Determinant of twisted chiral Dirac Operator on the Lattice

TL;DR

This paper computes the fermionic determinant for twisted chiral Dirac operators on the lattice using the overlap formulation, bridging lattice and continuum string theory results in two dimensions.

Contribution

It introduces a lattice calculation of the fermionic determinant for twisted chiral fermions, connecting lattice results with continuum string theory.

Findings

Lattice calculations match continuum string theory results as lattice spacing approaches zero.

Overlap formulation effectively computes fermionic determinants with twisted boundary conditions.

Provides a method to study chiral fermions on the lattice with boundary twists.

Abstract

Using the overlap formulation, we calculate the fermionic determinant on the lattice for chiral fermions with twisted boundary conditions in two dimensions. When the lattice spacing tends to zero we recover the results of the usual string-theory continuum calculations.