Supersymmetric domain walls in maximal 6D gauged supergravity I

TL;DR

This paper constructs and classifies a broad class of supersymmetric domain wall solutions in six-dimensional gauged supergravity, revealing their properties, gauge group origins, and dualities with super Yang-Mills theories.

Contribution

It explicitly constructs embedding tensors for various gauge groups and finds new supersymmetric domain wall solutions, including dyonic cases with reduced supersymmetry.

Findings

Constructed explicit embedding tensors for multiple gauge groups.

Found supersymmetric domain walls with different gauge group embeddings.

Established dualities with five-dimensional super Yang-Mills theories.

Abstract

We find a large class of supersymmetric domain wall solutions from six-dimensional $N=(2,2)$ gauged supergravity with various gauge groups. In general, the embedding tensor lives in $\mathbf{144}_c$ representation of the global symmetry $SO(5,5)$. We explicitly construct the embedding tensors in $\mathbf{15}^{-1}$ and $\overline{\mathbf{40}}^{-1}$ representations of $GL(5)\sim \mathbb{R}^+\times SL(5)\subset SO(5,5)$ leading to $CSO(p,q,5-p-q)$ and $CSO(p,q,4-p-q)\ltimes\mathbb{R}^4_{\boldsymbol{s}}$ gauge groups, respectively. These gaugings can be obtained from $S^1$ reductions of seven-dimensional gauged supergravity with $CSO(p,q,5-p-q)$ and $CSO(p,q,4-p-q)$ gauge groups. As in seven dimensions, we find half-supersymmetric domain walls for purely magnetic or purely electric gaugings with the embedding tensors in $\mathbf{15}^{-1}$ or $\overline{\mathbf{40}}^{-1}$ representations, respectively. In addition, for dyonic gauge groups with the embedding tensors in both $\mathbf{15}^{-1}$ and $\overline{\mathbf{40}}^{-1}$ representations, the domain walls turn out to be $\frac{1}{4}$-supersymmetric as in the seven-dimensional analogue. By the DW/QFT duality, these solutions are dual to maximal and half-maximal super Yang-Mills theories in five dimensions. All of the solutions can be uplifted to seven dimensions and further embedded in type IIB or M-theories by the well-known consistent truncation of the seven-dimensional $N=4$ gauged supergravity.