World-volume supermembrane instantons in the light-cone frame (original) (raw)
Properties of the eleven-dimensional supermembrane theory
Annals of Physics, 1988
We study in detail the structure of the Lorentz covariant, spacetime supersymmetric lldimensional supermembrane theory. We show that for a flat spacetime background, the spacetime supersymmetry becomes an N =8 world volume (rigid) supersymmetry in a "physical" gauge; we also present the field equations and transformation rules in a "lightcone" gauge. We semiclassically quantize the closed torodial supermembrane on a spacetime (Minkowki),
Physics Letters B, 1997
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 preserves any supersymmetry. Both solutions involve the octonionic structure constants but, perhaps surprisingly, they are unrelated to the octonionic instanton 2-form F , for which T rF ∧ F is neither self-dual nor anti-self-dual.
Instanton solutions of the self-dual membrane in various dimensions
Physics Letters B, 1998
We present some methods of determining explicit solutions for self-dual supermembranes in 4 + 1 and 8 + 1 dimensions with spherical or toroidal topology. For congurations of axial symmetry, the continuous S U( 1) T oda equation turns out to play a central role and a specic method of determining all the periodic solutions is suggested. A n umber of examples is studied in detail.
A note on the supersymmetries of the self-dual supermembrane
Physics Letters B, 1998
In this letter we discuss the supersymmetry issue of the self-dual supermembranes in (8 + 1) and (4 + 1)-dimensions. We nd that all genuine solutions of the (8 + 1)dimensional supermembrane, based on the exceptional group G 2 , preserve one of the sixteen supersymmetries while all solutions in (4 + 1)-dimensions preserve eight of them.
Non-collapsing membrane instantons in higher dimensions
Physics Letters B, 2002
We introduce a particular embedding of seven dimensional self-duality membrane equations in C 3 × R which breaks G2 invariance down to SU(3). The world-volume membrane instantons define SU(3) special lagrangian submanifolds of C 3 . We discuss in detail solutions for spherical and toroidal topologies assuming factorization of time. We show that the extra dimensions manifest themselves in the solutions through the appearance of a non-zero conserved charge which prevents the collapse of the membrane.
Dual instantons in antimembranes theory
Physical Review D, 2011
We introduce two ansatzs for the 3-form potential of Euclidean 11d supergravity on skew-whiffed AdS 4 × S 7 background which results in two scalar modes with m 2 = −2 on AdS 4 . Being conformally coupled with a quartic interaction it is possible to find the exact solutions of the scalar equation on this background. These modes turn out to be invariant under SU (4) subgroup of SO(8) isometry group, whereas there are no corresponding SU (4) singlet BPS operators of dimensions one or two on the boundary ABJM theory. Noticing the interchange of 8 s and 8 c representations under skew-whiffing in the bulk, we propose the theory of anti-membranes should similarly be obtained from ABJM theory by swapping these representations. In particular, this enables us to identify the dual boundary operators of the two scalar modes. We deform the boundary theory by the dual operators and examine the fermionic field equations and compare the solutions of the deformed theory with those of the bulk. 1 aimaanpu@theory.ipm.ac.ir 2 m.naghdi@modares.ac.ir
Open supermembranes in eleven dimensions
Physics Letters B, 1997
We consider open supermembranes in an eleven dimensional background. We show that, in a flat space-time, the world-volume action is kappa-symmetric and has global space-time supersymmetry if space-time has even dimensional topological defects where the membrane can end. An example of such topological defects is provided by the space-time with boundaries considered by Horava and Witten. In that case the world-volume action has reparametrisation anomalies whose cancellation requires the inclusion of a current algebra on the boundaries of the membrane. The role of kappa-anomalies in a general background is discussed. The tension of the membrane is related to the eleven dimensional gravitational constant with the aid of the Green-Schwarz mechanism allowing a consistency check of M-theory.
Aspects of supersymmetry in multiple membrane theories
Arxiv preprint arXiv:1012.2707, 2010
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 3 p 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 α ′2 terms of the non-abelian D2-brane theory gives rise to the l 3 p corrections of the Lorentzian Bagger-Lambert theory. We then apply this duality transformation to the α ′2 corrections of the D2-brane supersymmetry transformations. For the 'abelian' Bagger-Lambert theory we are able to uniquely determine the l 3 p corrections to the supersymmetry transformations of the scalar and fermion fields. Generalising to the 'non-abelian' Bagger-Lambert theory we are able to determine the l 3 p 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.
An introduction to the quantum supermembrane
2002
We review aspects of quantisation of the 11-dimensional supermembrane world volume theory. We explicitly construct vertex operators for the massless states and study interactions of supermembranes. The open supermembrane and its vertex operators are discussed. We show how our results have direct applications to Matrix theory by appropriate regularisation of the supermembrane.
The Matrix model and the non-commutative geometry of the supermembrane
Physics Letters B, 1999
This is a short note on the relation of the Matrix model with the non-commutative geometry of the 11-dimensional supermembrane. We put forward the idea that Mtheory is described by the t' Hooft topological expansion of the Matrix model in the large N-limit where all topologies of membranes appear. This expansion can faithfully be represented by the Moyal Yang-Mills theory of membranes. We discuss this conjecture in the case of finite N, where the non-commutative geometry of the membrane is given be the finite quantum mechanics. The use of the finite dimensional representations of the Heisenberg group reveals the cellular structure of a toroidal supemembrane on which the Matrix model appears as a non-commutatutive Yang-Mills theory. The Moyal star product on the space of functions in the case of rational values of Planck constant represents exactly this cellular structure. We also discuss the integrability of the instanton sector as well as the topological charge and the corresponding Bogomol'nyi bound.
