5 research outputs found
Topology and chiral symmetry breaking in SU(N) gauge theories
We study the low-lying eigenmodes of the lattice overlap Dirac operator for
SU(N) gauge theories with N=2,3,4 and 5 colours. We define a fermionic
topological charge from the zero-modes of this operator and show that, as N
grows, any disagreement with the topological charge obtained by cooling the
fields, becomes rapidly less likely. By examining the fields where there is a
disagreement, we are able to show that the Dirac operator does not resolve
instantons below a critical size of about rho = 2.5 a, but resolves the larger,
more physical instantons. We investigate the local chirality of the near-zero
modes and how it changes as we go to larger N. We observe that the local
chirality of these modes, which is prominent for SU(2) and SU(3), becomes
rapidly weaker for larger N and is consistent with disappearing entirely in the
limit of N -> infinity. We find that this is not due to the observed
disappearance of small instantons at larger N.Comment: 41 pages, 12 figures, RevTe
Properties of the Fixed Point Lattice Dirac Operator in the Schwinger Model
We present a numerical study of the properties of the Fixed Point lattice
Dirac operator in the Schwinger model. We verify the theoretical bounds on the
spectrum, the existence of exact zero modes with definite chirality, and the
Index Theorem. We show by explicit computation that it is possible to find an
accurate approximation to the Fixed Point Dirac operator containing only very
local couplings.Comment: 38 pages, LaTeX, 3 figures, uses style [epsfig], a few comments and
relevant references adde
Topological structures in lattice gauge theory
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