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Critical fields on the M5-brane and noncommutative open strings

E. Bergshoeff, D. S. Berman, J. P. van der Schaar, P. Sundell

TL;DR

This work derives a six-dimensional decoupling limit for the M5-brane in a near-critical field, introducing an open membrane metric that fixes a finite length scale $\ell_g$ and two noncommutativity parameters. By reducing the M5-brane on a two-torus, it connects to the known noncommutative open string (NCOS) and noncommutative Yang-Mills (NCYM) limits on D4- and D3-branes, and shows how S- and T-dualities arise from modular transformations of the open membrane torus. The key result is that the NCOS limit on the D4-brane is dual to a six-dimensional open membrane theory (NCOM) on the M5, with $\alpha'_{eff}=\theta=\ell_g^3/R$, and that the D3 NCOS/NCYM limits are related by torus modular invariance, encoded in open-membrane moduli such as $\tau_{OM}$ and $A_{OM}$. This provides a unified M-theory perspective on noncommutative open string theories and hints at a six-dimensional AdS/CFT-like structure for the self-dual string on the M5.

Abstract

The M5-brane is investigated near critical field-strength. We show that this limit on the M5-brane reduces to the noncommutative open string limit on the D4-brane. The reduction on a two-torus leads to both the noncommutative open string limit and the noncommutative Yang-Mills limit on the D3-brane. The decoupled noncommutative five-brane is identified with the strong coupling limit of the noncommutative open string theory on the D4-brane and S-duality on the noncommutative D3-brane is identified with a modular transformation on the five-brane. We argue that the open membrane metric defines a finite length scale on the worldvolume of the M5-brane in the decoupling limit. This length scale can be associated to the effective length scale of an open membrane.

Critical fields on the M5-brane and noncommutative open strings

TL;DR

This work derives a six-dimensional decoupling limit for the M5-brane in a near-critical field, introducing an open membrane metric that fixes a finite length scale and two noncommutativity parameters. By reducing the M5-brane on a two-torus, it connects to the known noncommutative open string (NCOS) and noncommutative Yang-Mills (NCYM) limits on D4- and D3-branes, and shows how S- and T-dualities arise from modular transformations of the open membrane torus. The key result is that the NCOS limit on the D4-brane is dual to a six-dimensional open membrane theory (NCOM) on the M5, with , and that the D3 NCOS/NCYM limits are related by torus modular invariance, encoded in open-membrane moduli such as and . This provides a unified M-theory perspective on noncommutative open string theories and hints at a six-dimensional AdS/CFT-like structure for the self-dual string on the M5.

Abstract

The M5-brane is investigated near critical field-strength. We show that this limit on the M5-brane reduces to the noncommutative open string limit on the D4-brane. The reduction on a two-torus leads to both the noncommutative open string limit and the noncommutative Yang-Mills limit on the D3-brane. The decoupled noncommutative five-brane is identified with the strong coupling limit of the noncommutative open string theory on the D4-brane and S-duality on the noncommutative D3-brane is identified with a modular transformation on the five-brane. We argue that the open membrane metric defines a finite length scale on the worldvolume of the M5-brane in the decoupling limit. This length scale can be associated to the effective length scale of an open membrane.

Paper Structure

This paper contains 5 sections, 45 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The M5--brane and the decoupling limit
  3. The NCOS limit on the D4--brane
  4. The noncommutative limits on the D3--brane
  5. Discussion

Figures (1)

  • Figure 1: The square on the left relates M-theory and IIA-superstring theory and their low energy limits. Similarly, the square on the right displays the relations between the D4-brane noncommutative open string theory (NCOS) and its M5-brane noncommutative open membrane (NCOM) origin, and their low energy limits.