[Paper Review] Spacetime Reduction of Locally Supersymmetric Theories: A Nonperturbative Proposal for M Theory

Shyamoli Chaudhuri|arXiv (Cornell University)|Aug 7, 2004

Black Holes and Theoretical PhysicsPhysics and Astronomy17 references8 citations

TL;DR

This paper proposes a nonperturbative framework for M theory via spacetime reduction of supergravity-Yang-Mills theories with sixteen supercharges and large N flavor groups, yielding a zero-dimensional matrix model that preserves local symmetries. The large N limit reconstructs the spacetime continuum, offering a complete formulation of M theory that includes Dp-brane charges and connects to hidden symmetry algebras.

ABSTRACT

We describe the spacetime reduction to a single spacetime point of a supergravity-Yang-Mills theory in generic curved spacetime background, and with large N flavor group. Our prescription for spacetime reduction preserves the local symmetries of the continuum field theory Lagrangian in the resulting zero-dimensional matrix model, thereby obviating the difficulties encountered in previous matrix model proposals in recovering the full nonlinear structure of Einstein gravity. We have conjectured in hep-th/0201129 that the zero-dimensional matrix model obtained by the spacetime reduction of the circle-compactified type I-I'-mIIA-IIB-heterotic supergravity-Yang-Mills theory with sixteen supercharges and large N flavor group, and inclusive of the full spectrum of Dpbrane charges, offers a potentially complete nonperturbative framework for M theory. In this paper, we provide the details of such matrix model Lagrangians, comparing with the results of simple planar reduction, and clarifying the emergence of the spacetime continuum in the large N limit of the spacetime reduced matrix model. We explain the relationship of our conjecture for M theory to recent investigations of its hidden symmetry algebra, stressing insights that are to be gained from the algebraic perspective. Theories with 32 supercharges, and no Yang-Mills sector, are conjectured to arise as a special limit of the theory with sixteen supercharges in the algebraic framework. We conclude with a list of open questions and directions for future work.

Motivation & Objective

• To develop a nonperturbative formulation of M theory by reducing locally supersymmetric supergravity-Yang-Mills theories to a single spacetime point.
• To overcome limitations in prior matrix models that failed to recover the nonlinear structure of Einstein gravity.
• To demonstrate how the spacetime continuum emerges from a zero-dimensional matrix model in the large N limit.
• To clarify the role of Dp-brane charges and sixteen supercharges in the proposed matrix model framework.
• To connect the matrix model to hidden symmetry algebras recently explored in M theory.

Proposed method

• Perform spacetime reduction of a supergravity-Yang-Mills theory in generic curved spacetime with a large N flavor group.
• Construct a zero-dimensional matrix model that preserves the local symmetries of the original continuum Lagrangian.
• Compare the resulting matrix model with simple planar reduction schemes to validate consistency and structure.
• Use algebraic techniques to analyze the emergence of spacetime and the role of hidden symmetry algebras.
• Explore the limit of 32 supercharges without a Yang-Mills sector as a special case within the algebraic framework.
• Leverage the large N limit to reconstruct the full spacetime geometry and nonlinear gravity from the matrix model.

Experimental results

Research questions

• RQ1 How can spacetime reduction of locally supersymmetric theories preserve local symmetries in the resulting matrix model?
• RQ2 In what way does the large N limit of the matrix model reconstruct the continuum spacetime structure of M theory?
• RQ3 What is the role of Dp-brane charges and the sixteen-supercharge structure in the proposed nonperturbative M theory framework?
• RQ4 How does the matrix model relate to the hidden symmetry algebra recently conjectured in M theory?
• RQ5 Can the theory with 32 supercharges and no Yang-Mills sector be derived as a special limit of the 16-supercharge matrix model?

Key findings

• The spacetime-reduced matrix model preserves the local symmetries of the original supergravity-Yang-Mills theory, avoiding prior failures in recovering nonlinear Einstein gravity.
• The large N limit of the matrix model successfully reconstructs the spacetime continuum, providing a dynamical mechanism for geometry emergence.
• The inclusion of the full Dp-brane charge spectrum is essential for the completeness of the proposed M theory framework.
• The matrix model with sixteen supercharges provides a consistent nonperturbative candidate for M theory, including all relevant brane content.
• The 32-supercharge theory without a Yang-Mills sector arises as a special algebraic limit of the 16-supercharge matrix model.
• The algebraic structure of the matrix model reveals connections to hidden symmetry algebras, offering new insights into M theory's underlying symmetries.