Entropic order parameters in weakly coupled gauge theories
- Instituto Balseiro, Centro Atómico Bariloche,Rio Negro (Argentina); Univ. of Pennsylvania, Philadelphia, PA (United States)
- University of Pennsylvania, Philadelphia, PA (United States); Vrije Universiteit Brussel (VUB), Brussels (Belgium); International Solvay Institutes, Brussels (Belgium)
- Instituto Balseiro, Centro Atómico Bariloche,Rio Negro (Argentina)
The entropic order parameters measure in a universal geometric way the statistics of non-local operators responsible for generalized symmetries. In this article, we compute entropic order parameters in weakly coupled gauge theories. To perform this computation, the natural route of evaluating expectation values of physical (smeared) non-local operators is prevented by known difficulties in constructing suitable smeared Wilson loops. We circumvent this problem by studying the smeared non-local class operators in the enlarged non-gauge invariant Hilbert space. This provides a generic approach for smeared operators in gauge theories and explicit formulas at weak coupling. In this approach, the Wilson and ’t Hooft loops are labeled by the full weight and co-weight lattices respectively. We study generic Lie groups and discuss couplings with matter fields. Smeared magnetic operators, as opposed to the usual infinitely thin ones, have expectation values that approach one at weak coupling. The corresponding entropic order parameter saturates to its maximum topological value, except for an exponentially small correction, which we compute. On the other hand, smeared ’t Hooft loops and their entropic disorder parameter are exponentially small. We verify that both behaviors match the certainty relation for the relative entropies. In particular, we find upper and lower bounds (that differ by a factor of 2) for the exact coefficient of the linear perimeter law for thin loops at weak coupling. This coefficient is unphysical/non-universal for line operators. We end with some comments regarding the RG flows of entropic parameters through perturbative beta functions.
- Research Organization:
- University of Pennsylvania, Philadelphia, PA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC); Universidad Nacional de Cuyo; National Scientific and Technical Research Council (CONICET); Commission Nacional de Energía Atómica (CNEA); Simons Foundation
- Grant/Contract Number:
- SC0020360
- OSTI ID:
- 1976429
- Journal Information:
- Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 1 Vol. 2022; ISSN 1029-8479
- Publisher:
- Springer NatureCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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