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

Kyle Aitken; Aleksey Cherman; Mithat Ünsal

doi:10.1007/JHEP09(2018)030

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

Kyle Aitken, Aleksey Cherman, Mithat Ünsal

Physics and Astronomy (Twin Cities)

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19 Scopus citations

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 ℝ³ × 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 ℝ⁴ limit.

Original language	English (US)
Article number	30
Journal	Journal of High Energy Physics
Volume	2018
Issue number	9
DOIs	https://doi.org/10.1007/JHEP09(2018)030
State	Published - Sep 1 2018

Bibliographical note

Funding Information:
We are grateful to P. Argyres, A. Kapustin, M. Shifman, T. Sulejmanpasic, and M. Ya-mazaki for helpful conversations, and owe a special thanks to L. G. Yaffe for insightful comments and advice on a preliminary version of the manuscript. K. A. is supported by the U.S. Department of Energy under Grant No. DE-SC0011637. A. C. and M. Ü. thank the KITP for its warm hospitality as part of the program ‘Resurgent Asymptotics in Physics and Mathematics’ during the final stages of the research in this paper. Research at KITP is supported by the National Science Foundation under Grant No. NSF PHY11-25915. A. C. is also supported by the U. S. Department of Energy via grants DE-FG02-00ER-41132, while M. Ü. is supported U. S. Department of Energy grant DE-FG02-03ER41260.

Publisher Copyright:
© 2018, The Author(s).

Keywords

Discrete Symmetries
Global Symmetries
Spontaneous Symmetry Breaking
Wilson, ’t Hooft and Polyakov loops

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10.1007/JHEP09(2018)030

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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 ℝ3 × 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 {\textquoteright}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 ℝ4 limit.",

keywords = "Discrete Symmetries, Global Symmetries, Spontaneous Symmetry Breaking, Wilson, {\textquoteright}t Hooft and Polyakov loops",

author = "Kyle Aitken and Aleksey Cherman and Mithat {\"U}nsal",

note = "Funding Information: We are grateful to P. Argyres, A. Kapustin, M. Shifman, T. Sulejmanpasic, and M. Ya-mazaki for helpful conversations, and owe a special thanks to L. G. Yaffe for insightful comments and advice on a preliminary version of the manuscript. K. A. is supported by the U.S. Department of Energy under Grant No. DE-SC0011637. A. C. and M. {\"U}. thank the KITP for its warm hospitality as part of the program {\textquoteleft}Resurgent Asymptotics in Physics and Mathematics{\textquoteright} during the final stages of the research in this paper. Research at KITP is supported by the National Science Foundation under Grant No. NSF PHY11-25915. A. C. is also supported by the U. S. Department of Energy via grants DE-FG02-00ER-41132, while M. {\"U}. is supported U. S. Department of Energy grant DE-FG02-03ER41260. Publisher Copyright: {\textcopyright} 2018, The Author(s).",

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doi = "10.1007/JHEP09(2018)030",

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AU - Cherman, Aleksey

AU - Ünsal, Mithat

N1 - Funding Information: We are grateful to P. Argyres, A. Kapustin, M. Shifman, T. Sulejmanpasic, and M. Ya-mazaki for helpful conversations, and owe a special thanks to L. G. Yaffe for insightful comments and advice on a preliminary version of the manuscript. K. A. is supported by the U.S. Department of Energy under Grant No. DE-SC0011637. A. C. and M. Ü. thank the KITP for its warm hospitality as part of the program ‘Resurgent Asymptotics in Physics and Mathematics’ during the final stages of the research in this paper. Research at KITP is supported by the National Science Foundation under Grant No. NSF PHY11-25915. A. C. is also supported by the U. S. Department of Energy via grants DE-FG02-00ER-41132, while M. Ü. is supported U. S. Department of Energy grant DE-FG02-03ER41260. Publisher Copyright: © 2018, The Author(s).

PY - 2018/9/1

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N2 - 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 ℝ3 × 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 ℝ4 limit.

AB - 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 ℝ3 × 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 ℝ4 limit.

KW - Discrete Symmetries

KW - Global Symmetries

KW - Spontaneous Symmetry Breaking

KW - Wilson, ’t Hooft and Polyakov loops

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JF - Journal of High Energy Physics

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ER -

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

Abstract

Bibliographical note

Keywords

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