Abstract
We define gauge theories whose gauge group includes charge conjugation as well as standard SU(N) transformations. When combined, these transformations form a novel type of group with a semidirect product structure. For N even, we show that there are exactly two possible such groups which we dub SU˜(N)I,II. We construct the transformation rules for the fundamental and adjoint representations, allowing us to explicitly build four-dimensional N=2 supersymmetric gauge theories based on SU˜(N)I,II and understand from first principles their global symmetry. We compute the Haar measure on the groups, which allows us to quantitatively study the operator content in protected sectors by means of the superconformal index. In particular, we find that both types of SU˜(N)I,II groups lead to non-freely generated Coulomb branches.
Highlights
Gauge symmetry governs the dynamics of a huge variety of systems, ranging form Condensed Matter to Particle Physics
There is a bijective correspondence between the simple real Lie algebras and the irreducible noncompact symmetric spaces of noncompact type which we briefly review in Appendix A; this relates the involution of the algebra θ to an involution on the group
In this paper we have discussed the case of the charge conjugation symmetry in gauge theories based on SU(N ) gauge groups in a systematic manner
Summary
Gauge symmetry governs the dynamics of a huge variety of systems, ranging form Condensed Matter to Particle Physics. A more related set-up is that discussed in [21], where after symmetry breaking one ends up with a remainder discrete charge conjugation symmetry which can produce Alice strings While this was mostly with an eye on the U (1) case, the non-abelian version plays a relevant role as well in the process of constructing orientifold theories, as discussed in [22]. As shown in [15] and soon after in [14,13] for other discrete gaugings of the like, it turns out that the gauge theories based on principal extension of SU(N ) provide the first examples of four-dimensional N = 2 theories with non-freely generated Coulomb branches. For the interest of the reader, we postpone to the appendices several technical details
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