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

Aitken, Kyle; Cherman, Aleksey; Ünsal, Mithat

doi:10.1007/jhep09(2018)030

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

Journal Article · 05 September 2018 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep09(2018)030 · OSTI ID:1507783

Aitken, Kyle ^[1]; Cherman, Aleksey ^[2]; Ünsal, Mithat ^[3]

Univ. of Washington, Seattle, WA (United States). Dept. of Physics; Univ. of Washington, Seattle, WA (United States)
Univ. of Washington, Seattle, WA (United States). Inst. for Nuclear Theory
North Carolina State Univ., Raleigh, NC (United States). Dept. of Physics

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.

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Research Organization:: Univ. of Washington, Seattle, WA (United States); North Carolina State Univ., Raleigh, NC (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

Grant/Contract Number:: FG02-00ER41132; FG02-03ER41260; SC0011637

OSTI ID:: 1507783

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 9 Vol. 2018; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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