Large Dimensions and Small Curvatures from Supersymmetric Brane Back-reaction

TL;DR

This work analyzes the back-reaction of codimension-two branes in a flux-stabilized 6D gauged chiral supergravity, focusing on how brane tension and brane-localized flux shape the bulk geometry and the 4D effective theory. By linearizing about rugby-ball backgrounds and coupling a current to stabilize the breathing mode, the authors derive how brane couplings lift bulk scale degeneracy, generate a moduli potential, and can engender exponentially large extra-dimensional volumes with suppressed on-brane curvature. The 4D effective theory is matched to the full 6D dynamics, revealing that the effective vacuum energy and dilaton mass depend sensitively on the dilaton-brane couplings (and flux), while flux quantization constrains the background and allows controlled tuning of ρ_eff. They explore simple illustrative cases, including dilaton-independent, linear, power-law, and exponential brane couplings, and argue that quantum corrections can be technically natural without destabilizing the large-volume or curvature-suppression outcomes. Overall, the results suggest robust mechanisms in higher-dimensional back-reacting brane systems for achieving large volumes and small vacuum energy, with potential implications for naturalness and cosmology in flux compactifications.

Abstract

We compute the back-reaction of pairs of codimension-two branes within an explicit flux-stabilized compactification, to trace how its properties depend on the parameters that define the brane-bulk couplings. Both brane tension and magnetic couplings to the stabilizing flux play an important role in the resulting dynamics, with the magnetic coupling allowing some of the flux to be localized on the branes (thus changing the flux-quantization conditions). We find that back-reaction lifts the classical flat directions of the bulk supergravity, and we calculate both the scalar potential and changes to the extra-dimensional and on-brane geometries that result, as functions of the assumed brane couplings. When linearized about simple rugby-ball geometries the resulting solutions allow a systematic exploration of the system's response. Several of the systems we explore have remarkable properties. Among these are a propensity for the extra dimensions to stabilize at exponentially large sizes, providing a mechanism for generating extremely large volumes. In some circumstances the brane-dilaton coupling allows the bulk dilaton to adjust to suppress the on-brane curvature parametrically below the change in brane tension, potentially providing a mechanism for reducing the vacuum energy. We explore the stability of this suppression to quantum effects in the case where their strength is controlled by the value of the field along the classical flat direction, and find it can (but need not) be stable.