Supersymmetric domain walls in maximal 6D gauged supergravity III

• Published in: arXiv.org
• Main Authors: Karndumri, Parinya, Nuchino, Patharadanai
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 15.10.2024
• Subjects: Domain walls; Embedding; Mathematical analysis; Physics - High Energy Physics - Theory; Representations; Subgroups; Supergravity; Supersymmetry; Symmetry; Tensors
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2312.15777

We continue our study of gaugings the maximal \(N=(2,2)\) supergravity in six dimensions with gauge groups obtained from decomposing the embedding tensor under \(\mathbb{R}^+\times SO(4,4)\) subgroup of the global symmetry \(SO(5,5)\). Supersymmetry requires the embedding tensor to transform in \(\mathbf{144}_c\) representation of \(SO(5,5)\). Under \(\mathbb{R}^+\times SO(4,4)\) subgroup, this leads to the embedding tensor in \((\mathbf{8}^{\pm 3}\), \(\mathbf{8}^{\pm 1},\mathbf{56}^{\pm 1})\) representations. Gaugings in \(\mathbf{8}^{\pm 3}\) representations lead to a translational gauge group \(\mathbb{R}^8\) while gaugings in \(\mathbf{8}^{\pm 1}\) representations give rise to gauge groups related to the scaling symmetry \(\mathbb{R}^+\). On the other hand, the embedding tensor in \(\mathbf{56}^{\pm 1}\) representations gives \(CSO(4-p,p,1)\sim SO(4-p,p)\ltimes \mathbb{R}^4\subset SO(4,4)\) gauge groups with \(p=0,1,2\). More interesting gauge groups can be obtained by turning on more than one representation of the embedding tensor subject to the quadratic constraints. In particular, we consider gaugings in both \(\mathbf{56}^{-1}\) and \(\mathbf{8}^{+3}\) representations giving rise to larger \(SO(5-p,p)\) and \(SO(4-p,p+1)\) gauge groups for \(p=0,1,2\). In this case, we also give a number of half-supersymmetric domain wall solutions preserving different residual symmetries. The solutions for gaugings obtained only from \(\mathbf{56}^{-1}\) representation are also included in these results when the \(\mathbf{8}^{+3}\) part is accordingly turned off.