Stability Analysis of the Chiral Transition in SU(4) Gauge Theory with Fermions in Multiple Representations

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.