D = 11 SUPERMEMBRANE INSTANTONS, W∞ STRINGS AND THE SUPER TODA MOLECULE
Exact instanton solutions to D = 11 spherical supermembranes moving in flat target spacetime backgrounds are construted. Our starting point is Super Yang-Mills theories, based on the infinite dimensional SU (∞) group, dimensionally reduced to one time dimension. In this fashion the super-Toda molecule equation is recovered preserving only one supersymmetry out of the N = 16 that one would have obtained otherwise. It is shown that the expected critical target spacetime dimensions for the (super) membrane (D = 11) D = 27 is closely related to that of the noncritical (super) W ∞ strings. A BRST analysis of these symmetries should yield information about the quantum consistency of the (D = 11) D = 27 dimensional (super) membrane. Comments on the role that Skyrmions might play in the two types of Spinning-Membrane actions construted so far is presented at the conclusion. Finally, the importance that integrability on light-lines in complex superspaces has in other types of solutions is emphasized.
Open supermembranes coupled to M-theory five-branes
Physics Letters B, 1998
We consider open supermembranes in eleven dimensions in the presence of closed M-Theory five-branes. It has been shown that, in a flat space-time, the worldvolume action is kappa invariant and preserves a fraction of the eleven dimensional supersymmetries if the boundaries of the membranes lie on the five-branes. We calculate the reparametrisation anomalies due to the chiral fermions on the boundaries of the membrane and examine their cancellation mechanism. We show that these anomalies cancel with the aid of a classical term in the world-volume action, provided that the tensions of the five-brane and the membrane are related to the eleven dimensional gravitational constant in a way already noticed in M-Theory. 1
Duality rotations in membrane theory
Nuclear Physics B, 1990
In analogy with a previous treatment of strings, it is shown that membrane theories exhibit global noncompact symmetries which have their origin in duality transformations on the three-dimensional worldvolume which rotate field equations into Bianchi identities. However, in contrast to the string, the worldvolume metric also transforms under duality by a conformal factor. In this way the Cremmer-Julia hidden symmetries of supergravity are seen to be a consequence of supermembrane duality. Moreover, the string duality follows from that of the membrane by simultaneous dimensional reduction. Generalization to higher-dimensional objects is straightforward.
Hamiltonian formulation of the supermembrane
Nuclear Physics B, 1988
The hamiltonian formulation of the supermembrane theory in eleven dimensions is given. The covariant split of the first and second class constraints is exhibited, and their Dirac brackets are computed.
Massive super-Yang–Mills quantum mechanics: Classification and the relation to supermembrane
Nuclear Physics B, 2006
We classify the supersymmetric mass deformations of all the super Yang-Mills quantum mechanics, which are obtained by dimensional reductions of minimal super Yang-Mills in spacetime dimensions: ten, six, four, three and two. The resulting actions can be viewed as the matrix descriptions of supermembranes in nontrivial backgrounds of one higher dimensional supergravity theories. We also discuss the utmost generalization of the light-cone formulation of the Nambu-Goto action for a p-brane, including time dependent backgrounds.
Instabilities of spherical membranes in supermembrane and matrix theory
Journal of High Energy Physics, 2000
Motivated by recent work we study rotating ellipsoidal membranes in the framework of the light-cone supermembrane theory. We investigate stability properties of these classical solutions which are important for the quantization of super membranes. We find the stability modes for all sectors of small multipole deformations. We exhibit an isomorphism of the linearized membrane equation with that of the SU(N) matrix model for every value of NNN. The boundaries of the linearized stability region are at a finite distance and they appear for finite size perturbations.
𝒩 = 6 Membrane Worldvolume Superalgebra
Journal of High Energy Physics, 2009
In arXiv:0806.0363 the worldvolume superalgebra of the N = 8 Bagger-Lambert theory was calculated. In this paper we derive the general form for the worldvolume superalgebra of the N = 6 Bagger-Lambert theory. For a particular choice of three-algebra we derive the superalgebra of the ABJM theory. We interpret the associated central charges in terms of BPS brane configurations. In particular we find the central charge corresponding to the energy bound of the BPS fuzzy-funnel configuration of the ABJM theory. We also derive general expressions for the BPS equations of the N = 6 Bagger-Lambert theory.
Supermembranes with fewer supersymmetries
Physics Letters B, 1996
The usual supermembrane solution of D = 11 supergravity interpolates between R 11 and AdS 4 × round S 7 , has symmetry P 3 × SO(8) and preserves 1/2 of the spacetime supersymmetries for either orientation of the round S 7 . Here we show that more general supermembrane solutions may be obtained by replacing the round S 7 by any seven-dimensional Einstein space M 7 . These have symmetry P 3 × G, where G is the isometry group of M 7 . For example, G = SO(5) × SO(3) for the squashed S 7 . For one orientation of M 7 , they preserve N/16 spacetime supersymmetries where 1 ≤ N ≤ 8 is the number of Killing spinors on M 7 ; for the opposite orientation they preserve no supersymmetries since then M 7 has no Killing spinors. For example N = 1 for the left-squashed S 7 owing to its G 2 Weyl holonomy, whereas N = 0 for the right-squashed S 7 . All these solutions saturate the same Bogomol'nyi bound between the mass and charge. Similar replacements of S D−p−2 by Einstein spaces M D−p−2 yield new super p-brane solutions in other spacetime dimensions D ≤ 11. In particular, simultaneous dimensional reduction of the above D = 11 supermembranes on S 1 leads to a new class of D = 10 elementary string solutions which also have fewer supersymmetries.