Strong Coupling Dynamics of the Higgs Branch: Rolling a Higgs by Collapsing an Instanton

TL;DR

This paper constructs a supergravity dual for strongly coupled gauge theories with hypermultiplets, analyzing Higgs branch dynamics and instanton collapse, revealing moduli-dependent deceleration near singularities with potential cosmological implications.

Contribution

It provides a novel supergravity description of Higgs branch dynamics, including instanton collapse, and explores the effects of vector multiplet moduli on the approach to singularities.

Findings

Decelerating approach to Higgs branch singularities.

Dynamics sensitive to vector multiplet moduli.

Potential implications for inflating cosmologies.

Abstract

We construct the dual supergravity description of strongly coupled, large $N$, eight-supercharge gauge theories with fundamental hypermultiplets at points on the mixed Coulomb-Higgs branch. With certain assumptions about unknown couplings of D-branes to supergravity, this construction gives the correct metric on the hypermultiplet (Higgs-branch) component the moduli space, which decouples from the vector multiplet (Coulomb-branch) moduli. Going beyond the geodesic approximation, we find that the dynamics of a hypermultiplet VEV rolling towards a singularity on the Higgs component of the moduli space is sensitive to the vector multiplet moduli. The dual description of the approach to the singularity involves collapsing ``instantons'' of a non-Abelian Dirac-Born-Infeld theory in a curved background. In general, we find a decelerating approach to the singularity, although the manner of deceleration depends on the vector multiplet moduli. Upon introducing a potential on the Higgs branch of a four dimensional ${\cal N}=2$ theory coupled to gravity, this deceleration mechanism might lead to interesting inflating cosmologies analogous those studied recently by Alishahiha, Silverstein and Tong.