From the planar limit to M-theory

Abstract

The large-N limit of gauge theories has been playing a crucial role in theoretical physics over the decades. Despite its importance, little is known outside the planar limit where the 't Hooft coupling $\lambda =g_{YM}^{2}N$ is fixed. In this Letter we consider more general large-N limit --- $\lambda$ grows with N, e.g., $g_{YM}^2$ is fixed. Such a limit is important particularly in recent attempts to find the nonpertubative formulation of M-theory. Based on various supporting evidence, we propose this limit is essentially identical to the planar limit, in the sense the order of the large-N limit and the strong coupling limit commute. For a wide class of large-N gauge theories, these two limits are smoothly connected, and the analytic continuation from the planar limit is justified. As simple examples, we reproduce a few properties of the six-dimensional N=(2, 0) theory on S^1 from the five-dimensional maximal super Yang-Mills theory, supporting the recent conjecture by Douglas and Lambert et al. that these two theories are identical.

5 pages, v2:references added and minor corrections, v3:published version

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Cited by in corpus (14)

• M-theoretic matrix models
• A proposal of the gauge theory description of the small Schwarzschild black hole in AdS${}_5\times$S${}^5$
• Borel summability of perturbative series in 4d N=2 and 5d N=1 theories
• How to resum perturbative series in 3d N=2 Chern-Simons matter theories
• Modular anomaly equations in N=2* theories and their large-N limit
• Bootstrap bounds on D0-brane quantum mechanics
• Exact Instanton Expansion of ABJM Partition Function
• Localization at large N in Chern-Simons-matter theories
• What lattice theorists can do for superstring/M-theory
• A new look at instantons and large-N limit
• S-duality invariant perturbation theory improved by holography
• Brick Walls for Black Holes in AdS/CFT
• Dualities from large N orbifold equivalence in Chern-Simons-matter theories with flavor
• Large $N$ limits of supersymmetric quantum field theories: A pedagogical overview