On Gauge-Invariant Boundary Conditions for 2d Gravity with Dynamical torsion

TL;DR

This paper demonstrates how to define gauge-invariant boundary conditions in 2D gravity with torsion, and computes the one-loop partition function and heat kernel for an $R^2+T^2$ model on a disk.

Contribution

It introduces a method for setting gauge-invariant boundary conditions in 2D gravity with torsion, even on non-totally geodesic boundaries, and calculates the one-loop partition function.

Findings

Gauge-invariant boundary conditions are possible on non-totally geodesic boundaries.

The one-loop partition function for the model is explicitly calculated.

The heat kernel associated with the model is derived.

Abstract

In the example of $R^2+T^2$ gravity on the unit two dimensional disk we demonstrate that in the presence of an independent spin connection it is possible to define local gauge invariant boundary conditions even on boundaries which are not totally geodesic. One-loop partition function and the corresponding heat kernel are calculated.