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On completeness and generalized symmetries in quantum field theory

Journal Article · · Modern Physics Letters A
 [1];  [2]
  1. Instituto Balseiro, Centro Atómico Bariloche, 8400 S.C. de Bariloche, Río Negro, Argentina
  2. David Rittenhouse Laboratory, University of Pennsylvania, 209 S.33rd Street, Philadelphia, PA 19104, USA; Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB) and The International Solvay Institutes, Pleinlaan 2, 1050 Brussels, Belgium

We review a notion of completeness in QFT arising from the analysis of basic properties of the set of operator algebras attached to regions. In words, this completeness asserts that the physical observable algebras produced by local degrees of freedom are the maximal ones compatible with causality. We elaborate on equivalent statements to this completeness principle such as the non-existence of generalized symmetries and the uniqueness of the net of algebras. We clarify that for non-complete theories, the existence of generalized symmetries is unavoidable and further that they always come in dual pairs with precisely the same “size”. Moreover, the dual symmetries are always broken together, be it explicitly or effectively. Finally, we comment on several issues raised in recent literature, such as the relationship between completeness and modular invariance, dense sets of charges, and absence of generalized symmetries in the bulk of holographic theories.

Research Organization:
Univ. of Pennsylvania, Philadelphia, PA (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
DOE Contract Number:
SC0020360
OSTI ID:
1980820
Journal Information:
Modern Physics Letters A, Vol. 36, Issue 36; ISSN 0217-7323
Publisher:
World Scientific Publishing
Country of Publication:
United States
Language:
English

References (37)

Monopoles, Duality, and String Theory journal February 2004
Symmetries and strings in field theory and gravity journal April 2011
Entropic order parameters for the phases of QFT journal April 2021
Generalized global symmetries journal February 2015
Topological operators and completeness of spectrum in discrete gauge theories journal December 2020
Non-invertible global symmetries and completeness of the spectrum journal September 2021
Generalized Free Fields and the AdS-CFT Correspondence journal August 2003
Emergent spacetime and holographic CFTs journal October 2012
Quantum complementarity through entropic certainty principles journal January 2021
Nets of Subfactors journal May 1995
Index for subfactors journal February 1983
Extension of Jones' theory on index to arbitrary factors journal March 1986
Index of subfactors and statistics of quantum fields. I journal December 1989
Index for von Neumann algebras with finite-dimensional centers journal January 1992
Minimal Index and Dimension for 2-C*-Categories with Finite-Dimensional Centers journal October 2018
The logic of causally closed spacetime subsets journal November 2002
Fracton phases of matter journal February 2020
Exotic symmetries, duality, and fractons in 2+1-dimensional quantum field theory journal January 2021
Exotic $U(1)$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory journal January 2020
Exotic $\mathbb{Z}_N$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory journal January 2021
Entanglement entropy and superselection sectors. Part I. Global symmetries journal February 2020
Standard and split inclusions of von Neumann algebras journal October 1984
Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics journal July 1990
Fields, observables and gauge transformations I journal March 1969
Fields, observables and gauge transformations II journal September 1969
Local observables and particle statistics I journal September 1971
Local observables and particle statistics II journal March 1974
Superselection sectors with braid group statistics and exchange algebras journal June 1989
Index of subfactors and statistics of quantum fields journal June 1990
Locality and the structure of particle states journal March 1982
On the phase transition towards permanent quark confinement journal June 1978
Variational approach to relative entropies with an application to QFT journal October 2021
On relative entropy and global index journal February 2020
A new handle on three-point coefficients: OPE asymptotics from genus two modular invariance journal October 2017
The large $N$ limit of superconformal field theories and supergravity journal January 1998
Anti de Sitter space and holography journal January 1998
Wormholes, emergent gauge fields, and the weak gravity conjecture journal January 2016

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