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Title: The large-N limit of superconformal field theories and supergravity

Abstract

The author shows that the large-N limits of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of anti-de Sitter spacetimes, spheres, and other compact manifolds. This is shown by taking some branes in the full M/string theory and then taking a low-energy limit where the field theory on the brane decouples from the bulk. He observes that, in this limit, he can still trust the near-horizon geometry for large N. The enhanced supersymmetries of the near-horizon geometry correspond to the extra supersymmetry generators present in the superconformal group (as opposed to just the super-Poincare group). The `t Hooft limit of 3 + 1 N = 4 super-Yang-Mills at the conformal point is shown to contain strings: they are IIB strings. He conjectures that compactifications of M/string theory on various anti-de Sitter spacetimes is dual to various conformal field theories. This leads to a new proposal for a definition of M-theory which could be extended to include five noncompact dimensions.

Authors:
 [1]
  1. Harvard Univ., Cambridge, MA (United States). Lyman Lab. of Physics
Publication Date:
Sponsoring Org.:
USDOE, Washington, DC (United States)
OSTI Identifier:
361743
Resource Type:
Journal Article
Resource Relation:
Journal Name: International Journal of Theoretical Physics; Journal Volume: 38; Journal Issue: 4; Other Information: PBD: Apr 1999
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; QUANTUM FIELD THEORY; CONFORMAL INVARIANCE; SUPERGRAVITY; SUPERSYMMETRY; STRING MODELS; SPACE-TIME; COMPACTIFICATION

Citation Formats

Maldacena, J. The large-N limit of superconformal field theories and supergravity. United States: N. p., 1999. Web. doi:10.1023/A:1026654312961.
Maldacena, J. The large-N limit of superconformal field theories and supergravity. United States. doi:10.1023/A:1026654312961.
Maldacena, J. Thu . "The large-N limit of superconformal field theories and supergravity". United States. doi:10.1023/A:1026654312961.
@article{osti_361743,
title = {The large-N limit of superconformal field theories and supergravity},
author = {Maldacena, J.},
abstractNote = {The author shows that the large-N limits of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of anti-de Sitter spacetimes, spheres, and other compact manifolds. This is shown by taking some branes in the full M/string theory and then taking a low-energy limit where the field theory on the brane decouples from the bulk. He observes that, in this limit, he can still trust the near-horizon geometry for large N. The enhanced supersymmetries of the near-horizon geometry correspond to the extra supersymmetry generators present in the superconformal group (as opposed to just the super-Poincare group). The `t Hooft limit of 3 + 1 N = 4 super-Yang-Mills at the conformal point is shown to contain strings: they are IIB strings. He conjectures that compactifications of M/string theory on various anti-de Sitter spacetimes is dual to various conformal field theories. This leads to a new proposal for a definition of M-theory which could be extended to include five noncompact dimensions.},
doi = {10.1023/A:1026654312961},
journal = {International Journal of Theoretical Physics},
number = 4,
volume = 38,
place = {United States},
year = {Thu Apr 01 00:00:00 EST 1999},
month = {Thu Apr 01 00:00:00 EST 1999}
}
  • We show that the large {ital N} limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of Anti-deSitter spacetimes, spheres and other compact manifolds. This is shown by taking some branes in the full M/string theory and then taking a low energy limit where the field theory on the brane decouples from the bulk. We observe that, in this limit, we can still trust the near horizon geometry for large {ital N}. The enhanced supersymmetries of the near horizon geometry correspond to the extra supersymmetry generators present inmore » the superconformal group (as opposed to just the super-Poincare group). The {close_quote}t Hooft limit of 3+1N=4 super-Yang-Mills at the conformal point is shown to contain strings: they are IIB strings. We conjecture that compactifications of M/string theory on various Anti-deSitter spacetimes is dual to various conformal field theories. This leads to a new proposal for a definition of M-theory which could be extended to include five non-compact dimensions. {copyright} {ital 1999 American Institute of Physics.}« less
  • We show that the large N limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of Anti-deSitter spacetimes, spheres and other compact manifolds. This is shown by taking some branes in the full M/string theory and then taking a low energy limit where the field theory on the brane decouples from the bulk. We observe that, in this limit, we can still trust the near horizon geometry for large N. The enhanced supersymmetries of the near horizon geometry correspond to the extra supersymmetry generators present in the superconformalmore » group (as opposed to just the super-Poincare group). The 't Hooft limit of 3+1N=4 super-Yang-Mills at the conformal point is shown to contain strings: they are IIB strings. We conjecture that compactifications of M/string theory on various Anti-deSitter spacetimes is dual to various conformal field theories. This leads to a new proposal for a definition of M-theory which could be extended to include five non-compact dimensions.« less
  • We consider field theories with sixteen supersymmetries, which include U(N) Yang-Mills theories in various dimensions, and argue that their large N limit is related to certain supergravity solutions. We study this by considering a system of D-branes in string theory and then taking a limit where the brane world volume theory decouples from gravity. At the same time we study the corresponding D-brane supergravity solution and argue that we can trust it in certain regions where the curvature (and the effective string coupling, where appropriate) are small. The supergravity solutions typically have several weakly coupled regions and interpolate between differentmore » limits of string M theory. {copyright} {ital 1998} {ital The American Physical Society}« less
  • We show that the N=8 superconformal Bagger-Lambert theory based on the Lorentzian 3-algebra can be derived by taking a certain scaling limit of the recently proposed N=6 superconformal U(N)xU(N) Chern-Simons-matter theories at level (k,-k). The scaling limit (and Inoenue-Wigner contraction) is to scale the trace part of the bifundamental fields as X{sub 0}{yields}{lambda}{sup -1}X{sub 0} and an axial combination of the two gauge fields as B{sub {mu}}{yields}{lambda}B{sub {mu}}. Simultaneously, we scale the level as k{yields}{lambda}{sup -1}k and then take {lambda}{yields}0 limit. Interestingly, the same constraint equation {partial_derivative}{sup 2}X{sub 0}=0 is derived by imposing finiteness of the action. In this scalingmore » limit, M2 branes are located far from the origin of C{sup 4}/Z{sub k} compared to their fluctuations and Z{sub k} identification becomes a circle identification. Hence, the scaled theory describes N=8 supersymmetric theory of 2-branes with dynamical coupling. The coupling constant is promoted to a space-time dependent SO(8) vector X{sub 0}{sup I} and we show that the scaled theory has a generalized conformal symmetry as well as manifest SO(8) with the transformation of the background fields X{sub 0}{sup I}.« less
  • Various effective field theories in four dimensions are shown to have exact nontrivial solutions in the limit as the number N of fields of some type becomes large. These include extended versions of the U (N) Gross-Neveu model, the nonlinear O(N) {sigma} model, and the CP{sup N{minus}1} model. Although these models are not renormalizable in the usual sense, the infinite number of coupling types allows a complete cancellation of infinities. These models provide qualitative predictions of the form of scattering amplitudes for arbitrary momenta, but because of the infinite number of free parameters, it is possible to derive quantitative predictionsmore » only in the limit of small momenta. For small momenta the large-N limit provides only a modest simplification, removing at most a finite number of diagrams to each order in momenta, except near phase transitions, where it reduces the infinite number of diagrams that contribute for low momenta to a finite number. {copyright} {ital 1997} {ital The American Physical Society}« less