Investigation of the domain wall fermion approach to chiral gauge theories on the lattice

Abstract

We investigate a recent proposal to construct chiral gauge theories on the lattice using domain wall fermions. We restrict ourselves to the finite volume case, in which two domain walls are present, with modes of opposite chirality on each of them. We couple the chiral fermions on only one of the domain walls to a gauge field. In order to preserve gauge invariance, we have to add a scalar field, which gives rise to additional light mirror fermion and scalar modes. We argue that in an anomaly-free model these extra modes would decouple if our model possesses a so-called strong coupling symmetric phase. However, our numerical results indicate that such a phase most probably does not exist.PACS number(s): 11.15.Ha. 12.38.G~

Chiral lattice gauge theories from warped domain walls and Ginsparg-Wilson fermions

“…Recently, a proposal [5,6] was made to implement this as a limit of a spontaneously broken higher dimensional gauge theory in a curved background field. Apart from the curvature that allows the decoupling of the gauge and fermion masses from each other, this is similar to the 'wave-guide model' [7,8], which is known not to give a chiral theory [9]. Unfortunately, the Goldstone mode that forms part of the gauge boson in the unitary gauge remains strongly coupled and the model cannot be analyzed without numerical simulations.…”

“…Tanmoy Bhattacharya and couple them with a Higgs' field as yψ k+1,+ φ ψ k,− + h.c.. When the gauge field is constant along the z direction, this model is known to be non-chiral [9] since either the gauge boson becomes as heavy as the edge state one is trying to remove, or new massless edge modes appear in the theory. The odd Kaluza-Klein modes of the gauge field, however, are not affected by the Higgs' mechanism, but since the masses for all of them are controlled by the same scale, this does not lead to a two-dimensional theory in the appropriate limit either.…”

Aspects of chiral symmetry and the lattice

“…One might think of the operator as representing a "filter" at x 5 = i through which only charge compensating pairs of Fermions can pass. The need for such an operator in a fully finite theory was emphasized by Eichten and Preskill (1986), although the detailed scheme presented there had technical difficulties (Golterman, Petcher, and Rivas, 1993).…”

“…Despite difficulties (Golterman, Petcher, and Rivas, 1993) with their specific model, the idea of including such terms remains compelling. In this section I will discuss a specific recent scheme (Creutz, Tytgat, Rebbi, and Xue, 1997) building on the domain-wall approach.…”

“…I now proceed in analogy to the "waveguide" picture (Golterman, Jansen, Petcher, and Vink, 1994) and restrict this charge violation to ∆Q to one layer at some interior x 5 = i. Then the Fermion hopping term from x 5 = i to i + 1…”