Heat kernel expansion and induced action for the matrix model Dirac operator

TL;DR

This paper computes the quantum effective action in Yang-Mills matrix models on 4D backgrounds, revealing noncommutative geometry aspects and hidden symmetries, with implications for emergent gravity and gauge theories.

Contribution

It introduces a method to derive noncommutative analogs of Seeley-de Witt coefficients for emergent gravity in matrix models, highlighting hidden symmetries in NC gauge theories.

Findings

Effective action expressed as generalized matrix models

Evidence of hidden SO(10) symmetry in NC N=4 SYM

Predicts non-trivial loop computations in gauge theory

Abstract

We compute the quantum effective action induced by integrating out fermions in Yang-Mills matrix models on a 4-dimensional background, expanded in powers of a gauge-invariant UV cutoff. The resulting action is recast into the form of generalized matrix models, manifestly preserving the SO(D) symmetry of the bare action. This provides noncommutative (NC) analogs of the Seeley-de Witt coefficients for the emergent gravity which arises on NC branes, such as curvature terms. From the gauge theory point of view, this provides strong evidence that the NC N=4 SYM has a hidden SO(10) symmetry even at the quantum level, which is spontaneously broken by the space-time background. The geometrical view proves to be very powerful, and allows to predict non-trivial loop computations in the gauge theory.