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AdS_7/CFT_6 Correspondence and Matrix Models of M5-Branes

Hidetoshi Awata, Shinji Hirano

TL;DR

This paper uses Bulk/Boundary (AdS/CFT) techniques to study the large $N$ limit of M5-brane matrix models, linking the near-horizon limit to the light-like DLCQ of M-theory. It identifies a generalized conformal symmetry in the D0+D4 system and interprets it as a DLCQ symmetry of the six-dimensional $(2,0)$ theory, then confirms this via scalar two-point functions computed in the near-horizon geometry of boosted M5-branes. The results are consistent with Seiberg–Sen's DLCQ arguments and with the expected behavior of the $(2,0)$ SCFT, providing evidence for both Maldacena's AdS/CFT and the Matrix Model program in this context. The analysis also clarifies the intricate relationship between near-horizon limits, boosts, and light-like compactifications in eleven dimensions, highlighting the role of a six-dimensional conformal group at the origin of the M5-brane moduli space.

Abstract

We study the large N limit of matrix models of M5-branes, or (2,0) six-dimensional superconformal field theories, by making use of the Bulk/Boundary correspondence. Our emphasis is on the relation between the near-horizon limit of branes and the light-like limit of M-theory. In particular we discuss a conformal symmetry in the D0 + D4 system, and interpret it as a conformal symmetry in the discrete light-cone formulation of M5-branes. We also compute two-point functions of scalars by applying the conjecture for the AdS/CFT correspondence to the near-horizon geometry of boosted M5-branes. We find an expected result up to a point subtle, but irrelevant to the IR behavior of the theory. Our analysis matches with the Seiberg and Sen's argument of a justification for the matrix model of M-theory.

AdS_7/CFT_6 Correspondence and Matrix Models of M5-Branes

TL;DR

This paper uses Bulk/Boundary (AdS/CFT) techniques to study the large limit of M5-brane matrix models, linking the near-horizon limit to the light-like DLCQ of M-theory. It identifies a generalized conformal symmetry in the D0+D4 system and interprets it as a DLCQ symmetry of the six-dimensional theory, then confirms this via scalar two-point functions computed in the near-horizon geometry of boosted M5-branes. The results are consistent with Seiberg–Sen's DLCQ arguments and with the expected behavior of the SCFT, providing evidence for both Maldacena's AdS/CFT and the Matrix Model program in this context. The analysis also clarifies the intricate relationship between near-horizon limits, boosts, and light-like compactifications in eleven dimensions, highlighting the role of a six-dimensional conformal group at the origin of the M5-brane moduli space.

Abstract

We study the large N limit of matrix models of M5-branes, or (2,0) six-dimensional superconformal field theories, by making use of the Bulk/Boundary correspondence. Our emphasis is on the relation between the near-horizon limit of branes and the light-like limit of M-theory. In particular we discuss a conformal symmetry in the D0 + D4 system, and interpret it as a conformal symmetry in the discrete light-cone formulation of M5-branes. We also compute two-point functions of scalars by applying the conjecture for the AdS/CFT correspondence to the near-horizon geometry of boosted M5-branes. We find an expected result up to a point subtle, but irrelevant to the IR behavior of the theory. Our analysis matches with the Seiberg and Sen's argument of a justification for the matrix model of M-theory.

Paper Structure

This paper contains 11 sections, 78 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Brane solutions in the near-horizon limit
  4. D0 + D4 bound states
  5. M5 branes boosted along the longitudinal direction
  6. The light-like limit and the near-horizon limit
  7. D0 + D4 bound states and '' boosted" M5-branes
  8. Conformal symmetry
  9. Two-point functions
  10. Scalars
  11. Discussions

Figures (2)

  • Figure 1: A D0 + D4 bound state: An adjoint hypermultiplet (two complex scalars $X=X^0 +iX^1, \tilde{X}=X^2 +iX^3$) comes from 0-0 strings, while the fundamental hypermultiplets ($q_i, \tilde{q}^i, \,\, i=1,\cdots, k$) are supplied from 0-4 and 4-0 strings.
  • Figure 2: The horizontal direction corresponds to the M(atrix) conjecture, while the vertical direction corresponds to the Maldacena conjecture. We discuss the matrix model and the DLCQ of M5-branes in the large N limit by making use of the Bulk/Boundary correspondence.