Vacuum structure of YangMills theory as a function of θ
Abstract
It is believed that in SU(N) YangMills theory observables are N branched functions of the topological θ angle. This is supposed to be due to the existence of a set of locallystable 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} × S^{1}. We find that while observables are indeed Nbranched functions of θ, there are only ≈ N/2 locallystable 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 nonzero 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:

 Univ. of Washington, Seattle, WA (United States). Dept. of Physics
 Univ. of Washington, Seattle, WA (United States). Inst. for Nuclear Theory
 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 Univ., Raleigh, NC (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP)
 OSTI Identifier:
 1507783
 Grant/Contract Number:
 FG0200ER41132; FG0203ER41260; 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 10298479
 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 YangMills 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 YangMills theory as a function of θ. United States. doi:10.1007/jhep09(2018)030.
Aitken, Kyle, Cherman, Aleksey, and Ünsal, Mithat. Thu .
"Vacuum structure of YangMills theory as a function of θ". United States. doi:10.1007/jhep09(2018)030. https://www.osti.gov/servlets/purl/1507783.
@article{osti_1507783,
title = {Vacuum structure of YangMills theory as a function of θ},
author = {Aitken, Kyle and Cherman, Aleksey and Ünsal, Mithat},
abstractNote = {It is believed that in SU(N) YangMills theory observables are N branched functions of the topological θ angle. This is supposed to be due to the existence of a set of locallystable 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 Nbranched functions of θ, there are only ≈ N/2 locallystable 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 nonzero 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}
}
Web of Science
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