Chiral symmetry breaking in models with unconventional supersymmetry

We investigate dynamical mass generation in a geometrically constructed gauge theory based on the super Lie algebra $su(2,2|3)$, in which gravity, Yang-Mills fields, and fermions are unified as components of a single gauge connection. The model contains no elementary scalar fields and no ad hoc four-fermion interactions. Instead, fermionic self-interactions arise unavoidably from the geometric structure of the theory, through nonminimal couplings and torsion associated with the unified connection. Upon reduction to an effective low-energy description, these interactions generate a Nambu-Jona-Lasinio--type potential that triggers chiral symmetry breaking and the formation of a fermion mass gap. In this framework, mass generation emerges as a direct consequence of the underlying gauge-geometric and algebraic structure, rather than as an independent dynamical assumption.