Supergravity duals of gauge field theories from SU(2) x U(1) gauged supergravity in five dimensions

TL;DR

This work constructs gravity duals for twisted gauge theories by analyzing an $SO(4)$-symmetric, purely magnetic non-Abelian and electric Abelian field solution in five-dimensional $SU(2)\times U(1)$ gauged ${\cal N}=4$ supergravity (Romans). It shows how this 5D theory arises from a chain of dimensional reductions starting from type IIB on $S^3$ and/or six-dimensional Romans' theory, and it uplifts the solution to massless type IIA/IIB supergravity. The dual field theory is a twisted NS5-brane worldvolume theory on $S^3\times T^2$, which in the IR reduces to a three-dimensional $\mathcal N=1$ SYM theory on a torus and is confining. By linking reductions from higher dimensions (e.g., 7D on $T^2$, 6D on a circle) to the 5D Romans framework, the paper provides concrete holographic descriptions of twisted gauge dynamics on curved manifolds and contributes new examples of AdS/CFT with confinement phenomena.

Abstract

We study the SO(4)-symmetric solution of the five-dimensional SU(2) x U(1) gauged N=4 supergravity theory obtained in [hep-th/0101202]. This solution contains purely magnetic non-Abelian and electric Abelian fields. It can be interpreted as a reduction of seven-dimensional gauged supergravity on a torus, which comes from type IIB supergravity on S^3. We also show how to obtain that solution from six-dimensional Romans' theory on a circle. We then up-lift the solution to massless type IIA supergravity. The dual gauge field theory is twisted and is defined on the worldvolume of a NS-fivebrane wrapped on S^3. Two other spatial directions of the NS-fivebrane are on a torus. In the IR limit it corresponds to a three-dimensional gauge field theory with two supercharges.