Branes for Higgs phases and exact conformal field theories

TL;DR

This work shows that Higgs-phase vacua of $Z_N$-symmetric SUSY Yang–Mills theories can be realized in string theory as multicenter supergravity solutions that in certain energy regimes are described by the exact CFT $SU(2)/U(1)\times SL(2,\mathbb{R})/U(1)$. It demonstrates how U-dualities map these backgrounds to purely gravitational configurations and connects them to the near-horizon geometry of D1–D5 black holes, with NS5/D5 on a circle providing explicit realizations of axionic instantons and their CFT descriptions in two limits. By performing coordinate redefinitions and T-dualities, the paper identifies exact CFTs $SU(2)_{kN}/U(1)\times SL(2,\mathbb{R})_{kN+4}/U(1)$ for large $N$ and $SU(2)_k/U(1)\times U(1)_R\times U(1)_Q$ for $N=1$, and discusses the supersymmetric structure and solitonic interpretation of these backgrounds. It further links the geometries to black-hole physics through dualities and explores how multicenter constructions might underpin non-BPS extensions and confinement-like phenomena, outlining open problems and future directions. Overall, the work forges a bridge between Higgs branches in gauge theories, exact worldsheet CFTs, and gravity/black-hole physics, offering a framework to interpolate between weak and strong coupling regimes.

Abstract

We consider multicenter supergravity solutions corresponding to Higgs phases of supersymmetric Yang-Mills theories with Z_N symmetric vacua. In certain energy regimes, we find a description in terms of a generalized wormhole solution that corresponds to the SL(2,R)/U(1) \times SU(2)/U(1) exact conformal field theory. We show that U-dualities map these backgrounds to purely gravitational ones and comment on the relation to the black holes arising from intersecting D1 and D5 branes. We also discuss supersymmetric properties of the various solutions and the relation to 2-dim solitons, on flat space, of the reduced axion-dilaton-gravity equations. Finally, we address the problem of understanding other supergravity solutions from the multicenter ones. As prototype examples we use rotating D3 branes and NS5 and D5 branes associated to non-Abelian duals of 4-dim hyper-Kahler metrics with SO(3) isometry.