UV Caps and Modulus Stabilization for 6D Gauged Chiral Supergravity

TL;DR

This work provides an explicit UV regularization of codimension-two brane singularities in 6D gauged chiral supergravity for all 4D-flat, axially symmetric bulk solutions. By inserting cylindrical 4-branes and filling their interiors with smooth 4D-flat cap geometries, the authors derive detailed matching conditions that connect cap-brane data to bulk parameters, proving that caps always exist and that the brane properties can determine the bulk solution. A central result is that cap-brane couplings generically break bulk scale invariance and lift degeneracies among bulk geometries, yielding a Goldberger-Wise–like stabilization of the extra-dimensional volume; the resulting 4D effective potential for the radion is computed, showing stabilization whenever scale invariance is broken. The framework enables a controlled UV completion of codimension-two branes and provides tools to study how UV brane physics shapes the IR bulk and low-energy 4D physics, with potential extensions to non-flat bulk geometries and higher dimensions.

Abstract

We describe an explicit UV regularization of the brane singularities for all 4D flat configurations of 6D gauged chiral supergravity compactified on axially symmetric internal spaces (for which the general solutions are known). All such solutions have two or fewer co-dimension two singularities, which we resolve in terms of microscopic co-dimension one cylindrical 4-branes, whose interiors are capped using the most general possible 4D flat solution of the 6D field equations. By so doing we show that such a cap is always possible for any given bulk geometry, and obtain an explicit relationship between the properties of the capped 4-branes and the various parameters which describe the bulk solution. We show how these branes generically stabilize the size of the extra dimensions by breaking the scale invariance which relates classical solutions to 6D supergravity, and we compute the scalar potential for this modulus in the 4D effective theory. The lifting of this marginal direction provides a natural realization of the Goldberger-Wise stabilization mechanism in six dimensions.