Spontaneously broken (-1)-form U(1) symmetries
Daniel Aloni, Eduardo García-Valdecasas, Matthew Reece, Motoo Suzuki
Abstract
Spontaneous breaking of symmetries leads to universal phenomena. We extend this notion to (-1) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mo stretchy="true" form="prefix">(</mml:mo> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="true" form="postfix">)</mml:mo> </mml:mrow> </mml:math> -form U(1) symmetries. The spontaneous breaking is diagnosed by a dependence of the vacuum energy on a constant background field \theta <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>θ</mml:mi> </mml:math> , 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. We discuss how known solutions to the problem are unified in this framework and explore some, so far unsuccessful, attempts to find new solutions.