Supermembranes and M (Atrix) Theory
Robert Helling1998, Arxiv preprint hep-th/9809103
Sign up for access to the world's latest research
checkGet notified about relevant papers
checkSave papers to use in your research
checkJoin the discussion with peers
checkTrack your impact
Abstract
AI
AI
This set of lectures provides an introduction to supermembranes and the maximally extended d = 11 theory, emphasizing the connection between supersymmetric matrix models and M(atrix) theory. The work discusses the evolution and significance of these theories in the larger context of non-perturbative string theory and quantum gravity, particularly in relation to the formulation of M-Theory. It highlights the roles of D-branes and the implications for a background-independent approach to quantum gravity.
Related papers
From Wrapped Supermembrane to M(atrix) Theory
The issue of justifying the matrix-theory proposal is revisited. We first discuss how the matrix-string theory is derived directly starting from the eleven dimensional supermem- brane wrapped around a circle of radius R = gsℓs, without invoking any stringy assump- tions, such as S- and T-dualities. This derivation provides us a basis for studying both string (R → 0)- and M (R → ∞)-theory limits of quantum membrane theory in a single unified framework. In particular, we show that two different boosts of supermembrane, namely one of unwrapped membrane along the M-theory circle and the other of membrane wrapped about a transervse direction which is orthogonal to the M-theory circle, give the same matrix theory in the 11 dimensional limit, R → ∞ (with N → ∞). We also discuss briefly the nature of possible covariantized matrix (string) theories.
From Wrapped Supermembrane to M(atrix) Theory From Wrapped Supermembrane to M(atrix) Theory
2002
The issue of justifying the matrix-theory proposal is revisited. We first discuss how the matrix-string theory is derived directly starting from the eleven dimensional supermembrane wrapped around a circle of radius R = g s ℓ s , without invoking any stringy assumptions, such as Sand T-dualities. This derivation provides us a basis for studying both string (R → 0)-and M (R → ∞)-theory limits of quantum membrane theory in a single unified framework. In particular, we show that two different boosts of supermembrane, namely one of unwrapped membrane along the M-theory circle and the other of membrane wrapped about a transervse direction which is orthogonal to the M-theory circle, give the same matrix theory in the 11 dimensional limit, R → ∞ (with N → ∞). We also discuss briefly the nature of possible covariantized matrix (string) theories.
Matrix regularization of an open supermembrane: Towards M-theory five-branes via open supermembranes
Physical Review D, 1998
We study open supermembranes in 11 dimensional rigid superspace with 6 dimensional topological defects (M-theory five-branes). After rederiving in the Green-Schwarz formalism the boundary conditions for open superstrings in the type IIA theory, we determine the boundary conditions for open supermembranes by imposing kappa symmetry and invariance under a fraction of 11 dimensional supersymmetry. The result seems to imply the self-duality of the three-form field strength on the fivebrane world volume. We show that the light-cone gauge formulation is regularized by a dimensional reduction of a 6 dimensional N=1 super Yang-Mills theory with the gauge group SO(N→ ∞). We also analyze the SUSY algebra and BPS states in the light-cone gauge.
M theory as a matrix model: A Conjecture
Physical Review D, 1997
From supermembrane to matrix string
Nuclear Physics B, 2001
We develop a systematic method of directly embedding supermembrane wrapped around a circle into matrix string theory. Our purpose is to study connection between matrix string and membrane from an entirely 11 dimensional point of view. The method does neither rely upon the DLCQ limit nor upon string dualities. In principle, this enables us to construct matrix string theory with arbitrary backgrounds from the corresponding supermembrane theory. As a simplest application of the formalism, the matrix-string action with a 7 brane background (Kaluza-Klein Melvin solution) with nontrivial RR vector field is given.
T-duality in M-theory and supermembranes
Physics Letters B, 1997
The (q 1 , q 2) SL(2, Z) string bound states of type IIB superstring theory admit two inequivalent (T-dual) representations in eleven dimensions in terms of a fundamental 2-brane. In both cases, the spectrum of membrane oscillations can be determined exactly in the limit g 2 → ∞, where g 2 is the type IIA string coupling. We find that the BPS mass formulas agree, and reproduce the BPS mass spectrum of the (q 1 , q 2) string bound state. In the non-BPS sector, the respective mass formulas apply in different corners of the moduli space. The axiomatic requirement of T-duality in M-theory permits to derive a discrete mass spectrum in a (thin torus) region where standard supermembrane theory undergoes instabilities.
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.
String Theory and Matrix Models
String Theory in a Nutshell, 2011
It is generally accepted that the double-scaled 1D matrix model is equivalent to the c = 1 string theory with tachyon condensation. There remain however puzzles that are to be claried in order to utilize this connection for our quest towards possible non-perturbative formulation of string theory. W e discuss some of the issues that are related to the space-time interpretation of matrix models, in particular, the questions of leg poles, causality, and black hole background. Finally, a speculation about a possible connection of a deformed matrix model with the idea of Dirichret brane is presented.
