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Matrix Perturbation Theory For M-theory On a PP-Wave

Keshav Dasgupta, Mohammad M. Sheikh-Jabbari, Mark Van Raamsdonk

TL;DR

The paper analyzes the BMN matrix model as a regulator of M-theory on the maximally supersymmetric pp-wave, deriving it from both a discretized supermembrane formulation and D0-brane dynamics in a suitable IIA background. It shows that for large μ, the theory splits into weakly interacting quadratic sectors around classical vacua, enabling exact spectrum calculations in the μ→∞ limit and a perturbative expansion about each vacuum. The authors identify a rich spectrum of oscillator modes, compute explicit BPS states, and quantify the perturbative regime with effective couplings that depend on the vacuum, before discussing the M-theory limit where flat directions and potential nonperturbative effects arise. The work clarifies how giant-graviton-like vacua and flux-induced mass terms shape the dynamics, and it highlights both the promise and limitations of perturbation theory in this pp-wave matrix framework for M-theory.

Abstract

In this paper, we study the matrix model proposed by Berenstein, Maldacena, and Nastase to describe M-theory on the maximally supersymmetric pp-wave. We show that the model may be derived directly as a discretized theory of supermembranes in the pp-wave background, or alternatively, from the dynamics of D0-branes in type IIA string theory. We consider expanding the model about each of its classical supersymmetric vacua and note that for large values of the mass parameter μ, interaction terms are suppressed by powers of 1/mu, so that the model may be studied in perturbation theory. We compute the exact spectrum about each of the vacua in the large μlimit and find the complete (infinite) set of BPS states, which includes states preserving 2, 4, 6, 8, or 16 supercharges. Through explicit perturbative calculations, we then determine the effective coupling that controls the perturbation expansion for large μand estimate the range of parameters and energies for which perturbation theory is valid.

Matrix Perturbation Theory For M-theory On a PP-Wave

TL;DR

The paper analyzes the BMN matrix model as a regulator of M-theory on the maximally supersymmetric pp-wave, deriving it from both a discretized supermembrane formulation and D0-brane dynamics in a suitable IIA background. It shows that for large μ, the theory splits into weakly interacting quadratic sectors around classical vacua, enabling exact spectrum calculations in the μ→∞ limit and a perturbative expansion about each vacuum. The authors identify a rich spectrum of oscillator modes, compute explicit BPS states, and quantify the perturbative regime with effective couplings that depend on the vacuum, before discussing the M-theory limit where flat directions and potential nonperturbative effects arise. The work clarifies how giant-graviton-like vacua and flux-induced mass terms shape the dynamics, and it highlights both the promise and limitations of perturbation theory in this pp-wave matrix framework for M-theory.

Abstract

In this paper, we study the matrix model proposed by Berenstein, Maldacena, and Nastase to describe M-theory on the maximally supersymmetric pp-wave. We show that the model may be derived directly as a discretized theory of supermembranes in the pp-wave background, or alternatively, from the dynamics of D0-branes in type IIA string theory. We consider expanding the model about each of its classical supersymmetric vacua and note that for large values of the mass parameter μ, interaction terms are suppressed by powers of 1/mu, so that the model may be studied in perturbation theory. We compute the exact spectrum about each of the vacua in the large μlimit and find the complete (infinite) set of BPS states, which includes states preserving 2, 4, 6, 8, or 16 supercharges. Through explicit perturbative calculations, we then determine the effective coupling that controls the perturbation expansion for large μand estimate the range of parameters and energies for which perturbation theory is valid.

Paper Structure

This paper contains 32 sections, 231 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. The matrix model from supermembranes
  3. Bosonic terms
  4. Fermionic terms
  5. The matrix model from D0-brane dynamics
  6. Relation to type IIA string theory
  7. D0-brane dynamics on compactified reduced pp-waves
  8. Classical supersymmetric vacua
  9. Action and symmetries
  10. Classical supersymmetric solutions
  11. Expansion about the classical vacua
  12. Exact spectrum in the large $\mu$ limit
  13. Expansion in terms of matrix spherical harmonics
  14. Spectrum of the irreducible vacuum
  15. Oscillator masses in a general reducible representation
  16. ...and 17 more sections

Figures (2)

  • Figure 1: Regime of validity for perturbation theory (conservative)
  • Figure 2: Low energy path between nearby vacua