Perturbative study for domain-wall fermions in 4+1 dimensions

Abstract

We investigate a U(1) chiral gauge model in 4+1 dimensions formulated on the lattice via the domain-wall method. We calculate an effective action for smooth background gauge fields at a fermion one loop level. From this calculation we discuss properties of the resulting 4 dimensional theory, such as gauge invariance of 2 point functions, gauge anomalies and an anomaly in the fermion number current.Comment: 39 pages incl. 9 figures, REVTeX+epsf, uuencoded Z-compressed .tar fil

Chiral gauge theory on the lattice with domain wall fermions

“…The explicit expressions for A and X(t) are obviously different from similar expressions given in [15][16][17] because of the differences in domain wall implementation as already discussed earlier.…”

“…with B(s) = F (p) + 1 = a 0 at s = 0, L s /2. It is to be noted that these boundary conditions are significantly different from the ones given in [15] because of the difference in implementation of the domain wall. G − 0,t and G + Ls/2,t (and the corresponding ones from G R ) are used to determine the free chiral propagators at the domain wall and anti-domain wall for comparison with numerical data in Fig.4.…”

“…With y = 1, S (0) F (ψ, ψ; y = 1) is the free domain wall action (2.1). Free fermion propagators at y = 1 are obtained in momentum space for 4-spacetime dimensions while staying in the coordinate space for the 5th dimension following [15] (results in [15][16][17] cannot be directly used because of difference in implementation of the domain wall (2.4)). The free action is written as,…”

Perturbative renormalization of the first moment of structure functions for domain-wall QCD

“…for the interaction of the quark current with one gluon and two gluons respectively, where p stands for the sum of the incoming and outgoing quark momenta. The construction of the tree-level quark propagator has been started in [2,19] and [20,21,22,23] and then completed and used in in the first full-fledged calculations of the renormalization of the quark self-energy and bilinears [18,24,25]. Further perturbative results for domain-wall fermions have been obtained in [26,27,28,29,30,31,32], and some perturbative calculations for nonstandard domain-wall actions have been carried out in [33].…”

The Anomaly Inflow of the domain-wall fermion in odd dimension

“…In fact the gauge anomaly should be cancelled even at a microscopic level. To understand the anomaly cancellation at the microscopic level, several studies of the exact effective action were carried out [11,12,13,14,15,16,17] in the infinite bulk mass limit. In this report, we readdress this issue in order to understand inflow mechanics further.…”