Generalized global symmetries of T[M] theories. Part I
- Creators
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Gukov, Sergei
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Hsin, Po-Shen
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Pei, Du
Abstract
We study reductions of 6d theories on a d-dimensional manifold M_d, focusing on the interplay between symmetries, anomalies, and dynamics of the resulting (6 − d)-dimensional theory T[M_d]. We refine and generalize the notion of "polarization" to polarization on M_d, which serves to fix the spectrum of local and extended operators in T[M_d]. Another important feature of theories T[M_d] is that they often possess higher-group symmetries, such as 2-group and 3-group symmetries. We study the origin of such symmetries as well as physical implications including symmetry breaking and symmetry enhancement in the renormalization group flow. To better probe the IR physics, we also investigate the 't Hooft anomaly of 5d Chern-Simons matter theories. The present paper focuses on developing the general framework as well as the special case of d = 0 and 1, while an upcoming paper will discuss the case of d = 2, 3 and 4.
Additional Information
© 2021 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: November 12, 2020; Revised: March 21, 2021; Accepted: March 22, 2021; Published: April 23, 2021. We would like to thank Dan Freed, Anton Kapustin, Pavel Putrov, Nathan Seiberg, Cumrun Vafa, Juven Wang, Edward Witten, and Shing-Tung Yau for illuminating discussions and comments. We would like to especially thank Nikita Sopenko for participation at the early stage of this project. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664227. The work of P.-S. H. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, and by the Simons Foundation through the Simons Investigator Award. The work of D.P. is supported by the Center for Mathematical Sciences and Applications at Harvard University, and by an NSF grant DMS-0932078, administered by the Mathematical Sciences Research Institute while the author was in residence at MSRI for the program "Holomorphic differentials in mathematics and physics" during the Fall of 2019.Attached Files
Published - Gukov2021_Article_GeneralizedGlobalSymmetriesOfT.pdf
Accepted Version - 2010.15890.pdf
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Additional details
- Eprint ID
- 106619
- Resolver ID
- CaltechAUTHORS:20201111-130432310
- DE-SC0011632
- Department of Energy (DOE)
- DMS-1664227
- NSF
- Simons Foundation
- DMS-0932078
- NSF
- SCOAP3
- Created
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2020-11-11Created from EPrint's datestamp field
- Updated
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2021-08-11Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics
- Other Numbering System Name
- CALT-TH
- Other Numbering System Identifier
- 2020-045