Gauge theories with non-trivial boundary conditions

Peng Cheng

Published 2023-02-07Version 1

We study gauge theories between two parallel boundaries with non-trivial boundary conditions, which is aimed at better understanding the Bekenstein-Hawking entropy. Boundary modes due to the boundary conditions are carefully analyzed, besides which we also find Wilson lines stretched between different boundaries because of the interplay between the two boundaries. Those Wilson lines are non-local modes and are confirmed as physical variables in the phase space. The corresponding symplectic form and commutation relations are also derived in the canonical formulation. Other interesting physics, like the winding modes of those Wilson lines, are also studied. There are bulk fluctuation modes, boundary edge modes, Wilson lines, and other interesting modes in the phase space. We derive the partition function and entropy via the Euclidean path integral and demonstrate transitions between the dominance of different modes as we vary the temperature.