Consistent Sphere Reductions and Universality of the Coulomb Branch in the Domain-Wall/QFT Correspondence

TL;DR

This paper proves that certain D-dimensional theories with gravity, antisymmetric fields, and a dilaton can be consistently reduced on spheres, leading to domain wall solutions and a universal scalar spectrum in lower dimensions.

Contribution

It establishes a general framework for consistent sphere reductions in theories with specific field content, extending to various dimensions and revealing universal properties.

Findings

Consistent sphere reduction is possible for n ≤ 5 with specified D ranges.

Constructed domain wall solutions and lifted them to higher dimensions.

Discovered a universal structure in the scalar spectrum of domain-wall backgrounds.

Abstract

We prove that any D-dimensional theory comprising gravity, an antisymmetric n-index field strength and a dilaton can be consistently reduced on S^n in a truncation in which just $n$ scalar fields and the metric are retained in (D-n)-dimensions, provided only that the strength of the couping of the dilaton to the field strength is appropriately chosen. A consistent reduction can then be performed for n\le 5; with D being arbitrary when n\le 3, whilst D\le 11 for n=4 and D\le 10 for n=5. (Or, by Hodge dualisation, $n$ can be replaced by (D-n) in these conditions.) We obtain the lower dimensional scalar potentials and construct associated domain wall solutions. We use the consistent reduction Ansatz to lift domain-wall solutions in the (D-n)-dimensional theory back to D dimensions, where we show that they become certain continuous distributions of (D-n-2)-branes. We also examine the spectrum for a minimally-coupled scalar field in the domain-wall background, showing that it has a universal structure characterised completely by the dimension n of the compactifying sphere.