Nonperturbative Regulator for Chiral Gauge Theories?

Abstract

We propose a nonperturbative gauge invariant regulator for d-dimensional chiral gauge theories on the lattice. The method involves simulating domain wall fermions in d + 1 dimensions with quantum gauge fields that reside on one d-dimensional surface and are extended into the bulk via gradient flow. The result is a theory of gauged fermions plus mirror fermions, where the mirror fermions couple to the gauge fields via a form factor that becomes exponentially soft with the separation between domain walls. The resultant theory has a local d-dimensional interpretation only if the chiral fermion representation is anomaly free. A physical realization of this construction would imply the existence of mirror fermions in the standard model that are invisible except for interactions induced by vacuum topology, and which could gravitate differently than conventional matter.

One-loop perturbative coupling of A and A★ through the chiral overlap operator

“…Recently, Grabowska and Kaplan proposed a four-dimensional lattice formulation of chiral gauge theories [1]. This formulation is based on the so-called overlap operator, which can be obtained from their five-dimensional domain-wall formulation [2] 1 by the traditional way [4][5][6]. In this formulation, along the fifth dimension, the original gauge field A is deformed by the gradient flow [7][8][9][10] for infinite flow time.…”

On the infinite gradient-flow for the domain-wall formulation of chiral lattice gauge theories

“…In this section, we first review briefly the construction of U(1) chiral lattice gauge theories with exact gauge invariance based on the overlap Dirac operator/the Ginsparg-Wilson relation [13], and its implementation based on the domain wall fermion [21]. 1 We do not consider here the so-called chiral solution of the Ginsparg-Wilson relation [2] and the related issues [10][11][12]. As far as the authors understand, the chiral solution is derived by a wrong use of the subtraction scheme which is applicable only to vector-like theories, where the sizable direct coupling among the target wall with U (x, µ) and the mirror wall with U (x, µ) is introduced by the use of the Pauli-Villars spinor-boson with the anti-periodic boundary condition.…”

“…We now implement the original proposal by Grabowska and Kaplan [1,3] by using the domain wall fermion defined in the interval x 5 ∈ [−N, N + 1] of the extra fifth dimension (Shamir's version). We can define the effective action in the formulation of Grabowska and Kaplan as…”

“…In this paper, we examine the proposal by Grabowska and Kaplan (GK) to use the (infinite) gradient flow in the domain-wall formulation of chiral lattice gauge theories. 1 We consider the case of Abelian theories in detail, for which an exact gauge-invariant formulation has been obtained [13] based on the Ginsparg-Wilson relation [14,15]/the overlap Dirac operator [16][17][18][19][20] and its relation to domain wall formulation has been clarified [21]. Based on these known results, we relate GK's formulation to the exact gauge-invariant one and examine the locality property of the former in relation to the latter.…”

A calculation of the gauge anomaly with the chiral overlap operator

“…Moreover, as shown in the two-dimensional U(1) gauge theory in Refs. [1,7], the gauge field is expected to be evolved into a pure gauge so that the right-handed fermion on the other domain wall does not interact with the physical degrees of freedom of the gauge field. Thus we expect that the (2n + 1)-dimensional domain-wall fermion with the gauge field evolved by the gradient flow results in a 2n-dimensional effective theory in which only the left-handed fermion couples to the physical degrees of freedom of the gauge field.…”