Scaling BPS Solutions and pure-Higgs States

TL;DR

This paper explores the spectrum of BPS states in string theory compactified on Calabi-Yau manifolds, identifying pure-Higgs states that exist only under certain charge configurations and analyzing their properties and implications.

Contribution

It explicitly computes the Higgs-branch BPS spectrum for a three-center quiver with a loop, revealing pure-Higgs states and their exponential degeneracy, and establishes their relation to Coulomb states.

Findings

Pure-Higgs states exist only when charges form a scaling solution.

The degeneracy of pure-Higgs states grows exponentially with charge.

Pure-Higgs states are in the kernel of the Higgs-Coulomb map.

Abstract

Depending on the value of the coupling, BPS states of type II string theory compactified on a Calabi-Yau manifold can be described as multicenter supergravity solutions or as states on the Coulomb or the Higgs branch of a quiver gauge theory. While the Coulomb-branch states can be mapped one-to-one to supergravity states, this is not automatically so for Higgs-branch states. In this paper we explicitly compute the BPS spectrum of the Higgs branch of a three-center quiver with a closed loop, and identify the subset of states that are in one-to-one correspondence with Coulomb/supergravity multicenter states. We also show that there exist additional "pure-Higgs" states, that exist if and only if the charges of the centers can form a scaling solution. Using generating function techniques we compute the large charge degeneracy of the "pure-Higgs" sector and show that it is always exponential. We also construct the map between Higgs- and Coulomb-branch states, discuss its relation to the Higgs-Coulomb map of one of the authors and Verlinde, and argue that the pure Higgs states live in the kernel of this map. Given that these states have no obvious description on the Coulomb branch or in supergravity, we discuss whether they can correspond to a single-center black hole or can be related to more complicated horizonless configurations.