Traces on orbifolds: Anomalies and one-loop amplitudes

TL;DR

This paper develops a general framework for calculating one-loop amplitudes such as anomalies and vacuum energies on a wide class of orbifolds, using trace evaluations over orbifold Hilbert spaces.

Contribution

It introduces a unified method to compute one-loop amplitudes on various orbifolds by expressing them as traces over hyper surfaces with local projections.

Findings

Applicable to non-prime orbifolds like T^6/Z_4

Handles non-Abelian orbifolds such as T^4/D_4

Provides a general trace-based computational approach

Abstract

In the recent literature one can find calculations of various one--loop amplitudes, like anomalies, tadpoles and vacuum energies, on specific types of orbifolds, like S^1/Z_2. This work aims to give a general description of such one--loop computations for a large class of orbifold models. In order to achieve a high degree of generality, we formulate these calculations as evaluations of traces of operators over orbifold Hilbert spaces. We find that in general the result is expressed as a sum of traces over hyper surfaces with local projections, and the derivatives perpendicular to these hyper surfaces are rescaled. These local projectors naturally takes into account possible non--periodic boundary conditions. As the examples T^6/Z_4 and T^4/D_4 illustrate, the methods can be applied to non--prime as well as non--Abelian orbifolds.