Holographic Duals of Symmetry Broken Phases

Andrea Antinucci, Francesco Benini, Giovanni Rizi
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Abstract

A novel interpretation of Symmetry Topological Field Theories (SymTFTs) as theories of gravity is explored by proposing a holographic duality where the bulk SymTFT (with the gauging of a suitable Lagrangian algebra) is dual to the universal effective field theory (EFT) that describes spontaneous symmetry breaking on the boundary. The authors tested this conjecture in various dimensions and with many examples involving different continuous symmetry structures, including non‐Abelian and non‐invertible symmetries, as well as higher groups. For instance, many Abelian SymTFTs are found to be dual to free theories of Goldstone bosons or generalized Maxwell fields, while non‐Abelian SymTFTs relate to non‐linear sigma models with target spaces defined by the symmetry groups. The analysis is also extended to include the non‐invertible axial symmetry, which is shown to be dual to axion‐Maxwell theory, and a non‐Abelian 2‐group structure in four dimensions, deriving a new parity‐violating interaction that has implications for the low‐energy dynamics of QCD.
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对称破缺相的全息二重性
通过提出一种全息对偶性,探索了对称拓扑场论(SymTFT)作为引力理论的一种新解释,在这种对偶性中,体SymTFT(具有合适的拉格朗日代数的测量)与描述边界上自发对称破缺的普适有效场论(EFT)是对偶的。作者在不同维度上用许多例子检验了这一猜想,这些例子涉及不同的连续对称结构,包括非阿贝尔对称和非可逆对称,以及高次群。例如,发现许多阿贝尔 SymTFT 与金石玻色子或广义麦克斯韦场的自由理论是对偶的,而非阿贝尔 SymTFT 则与目标空间由对称群定义的非线性西格玛模型有关。分析还扩展到包括不可逆轴对称,证明它与轴子-麦克斯韦理论是对偶的,以及四维中的非阿贝尔 2 群结构,推导出一种新的违反奇偶性的相互作用,对 QCD 的低能动力学有影响。
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