Gluing formulas for determinants of Dolbeault laplacians on Riemann surfaces

TL;DR

This paper derives gluing formulas for zeta-regularized determinants of Dolbeault Laplacians on Riemann surfaces, enabling computations related to boundary conditions and bosonization constants.

Contribution

It introduces new gluing formulas for determinants of Dolbeault Laplacians on Riemann surfaces with boundary, incorporating boundary conditions via bundle trivializations.

Findings

Derived explicit gluing formulas for determinants

Connected formulas to bosonization constants

Provided a framework for boundary condition analysis

Abstract

We present gluing formulas for zeta regularized determinants of Dolbeault laplacians on Riemann surfaces. These are expressed in terms of determinants of associated operators on surfaces with boundary satisfying local elliptic boundary conditions. The conditions are defined using the additional structure of a framing, or trivialization of the bundle near the boundary. An application to the computation of bosonization constants follows directly from these formulas.