Quantum analysis of gauge-covariant Hadamard descent

Develop a full quantum-mechanical analysis of the Hadamard descent of non-Abelian Yang–Mills theory, including the effects of the chiral-anomaly-induced Jacobian associated with the fermionic field redefinition.

Background

The paper formulates Hadamard descent for non-Abelian Yang–Mills theory in a gauge-covariant manner and derives a lower-dimensional Yang–Mills–Higgs theory. In the fermionic sector, the extra-dimensional gauge connection produces a pseudoscalar Yukawa coupling that can be converted classically into a fermion mass term by a chiral field redefinition.

The authors note that, at the quantum level, this field redefinition may generate a nontrivial Jacobian in the fermionic functional measure and consequently a topological contribution through the chiral anomaly. Because the analysis is restricted to the classical reduced theory, a complete quantum treatment remains unresolved.

References

At the quantum level, the same redefinition may induce a non-trivial Jacobian in the fermionic measure through the chiral anomaly; the present analysis has been restricted to the classical reduced theory. A full quantum mechanical analysis of the Hadamard descent is an interesting open problem to be addressed in future works.

— Gauge-covariant Hadamard descent in Yang-Mills theory  (2610.08515 - Vacchiano et al., 6 Oct 2026) in Section Conclusions