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Transverse Fivebranes in Matrix Theory

Juan Maldacena, Mohammad M. Sheikh-Jabbari, Mark Van Raamsdonk

Abstract

M-theory on the maximally supersymmetric plane wave background of eleven-dimensional supergravity admits spherical BPS transverse M5-branes with zero light-cone energy. We give direct evidence that the single M5-brane state corresponds to the trivial (X=0) classical vacuum in the large N limit of the plane wave matrix theory. In particular, we show that the linear fluctuation spectrum of the spherical fivebrane matches exactly with the set of exactly protected excited states about the X=0 vacuum in the matrix model. These states include geometrical fluctuations of the sphere, excitations of the worldvolume two-form field, and fermion excitations. In addition, we propose a description of multiple fivebrane states in terms of matrix model vacua. Finally, we discuss how to obtain the continuum D2/M2 and NS5/M5 theories on spheres from the matrix model. The matrix model can be viewed as a regularization for these theories.

Transverse Fivebranes in Matrix Theory

Abstract

M-theory on the maximally supersymmetric plane wave background of eleven-dimensional supergravity admits spherical BPS transverse M5-branes with zero light-cone energy. We give direct evidence that the single M5-brane state corresponds to the trivial (X=0) classical vacuum in the large N limit of the plane wave matrix theory. In particular, we show that the linear fluctuation spectrum of the spherical fivebrane matches exactly with the set of exactly protected excited states about the X=0 vacuum in the matrix model. These states include geometrical fluctuations of the sphere, excitations of the worldvolume two-form field, and fermion excitations. In addition, we propose a description of multiple fivebrane states in terms of matrix model vacua. Finally, we discuss how to obtain the continuum D2/M2 and NS5/M5 theories on spheres from the matrix model. The matrix model can be viewed as a regularization for these theories.

Paper Structure

This paper contains 15 sections, 55 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The fivebrane spectrum from matrix theory
  3. Perturbation theory
  4. Protected quantities
  5. Multiple fivebranes
  6. Evidence for the proposal
  7. Chiral operators for multiple membranes and fivebranes
  8. The matrix model as a regularization of the D2/M2 brane theories
  9. Decoupling limits
  10. Gravity perspective
  11. The matrix model as a regularization of the NS5/M5 theories
  12. Protected states in the matrix theory spectrum
  13. Linear fluctuation spectrum of the fivebrane
  14. Decoupled 2+1 dimensional field theory from the matrix model
  15. Relationship to the Polchinski-Strassler discussion of ${ \cal N} = 1^*$ theories.

Figures (2)

  • Figure 1: $SU(4) \times SU(2)$ tableau and energies for exactly protected excitations about the $X=0$ vacuum.
  • Figure 2: Dual membrane and fivebrane interpretations for general vacua.