Abstract
We study “vacuum crossing”, which occurs when the vacua of a theory are exchanged as we vary some periodic parameter θ in a closed loop. We show that vacuum crossing is a useful non-perturbative tool to study strongly-coupled quantum field theories, since finding vacuum crossing in a weakly-coupled regime of the theory can lead to nontrivial consequences in the strongly-coupled regime. We start by discussing a mechanism where vacuum crossing occurs due to an anomaly, and then discuss some applications of vacuum crossing in general. In particular, we argue that vacuum crossing can be used to check IR dualities and to look for emergent IR symmetries.
Highlights
Where A is a background gauge field for some symmetry and the phase ω is a local functional of A which cannot be removed by adding local counterterms of the gauge fields to the theory
Vacuum crossing is always related to a broken symmetry in these SUSY WZ theories. It is intuitively clear why vacuum crossing must be related to a symmetry as long as we do not cross a phase transition or a moduli space as we go around the loop in parameter space
If vacuum crossing occurs close enough to a conformal field theory (CFT), and if we do not cross a phase transition or a moduli space as we go around the loop in parameter space, this vacuum crossing must be related to the existence of a spontaneously broken symmetry
Summary
As we take θ in a loop to θ + 2π (which is equivalent to t → t + 1), we find that the vacua (2.1) are exchanged cyclically, and so we have vacuum crossing Vacuum crossing in this theory is related to the existence of an AISC between the θ parameter and the PSU(Nf ) symmetry [6, 11]. It is easy to see that we have vacuum crossing as we take θ → θ + 2π Once again, this is related to an AISC which exists in this theory [12] (see [1]) between the θ-parameter and the Zq 1-form symmetry. Since the Witten index of this theory is nonzero, we again find that vacuum crossing was necessary for consistency with the AISC
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