Exploring 2-group global symmetries

By Clay Córdova, T. Dumitrescu, K. Intriligator. Journal of High Energy Physics, 2018

273 citations recorded by the source corpus.

A bstractWe analyze four-dimensional quantum field theories with continuous 2-group global symmetries. At the level of their charges, such symmetries are identical to a product of continuous flavor or spacetime symmetries with a 1-form global symmetry U(1)B(1), which arises from a conserved 2-form current JB(2). Rather, 2-group symmetries are characterized by deformed current algebras, with quantized structure constants, which allow two flavor currents or stress tensors to fuse into JB(2). This leads to unconventional Ward identities, which constrain the allowed patterns of spontaneous 2-group symmetry breaking and other aspects of the renormalization group flow. If JB(2) is coupled to a 2-form background gauge field B(2), the 2-group current algebra modifies the behavior of B(2) under background gauge transformations. Its transformation rule takes the same form as in the Green-Schwarz mechanism, but only involves the background gauge or gravity fields that couple to the other 2-group currents. This makes it possible to partially cancel reducible ’t Hooft anomalies using Green-Schwarz counterterms for the 2-group background gauge fields. The parts that cannot be cancelled are reinterpreted as mixed, global anomalies involving U(1)B(1), which receive contributions from topological, as well as massless, degrees of freedom. Theories with 2-group symmetry are constructed by gauging an abelian flavor symmetry with suitable mixed ’t Hooft anomalies, which leads to many simple and explicit examples. Some of them have dynamical string excitations that carry U(1)B(1) charge, and 2-group symmetry determines certain ’t Hooft anomalies on the world sheets of these strings. Finally, we point out that holographic theories with 2-group global symmetries have a bulk description in terms of dynamical gauge fields that participate in a conventional Green-Schwarz mechanism.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0601c6293fea99d72c20be9a48d331b00473fdca

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Citations in the corpus

Anomalies in the space of coupling constants and their dynamical applications II (2019, background): “25 This means that the mixed anomaly between the periodicity of θ and the one-form ZN global symmetry is cancelled at the cost of making the background field B participate together with A in a higher group structure [59–61].”
On gauging finite subgroups (2017, background): “2The appearance of two-group symmetry when one gauges a continuous symmetry with a suitable mixed anomaly is also discussed in a recent paper [7].”
Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions (2022, background): “2) form a natural component of the algebraic structure of a higher fusion category [52–62], generalizing the simpler higher algebraic structures defining higher-form and higher group global symmetry [1, 63, 64].”
On 2-group global symmetries and their anomalies (2018, methodology): “9) can occur in Abelian gauge theories where ∗j(2) is the field strength of a dynamical gauge field [16].”
Top down approach to 6D SCFTs (2018, methodology): “Using the prescription of [79] (see also [73, 72], one can actually compute the anomaly polynomial I8 for any 6D SCFT in our classification.”