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

Understand

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.