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We present exact nonperturbative vacuum solutions to chiral gauge theories based on the $E_6$gauge group and several matter fermions in the fundamental $27$-dimensional representation. They are obtained when supersymmetric versions are perturbed by small supersymmetry breaking by anomaly mediation. The universality classes obtained are very different from what can be conjectured by the tumbling hypothesis. In particular, the case with three $27\mathrm{s}$may have an unbroken SU(3) symmetry with massless composite fermions in $10$of SU(3). For this case, we employed numerical techniques to obtain the exact ground state. 

We present exact results in softly broken supersymmetric $\mathrm{SU}\left(N_C\right)$chiral gauge theories with charged fermions in one antisymmetric, $N_F$fundamental, and $N_C+N_F-4$antifundamental representations. We achieve this by considering the supersymmetric version of these theories and utilizing anomaly mediated supersymmetry breaking at a scale $m\ll \mathrm{\Lambda }$to generate a vacuum. The connection to nonsupersymmetric theories is then conjectured in the limit $m\to \infty$. For odd $N_C$, we determine the massless fermions and unbroken global symmetries in the infrared. For even $N_C$, we find global symmetries are nonanomalous and no massless fermions. In all cases, the symmetry breaking patterns differ from what the tumbling hypothesis would suggest. 

Insect diversification has been catalyzed by widespread specialization on novel hosts - a process underlying exceptional radiations of phytophagous beetles, lepidopterans, parasitoid wasps, and inordinate lineages of symbionts, predators and other trophic specialists. The strict fidelity of many such interspecies associations is posited to hinge on sensory tuning to host-derived cues, a model supported by studies of neural function in host-specific model species. Here, we investigated the sensory basis of symbiotic interactions between a myrmecophile rove beetle and its single, natural host ant species. We show that host cues trigger analogous behaviors in both ant and symbiont. Cuticular hydrocarbons - the ant's nestmate recognition pheromones - elicit partner recognition by the beetle and execution of ant grooming behavior, integrating the beetle into the colony via chemical mimicry. The beetle also follows host trail pheromones, permitting inter-colony dispersal. Remarkably, the rove beetle also performs its symbiotic behaviors with ant species separated by ~95 million years, and shows minimal preference for its natural host over non-host ants. Experimentally validated agent-based modeling supports a scenario in which specificity is enforced by physiological constraints on symbiont dispersal, and negative fitness interactions with alternative hosts, rather than via sensory tuning. Enforced specificity may be a pervasive mechanism of host range restriction of specialists embedded within host niches. Chance realization of latent compatibilities with alternative hosts may facilitate host switching, enabling deep-time persistence of obligately symbiotic lineages.