The Overlap - Dirac Operator : Topology and Chiral Symmetry Breaking
نویسندگان
چکیده
In these proceedings, we review some basic properties of the overlap Dirac operator and how its index can be computed by spectral flow techniques. One of the side results is that for fermions in the adjoint representation of SU(N) we find evidence for fractional topological charge. The presentation is pedagogical with the intent of illustrating the origin of numerical difficulties in simulating overlap and domain wall fermions. Recent results from our work using overlap fermions can be found in references [1, 2, 3, 4]. The massive overlap Dirac operator derived from the overlap formalism [5] is
منابع مشابه
Topology and Chiral Symmetry in Qcd with Overlap Fermions Fsu-scri-99c-72 Jlab-thy-99-41
We briefly review1 the overlap formalism for chiral gauge theories, the overlap Dirac operator for massless fermions and its connection to domain wall fermions. We describe properties of the overlap Dirac operator, and methods to implement it numerically. Finally, we give some examples of quenched calculations of chiral symmetry breaking and topology with overlap fermions. 1. Overlap formula fo...
متن کاملar X iv : h ep - l at / 0 30 90 11 v 1 3 S ep 2 00 3 1 Chiral symmetry breaking and topology for all
We investigate spontaneous chiral symmetry breaking in SU(N) gauge theories at large N using overlap fermions. The exact zero modes and the low-lying modes of the Dirac operator provide the tools to gain insight into the interplay between chiral symmetry breaking and topology. We find that topology indeed drives chiral symmetry breaking at N = 3 as well as at large N. By comparing the results o...
متن کاملUnderstanding chiral symmetry breaking with the overlap action
A chiral fermion action allows one to do very clean studies of chiral symmetry breaking in QCD. I will briefly describe how to compute with the overlap action (relatively) cheaply, and then turn to physics: Low modes of the Dirac operator show a “lumped” chiral density which peaks at the locations of instantons and anti-instantons. These modes dominate correlation functions at small quark mass ...
متن کاملLow energy effective action of domain-wall fermion and the Ginsparg-Wilson relation
We derive the effective action of the light fermion field of the domain-wall fermion, which is referred as q(x) by Furman and Shamir. The inverse of the effective Dirac operator turns out to be identical to the inverse of the truncated overlap Dirac operator, except a local contact term which would give the chiral symmetry breaking in the Ginsparg-Wilson relation. This result allows us to relat...
متن کاملLow-lying Dirac Eigenmodes, Topological Charge Fluctuations and the Instanton Liquid Model
The local structure of low-lying eigenmodes of the overlap Dirac operator is studied. It is found that these modes cannot be described as linear combinations of ’t Hooft “would-be” zeromodes associated with instanton excitations that underly the Instanton Liquid Model. This implies that the instanton liquid scenario for spontaneous chiral symmetry breaking in QCD is not accurate. More generally...
متن کامل