Abstract
We undertake a systematic study of the 4-dimensional SU(N) 2-index chiral gauge theories and investigate their faithful global symmetries and dynamics. These are a finite set of theories with fermions in the 2-index symmetric and anti-symmetric representations, with no fundamentals, and they do not admit a large-N limit. We employ a combination of perturbative and nonperturbative methods, enabling us to constrain their infrared (IR) phases. Specifically, we leverage the ’t Hooft anomalies associated with continuous and discrete groups to eliminate a few scenarios. In some cases, the anomalies rule out the possibility of fermion composites. In other cases, the interplay between the continuous and discrete anomalies leads to multiple higher-order condensates, which inevitably form to match the anomalies. Further, we pinpoint the most probable symmetry-breaking patterns by searching for condensates that match the full set of anomalies resulting in the smallest number of IR degrees of freedom. Higher-loop β-function analysis suggests that a few theories may flow to a conformal fixed point.
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Acknowledgments
We would like to thank Nakarin Lohitsiri and Erich Poppitz for various illuminating discussions and comments on the manuscript. M.A. acknowledges the hospitality at the University of Toronto, where part of this work was completed. This work is supported by STFC through grant ST/T000708/1.
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Anber, M.M., Chan, S.Y.L. 2-index chiral gauge theories. J. High Energ. Phys. 2023, 25 (2023). https://doi.org/10.1007/JHEP10(2023)025
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DOI: https://doi.org/10.1007/JHEP10(2023)025