Abstract
We present a Pisarski-Wilczek stability analysis of SU(4) gauge theory coupled simultaneously to fermions charged under the fundamental and two-index antisymmetric representations of the gauge group. We carry out the calculation to one loop in the $\epsilon$ expansion, assuming that the two species of fermion undergo a simultaneous chiral transition. The results indicate that the chiral transition is first order.
Highlights
Gauge theories coupled to fermions charged under multiple different irreducible representations of the gauge group (“multirep theories”) are an old idea in beyond Standard Model phenomenology
IV, we review the results of the calculation for the single-irrep subsectors of the theory, which have been examined previously [18,19,20,21] and whose fixed points span a subset of the fixed points of the full
When fermions are charged under real irreps like the A2 of SU(4), chiral symmetry is enhanced by an additional Z2 relating color and anticolor [22,23]
Summary
Gauge theories coupled to fermions charged under multiple different irreducible representations (irreps) of the gauge group (“multirep theories”) are an old idea in beyond Standard Model phenomenology. Multirep theories were long ago speculated to exhibit interesting phase structure via the mechanism of “tumbling” or “condensation in the most attractive channel” [1]. If observed, such a mechanism would provide a natural means of dynamically generating separated scales. Original lattice tests of this phenomenon using quenched fermions suggested it would occur [12,13,14,15], but recent lattice investigations indicate that phase separation is at least not a universal feature of vectorlike multirep theories [8,9,10]. The rest of this paper presents a Pisarski-Wilczek stability analysis applicable to the chiral transition in both Ferretti’s model and our collaboration’s lattice deformation of this theory. In the Conclusion, we discuss the robustness of the predictions of the calculation against higher-order corrections (which are known to find fixed points in the single-irrep sectors that our treatment misses) and comment on future applications of the methods used here
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