One-Loop Effective Action in Orbifold Compactifications

TL;DR

This paper develops a formalism to compute the one-loop effective action in orbifold compactifications, separating UV-sensitive and insensitive parts, with applications to 6d gauge theory and 11d supergravity.

Contribution

It introduces a covariant background formalism for calculating one-loop effective actions in orbifold compactifications, including explicit heat kernel computations on tori.

Findings

Derived generic expressions for one-loop effective actions in orbifold models.

Separated UV-sensitive and UV-insensitive contributions explicitly.

Applied methods to 6d gauge theory and 11d supergravity examples.

Abstract

We employ the covariant background formalism to derive generic expressions for the one-loop effective action in field theoretic orbifold compactifications. The contribution of each orbifold sector is given by the effective action of its fixed torus with a shifted mass matrix. We thus study in detail the computation of the heat kernel on tori. Our formalism manifestly separates UV sensitive (local) from UV-insensitive (nonlocal) renormalization. To exemplify our methods, we study the effective potential of 6d gauge theory as well as kinetic terms for gravitational moduli in 11d supergravity.