BPS bound states, supermembranes, and T-duality in M theory
Dualities in Gauge and String Theories, 1998
This is an introductory review on the eleven-dimensional description of the BPS bound states of type II superstring theories, and on the role of supermembranes in M-theory. The first part describes classical solutions of 11d supergravity which upon dimensional reduction and T-dualities give bound states of NS-NS and R-R p-branes of type IIA and IIB string theories. In some cases (e.g. (q 1 , q 2) string bound states of type IIB string theory), these non-perturbative objects admit a simple eleven-dimensional description in terms of a fundamental 2-brane. The BPS excitations of such 2-brane are calculated and shown to exactly match the mass spectrum for the BPS (q 1 , q 2) string bound states. Different 11d representations of the same bound state can be used to provide inequivalent (T-dual) descriptions of the oscillating BPS states. This permits to test T-duality beyond perturbation theory and, in certain cases, to evade membrane instabilities by going to a stable T-dual representation. We finally summarize the results indicating in what regions of the modular parameter space a supermembrane description for M-theory on R 9 × T 2 seems to be adequate.
Three-algebra for supermembrane and two-algebra for superstring
Journal of High Energy Physics, 2009
While string or Yang-Mills theories are based on Lie algebra or two-algebra structure, recent studies indicate that M-theory may require a one higher, three-algebra structure. Here we construct a covariant action for a supermembrane in eleven dimensions, which is invariant under global supersymmetry, local fermionic symmetry and worldvolume diffeomorphism. Our action is classically on-shell equivalent to the celebrated Bergshoeff-Sezgin-Townsend action. However, the novelty is that we spell the action genuinely in terms of Nambu three-brackets: All the derivatives appear through Nambu brackets and hence it manifests the three-algebra structure. Further the double dimensional reduction of our action gives straightforwardly to a type IIA string action featuring two-algebra. Applying the same method, we also construct a covariant action for type IIB superstring, leading directly to the IKKT matrix model.
Related papers
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),
Regularized supermembrane theory and static configurations of M-Theory
European Physical Journal C, 1999
We suggest that the static configurations of M-theory may be described by the matrix regularization of the supermembrane theory in static regime. We compute the long-range interaction between a M2-brane and an anti-M2-brane in agreement with the 11-dimensional supergravity result.
Matrix string theory
Nuclear Physics B, 1997
Via compactification on a circle, the matrix model of M-theory proposed by Banks et al suggests a concrete identification between the large N limit of two-dimensional N = 8 supersymmetric Yang-Mills theory and type IIA string theory. In this paper we collect evidence that supports this identification. We explicitly identify the perturbative string states and their interactions, and describe the appearance of D-particle and D-membrane states. * Here we work in string units α = 1. A derivation of (1) from matrix theory and a discussion of our normalizations is given in the appendix.
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.
6 STRING THEORY AND MATRIX MODELS a
2016
It is generally accepted that the double-scaled 1D matrix model is equivalent to the c = 1 string theory with tachyon condensation. There remain however puzzles that are to be clarified in order to utilize this connection for our quest towards possible non-perturbative formulation of string theory. We discuss some of the issues that are related to the space-time interpretation of matrix models, in particular, the questions of leg poles, causality, and black hole background. Finally, a speculation about a possible connection of a deformed matrix model with the idea of Dirichret brane is presented.
On the quantum mechanics of M (atrix) theory
Nuclear Physics B, 1998
We present a study of M(atrix) theory from a purely canonical viewpoint. In particular, we identify free particle asymptotic states of the model corresponding to the supergraviton multiplet of eleven dimensional supergravity. These states have a natural interpretation as excitations in the flat directions of the matrix model potential. Furthermore, we provide the split of the matrix model Hamiltonian into a free part describing the free propagation of these particle states along with the interaction Hamiltonian describing their interactions. Elementary quantum mechanical perturbation theory then yields an effective potential for these particles as an expansion in their inverse separation. Remarkably we find that the leading velocity independent terms of the effective potential cancel in agreement with the fact that there is no force between stationary D0 branes. The scheme we present provides a framework in which one can perturbatively compute the M(atrix) theory result for the eleven dimensional supergraviton S matrix.
Note on M (Atrix) Theory In Seven Dimensions With Eight Supercharges
Physical Review D, 1997
We consider M(atrix) theory compactifications to seven dimensions with eight unbroken supersymmetries. We conjecture that both M(atrix) theory on K3 and Heterotic M(atrix) theory on T 3 are described by the same 5+1 dimensional theory with N = 2 supersymmetry broken to N = 1 by the orbifold projection. The emergence of the extra dimension follows from a recent result of Rozali (hep-th/9702136). We show that the seven dimensional duality between M-theory on K3 and Heterotic string theory on T 3 is realised in M(atrix) theory as the exchange of one of the dimensions with this new dimension.
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
On the string interpretation of M(atrix) theory
Physics Letters B, 1997
It has been proposed recently that, in the framework of M(atrix) theory, N = 8 supersymmetric U (N ) Yang-Mills theory in 1+1 dimensions gives rise to type IIA long string configurations. We point out that the quantum moduli space of SYM 1+1 gives rise to two quantum numbers, which fit very well into the M(atrix) theory. The two quantum numbers become familiar if one switches to a IIB picture, where they represent configurations of D-strings and fundamental strings. We argue that, due to the SL(2, Z) symmetry, of the IIB theory, such quantum numbers must represent configurations that are present also in the IIA framework.
A Matrix Model for Static Configurations of M-Theory
1997
We suggest that the static configurations of M-theory are described by the matrix regularisation of the supermembrane theory in static gauge. We compute long range interaction between a M-2-brane and an anti-M-2-brane in agreement with the 11 dimensional supergravity result.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.