A Toolkit for Perturbing Flux Compactifications

TL;DR

This paper introduces a perturbative method for solving boundary value problems in type IIB flux compactifications, enabling systematic computation of corrections to warped throat geometries and physical effects.

Contribution

It develops a new iterative expansion scheme with a triangular structure for solving equations in flux compactifications, applicable to warped Calabi-Yau cones.

Findings

Derived explicit Green's function solutions for supergravity fields.

Provided an algorithm for systematic corrections to warped throat geometries.

Presented a method to estimate sizes of physical effects in warped geometries.

Abstract

We develop a perturbative expansion scheme for solving general boundary value problems in a broad class of type IIB flux compactifications. The background solution is any conformally Calabi-Yau compactification with imaginary self-dual (ISD) fluxes. Upon expanding in small deviations from the ISD solution, the equations of motion simplify dramatically: we find a simple basis in which the n-th order equations take a triangular form. This structure implies that the system can be solved iteratively whenever the individual, uncoupled equations can be solved. We go on to demonstrate the solution of the system for a general warped Calabi-Yau cone: we present an algorithm that yields an explicit Green's function solution for all the supergravity fields, to any desired order, in terms of the harmonic functions on the base of the cone. Our results provide a systematic procedure for obtaining the corrections to a warped throat geometry induced by attachment to a compact bulk. We also present a simple method for determining the sizes of physical effects mediated through warped geometries.