Chiral Lattice Gauge Theories from Warped Domain Walls and Ginsparg-Wilson Fermions

TL;DR

The paper tackles the long-standing problem of lattice formulations for chiral gauge theories by proposing and analyzing two complementary routes. First, a warped AdS$_3$-based construction yields a 2D chiral gauge theory in the IR with a light gauge mode and a predominantly chiral fermion spectrum, avoiding strong coupling to Goldstone modes and separating gauge- and fermion-mass scales. Second, a strictly 2D, one-site model with Ginsparg-Wilson fermions achieves exact lattice chiral symmetries and reproduces the correct anomaly structure, with a preliminary strong-Yukawa analysis suggesting a stable chiral spectrum in the symmetric phase. Together, these approaches offer concrete avenues for realizing lattice chiral gauge theories, potentially informing 4D implementations and the definition of the fermion measure, while highlighting the distinct advantages and open questions of warped-domain-wall versus GW-based constructions.

Abstract

We propose a construction of a 2-dimensional lattice chiral gauge theory. The construction may be viewed as a particular limit of an infinite warped 3-dimensional theory. We also present a "single-site'' construction using Ginsparg-Wilson fermions which may avoid, in both 2 and 4 dimensions, the problems of waveguide-Yukawa models.

Figures (5)

• Figure 1: The wave guide approach to a chiral gauge theory. Circles represent Weyl fermions. Solid lines represent mass terms and a charged scalar couples the charged fermion, $\bar{\psi}_{k+1,+}$, to the neutral fermion, $\psi_{k,-}$.
• Figure 2: The wavefunctions of the exponentially light modes before adding masses which couple the neutral and charged sectors. The right half is charged with the $l_-$ mode localized on the far right. The $n_+$ mode is localized on the far left. The two modes in the middle, $n_-$ and $l_+$ will pick up a mass though the Yukawa coupling with the Higgs on the wall.
• Figure 3: (Color online) Mass ratios of the light modes as a function of lattice size, $N$. The growing lines give $\left({m_{KK}\over m_{A 0}}\right)^2$, the ratio the KK modes' mass to that of the light gauge boson. The green (highest intercept) line is for the first gauge KK mode, while the red (middle intercept) line is for the first fermion KK mode. The falling (negative intercept) line gives the mass of the lightest fermion mode, $m_{f 0}$, by showing $2\ln{ m_{f 0} \over m_{A 0}}$. Clearly, there is an exponentially light fermion in the spectrum.
• Figure 4: A schematic representation of the location of all (exponentially light) modes which are needed for the 345 theory to have the correct anomaly properties. The right half is gauged; the left is neutral. After introducing the UV-brane mass terms from equations (\ref{['MequalsD']},\ref{['MequalsminusD']},\ref{['eq:ChargedNeutralCoupling']}), the only remaining light modes will be the $3_-$, $4_-$, and $5_+$ from the righthand side as well as one Weyl combination of the $n^1_+$ and $n^2_+$ from the lefthand side.
• Figure 5: The 2-dimensional model using GW fermions. The lines represent arbitrary ${\cal O}(1/a)$ masses of both Dirac and Majorana type. Due to the chiral symmetry present in the GW formulation, each fermion is exactly massless before an explicit mass term is added. Therefore, four modes remain massless: $n_+$, $3_-$, $5_+$, and $4_-$.