Characterize the infrared condensate structure

Determine how many fermion bilinear or composite condensates form in the infrared across the catalog of asymptotically free and anomaly-free SU\((N)\) chiral gauge theories, in order to characterize the resulting global-symmetry-breaking patterns and their anomaly matching.

Background

The paper analyzes possible bosonic composite operators whose condensation could spontaneously break the continuous global symmetries of the EKK chiral gauge theories. It gives general index-counting constraints and examples of candidate condensates, but does not determine which condensates actually form dynamically.

The number and structure of infrared condensates control the resulting symmetry-breaking pattern and therefore affect whether the mixed ’t Hooft anomalies can be matched. The authors state that only a few examples are known, leaving the general condensate-counting problem unresolved.

References

Determining how many condensates form in the IR in general remains an open problem, with only a few examples where the global symmetry breaking pattern is known (see and references therein).

— On asymptotically and anomaly-free SU(N) chiral gauge theories for arbitrarily large N  (2609.21129 - Beck et al., 17 Sep 2026) in Section 7.2, “Bosonic operators”