Abstract
We establish the non-perturbative validity of the gauge anomaly cancellation condition in an effective electroweak theory of massless fermions with finite momentum cut-off and Fermi interaction. The requirement that the current is conserved up to terms smaller than the energy divided by the cut-off scale, which is the natural condition as gauge invariance is only emerging, produces the same constraint on charges as in the Standard Model. The result holds at a non-perturbative level as the functional integrals are expressed by convergent power series expansions and are analytic in a finite domain.
Highlights
In a chiral theory, classical gauge invariance can be broken at the quantum level by anomalies, a fact producing a lack of renormalizability and of internal consistency
We have considered a two-species Standard Model with chiral fermions and a momentum cutoff, with the gauge fields integrated out to produce a current-current interaction
The functional integrals expressing the theory are well defined at a nonperturbative level and analytic in a finite disk in the infinite volume limit
Summary
Classical gauge invariance can be broken at the quantum level by anomalies, a fact producing a lack of renormalizability and of internal consistency. The requirement that the current is conserved up to terms of the energy divided by the cutoff scale, which is the natural condition in the effective quantum field theory as gauge symmetry is emerging, provides the same constraint on charges as is found in the Standard Model at a perturbative level. It is, a robust condition holding at a nonperturbative level in an effective theory and even when gauge symmetry is classically not exact. III, we present the renormalization group analysis, and the Appendixes contain the more mathematical details
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