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Title: Vacuum structure of Yang-Mills theory as a function of θ

Abstract

It is believed that in SU(N) Yang-Mills theory observables are N -branched functions of the topological θ angle. This is supposed to be due to the existence of a set of locally-stable candidate vacua, which compete for global stability as a function of θ. We study the number of θ vacua, their interpretation, and their stability properties using systematic semiclassical analysis in the context of adiabatic circle compactification on $$ \mathbb{R}$$3 × S1. We find that while observables are indeed N-branched functions of θ, there are only ≈ N/2 locally-stable candidate vacua for any given θ. We point out that the different θ vacua are distinguished by the expectation values of certain magnetic line operators that carry non-zero GNO charge but zero ’t Hooft charge. Finally, we show that in the regime of validity of our analysis YM theory has spinodal points as a function of θ, and gather evidence for the conjecture that these spinodal points are present even in the $$ \mathbb{R}$$4 limit.

Authors:
 [1];  [2];  [3]
  1. Univ. of Washington, Seattle, WA (United States). Dept. of Physics
  2. Univ. of Washington, Seattle, WA (United States). Inst. for Nuclear Theory
  3. North Carolina State Univ., Raleigh, NC (United States). Dept. of Physics
Publication Date:
Research Org.:
Univ. of Washington, Seattle, WA (United States); North Carolina State University, Raleigh, NC (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1507783
Grant/Contract Number:  
FG02-00ER41132; FG02-03ER41260; SC0011637
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 9; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Discrete Symmetries, Global Symmetries, Spontaneous Symmetry Breaking, Wilson, 't Hooft and Polyakov loops

Citation Formats

Aitken, Kyle, Cherman, Aleksey, and Ünsal, Mithat. Vacuum structure of Yang-Mills theory as a function of θ. United States: N. p., 2018. Web. doi:10.1007/jhep09(2018)030.
Aitken, Kyle, Cherman, Aleksey, & Ünsal, Mithat. Vacuum structure of Yang-Mills theory as a function of θ. United States. https://doi.org/10.1007/jhep09(2018)030
Aitken, Kyle, Cherman, Aleksey, and Ünsal, Mithat. Thu . "Vacuum structure of Yang-Mills theory as a function of θ". United States. https://doi.org/10.1007/jhep09(2018)030. https://www.osti.gov/servlets/purl/1507783.
@article{osti_1507783,
title = {Vacuum structure of Yang-Mills theory as a function of θ},
author = {Aitken, Kyle and Cherman, Aleksey and Ünsal, Mithat},
abstractNote = {It is believed that in SU(N) Yang-Mills theory observables are N -branched functions of the topological θ angle. This is supposed to be due to the existence of a set of locally-stable candidate vacua, which compete for global stability as a function of θ. We study the number of θ vacua, their interpretation, and their stability properties using systematic semiclassical analysis in the context of adiabatic circle compactification on $ \mathbb{R}$3 × S1. We find that while observables are indeed N-branched functions of θ, there are only ≈ N/2 locally-stable candidate vacua for any given θ. We point out that the different θ vacua are distinguished by the expectation values of certain magnetic line operators that carry non-zero GNO charge but zero ’t Hooft charge. Finally, we show that in the regime of validity of our analysis YM theory has spinodal points as a function of θ, and gather evidence for the conjecture that these spinodal points are present even in the $ \mathbb{R}$4 limit.},
doi = {10.1007/jhep09(2018)030},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2018,
place = {United States},
year = {2018},
month = {9}
}

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Cited by: 16 works
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Figures / Tables:

Figure 1 Figure 1: [Color Online.] An sketch of the phase structure of SU(N) YM theory for N = 4 as a function of θ. The vertical axis depicts the vacuum energy density. The gray dashed curves indicate the energy density associated with the four distinct θ-extrema. The colored bold curves indicatemore » the vacuum energy density associated with the thermodynamically stable vacuum branch for any given θ . The black dots at the cusps label the locations of quantum phase transitions. These phase transitions are associated with changes in the expectation values of GNO 't Hooft magnetic holonomies, as discussed in the main text.« less

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