A Ginsparg Wilson renormalisation group approach to lattice CP symmetry

Abstract

There is a long standing challenge in lattice QCD concerning the relationship between C Psymmetry and lattice chiral symmetry: naïvely the chiral symmetry transformations are not invariant under C P. With results similar to a recent work by Igarashi and Pawlowski, I show that this is because charge conjugation symmetry has been incorrectly realised on the lattice. The naive approach, to directly use the continuum charge conjugation relations on the lattice, fails because the renormalisation group blockings required to construct a doubler free lattice theory from the continuum are not invariant under charge conjugation. Correctly taking into account the transformation of these blockings leads to a modified lattice C P symmetry for the fermion fields, which, for gauge field configurations with trivial topology, has a smooth limit to continuum C P as the lattice spacing tends to zero. After constructing C P transformations for one particular group of lattice chiral symmetries, I construct a lattice chiral gauge theory which is C P invariant and whose measure is invariant under gauge transformations and C P.

Chiral Lattice Gauge Theories via Mirror–fermion Decoupling: A Mission (Im)possible?

“…Note that the above remarks refer to the continuum CP transformation: recently ref. 61 argued that in the trivial topological sector it is possible to define a lattice-modified version of CP, (which, like the modified chiral symmetry, reduces to the usual continuum CP-transform), under which the chiral action (26) (and measure) is invariant; see also 62,63 .…”