Exploring 2-group global symmetries

Clay Córdova (School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, 08540, U.S.A.) ; Thomas Dumitrescu (Department of Physics, Harvard University, Cambridge, MA, 02138, U.S.A.; Mani L. Bhaumik Institute for Theoretical Physics, UCLA Department of Physics and Astronomy, Los Angeles, CA, 90095, U.S.A.) ; Kenneth Intriligator (Department of Physics, University of California, San Diego, La Jolla, CA, 92093, U.S.A.)

We 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 J B (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 J B (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 J B (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.

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      "source": "Springer", 
      "value": "We 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 J   B  (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 J   B  (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 J   B  (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 \u2019t 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 \u2019t 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 \u2019t 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."
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Published on:
07 May 2019
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2019 (2019)
Issue 2
Pages 1-110
DOI:
https://doi.org/10.1007/JHEP02(2019)184
arXiv:
1802.04790
Copyrights:
The Author(s)
Licence:
CC-BY-3.0

Fulltext files: