Lattice chirality and the decoupling of mirror fermions

Abstract

We show, using exact lattice chirality, that partition functions of lattice gauge theories with vectorlike fermion representations can be split into "light" and "mirror" parts, such that the "light" and "mirror" representations are chiral. The splitting of the full partition function into "light" and "mirror" is well defined only if the two sectors are separately anomaly free. We show that only then is the generating functional, and hence the spectrum, of the mirror theory a smooth function of the gauge field background. This explains how ideas to use additional non-gauge, high-scale mirror-sector dynamics to decouple the mirror fermions without breaking the gauge symmetry-for example, in symmetric phases at strong mirror Yukawa couplingare forced to respect the anomaly-free condition when combined with the exact lattice chiral symmetry. Our results are also useful in explaining a paradox posed by a recent numerical study of the mirror-fermion spectrum in a toy would-be-anomalous two-dimensional theory. In passing, we prove some general properties of the partition functions of arbitrary chiral theories on the lattice that should be of interest for further studies in this field.

On the decoupling of mirror fermions

“…In Section 3, we briefly review some theoretical developments that have appeared previously (for a more thorough discussion we refer the reader to the original references [8,46,[48][49][50]). Various exact (independent of the coupling) identities obeyed by the mirror polarization operator on the lattice were derived there and provide essential consistency checks on our computer code.…”

“…As mentioned above, we are not going to integrate over the gauge field, since we treat it as a background field. Due to the exact lattice chiral symmetry, in the case where the light and mirror sectors are separately anomaly free, the partition function can be split into light and mirror parts in a way which is nonsingular over the entire field space [48]. The splitting of the partition function into light and mirror sectors is achieved by decomposing the Dirac fermions A, B, C, X into chiral parts through the chiral eigenvectors of γ 5 andγ 5 , as we now briefly review.…”

Higgs boson mass bounds in the presence of a very heavy fourth quark generation

“…The interest in lattice Higgs-Yukawa models has therefore recently been renewed [4][5][6][15][16][17][18][19][20].…”

Upper Higgs boson mass bounds from a chirally invariant lattice Higgs-Yukawa model

“…This new development allows to maintain the chiral character of the Higgs-fermion coupling structure of the Standard Model on the lattice while simultaneously lifting the fermion doublers, thus eliminating manifestly the main objection to the earlier investigations. The interest in lattice Higgs-Yukawa models has therefore recently been renewed [32][33][34][35][36][37][38][39]. In particular, the phase diagram of the new, chirally invariant Higgs-Yukawa model has been discussed analytically by means of a large N f calculation [35,37] as well as numerically by direct Monte-Carlo computations [36].…”