Spontaneously Broken (−1)-Form U(1) Symmetries

Spontaneously Broken (−1)-Form U(1) Symmetries

31 Jul 2024 | Daniel Aloni, Eduardo García-Valdecasas, Matthew Reece, Motoo Suzuki
This paper explores the spontaneous breaking of (-1)-form U(1) symmetries in quantum field theory, with a focus on their implications for the Strong CP problem. The authors argue that a (-1)-form U(1) symmetry is a useful concept that provides a unifying framework for understanding various dynamical phenomena. They define a (-1)-form U(1) global symmetry as a symmetry associated with a conserved 0-form current, which can be coupled to a background axion field. The spontaneous breaking of this symmetry is diagnosed by a dependence of the vacuum energy on a constant background field θ, which can be probed by the topological susceptibility. This leads to a reinterpretation of the Strong CP problem as arising from a spontaneously broken instantonic symmetry in QCD. The authors discuss how known solutions to the problem are unified in this framework and explore some unsuccessful attempts to find new solutions. They also examine gauge theories as spontaneously broken phases, focusing on Maxwell theory in various dimensions and the Schwinger model. The paper concludes with an outlook on future research directions.This paper explores the spontaneous breaking of (-1)-form U(1) symmetries in quantum field theory, with a focus on their implications for the Strong CP problem. The authors argue that a (-1)-form U(1) symmetry is a useful concept that provides a unifying framework for understanding various dynamical phenomena. They define a (-1)-form U(1) global symmetry as a symmetry associated with a conserved 0-form current, which can be coupled to a background axion field. The spontaneous breaking of this symmetry is diagnosed by a dependence of the vacuum energy on a constant background field θ, which can be probed by the topological susceptibility. This leads to a reinterpretation of the Strong CP problem as arising from a spontaneously broken instantonic symmetry in QCD. The authors discuss how known solutions to the problem are unified in this framework and explore some unsuccessful attempts to find new solutions. They also examine gauge theories as spontaneously broken phases, focusing on Maxwell theory in various dimensions and the Schwinger model. The paper concludes with an outlook on future research directions.
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Understanding Spontaneously Broken %24(-1)%24-Form U(1) Symmetries