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) |
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Article number | 30 |
Journal | Journal of High Energy Physics |
Volume | 2018 |
Issue number | 9 |
DOIs | |
State | Published - Sep 1 2018 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2018, The Author(s).
Keywords
- Discrete Symmetries
- Global Symmetries
- Spontaneous Symmetry Breaking
- Wilson, ’t Hooft and Polyakov loops