Permutations of massive vacua

• Main Authors: Antoine Bourget, Jan Troost
• Format: Article
• Language: English
• Published: SpringerOpen 2017-05-01
• Series: Journal of High Energy Physics
• Subjects: Supersymmetric Gauge Theory; Supersymmetry and Duality; Gauge Symmetry
• Online Access: http://link.springer.com/article/10.1007/JHEP05(2017)042

Abstract We discuss the permutation group G of massive vacua of four-dimensional gauge theories with N $$ \mathcal{N} $$ = 1 supersymmetry that arises upon tracing loops in the space of couplings. We concentrate on superconformal N $$ \mathcal{N} $$ = 4 and N $$ \mathcal{N} $$ = 2 theories with N $$ \mathcal{N} $$ = 1 supersymmetry preserving mass deformations. The permutation group G of massive vacua is the Galois group of characteristic polynomials for the vacuum expectation values of chiral observables. We provide various techniques to effectively compute characteristic polynomials in given theories, and we deduce the existence of varying symmetry breaking patterns of the duality group depending on the gauge algebra and matter content of the theory. Our examples give rise to interesting field extensions of spaces of modular forms.