-gravitational six-dimensional string theories, defined as the decoupling limit of NS5-branes in the background of near-critical electrical two- and three-form RR fields. These theories are space-time non-commutative Little String Theories with open branes. The theory with (2,0) supersymmetry has an open membrane in the spectrum and reduces to OM theory at low energies. The theory with (1,1) supersymmetry has an open string in the spectrum and reduces to 5+1 dimensional NCOS theory for weak NCOS coupling and low energies. The theories are shown to be T…
We find the dyonic worldvolume solitons due to parallel (p,q) strings ending on a D-3-brane. These solutions preserve 1/4 of bulk supersymmetry. Then we investigate the scattering of well-separated dyons and find that their moduli space is a toric hyper-Kähler manifold. In addition, we present the worldvolume solitons of the D-3-brane which are related by duality to the M-theory configuration of two orthogonal membranes ending on a M-5-brane. We show that these solitons preserve 1/8 of supersymmetry and compute their effective action.
