Resolved gravity duals of ${\cal N}=4$ quiver field theories in 2+1 dimensions

TL;DR

This paper constructs and analyzes gravity duals of 2+1 dimensional ${ m N}=4$ quiver gauge theories with arbitrary gauge group product structures, using resolved M-theory backgrounds and fluxes, and discusses string correction effects.

Contribution

It generalizes previous ${ m N}=4$ quiver gauge theory duals to arbitrary gauge groups using resolved M-theory backgrounds with fluxes.

Findings

Constructed gravity duals for general ${ m N}=4$ quiver theories.

Described M-theory lift of Page charge quantization.

Clarified string correction roles in different regimes.

Abstract

We generalize the construction by Aharony, Hashimoto, Hirano, and Ouyang of ${\cal N}=4$ quiver gauge theory with gauge group $U(N+M) \times U(N)$, $k$ fundamentals charged under $U(N)$ and bi-fundamentals, to the case with gauge group $\prod_{i=1}^{\hat k} U(N_i)$ with $k_i$ fundamentals charged under $U(N_i)$. This construction is facilitated by considering the resolved $ALE_{\hat k} \times TN_{k}$ background in M-theory including non-trivial fluxes through the resolved 4-cycles in the geometry. We also describe the M-theory lift of the IIA Page charge quantization condition. Finally, we clarify the role of string corrections in various regimes of parameter space.