The SU(N) Matrix Model at Two Loops

TL;DR

This paper develops a framework for two-loop calculations of the effective action in the SU(N) matrix model, crucial for testing its connection to M-theory and supergravity, and explicitly computes the case for a D0-brane scattering scenario.

Contribution

It introduces a method for two-loop effective action calculations in the SU(N) matrix model and verifies results for specific D0-brane scattering configurations.

Findings

Two-loop effective action computed for a D0-brane scattering background.

Results agree with known N=2 cases, validating the approach.

Framework facilitates testing of the matrix model's relation to M-theory.

Abstract

Multi-loop calculations of the effective action for the matrix model are important for carrying out tests of the conjectured relationship of the matrix model to the low energy description of M-theory. In particular, comparison with N-graviton scattering amplitudes in eleven-dimensional supergravity requires the calculation of the effective action for the matrix model with gauge group SU(N). A framework for carrying out such calculations at two loops is established in this paper. The two-loop effective action is explicitly computed for a background corresponding to the scattering of a single D0-brane from a stack of N-1 D0-branes, and the results are shown to agree with known results in the case N=2.