A numerical test of the continuum index theorem on the lattice

Details A numerical test of the continuum index theorem on the lattice A numerical test of the continuum index theorem on the lattice

1997-02-06

arxiv.org/abs/hep-lat/9702005v1

Nucl.Phys. B506 (1997) 373-386

Physics

High Energy Physics

High Energy Physics - Lattice

17 pages, 5 figures, plain TeX, uses epsf

Scientific paper

10.1016/S0550-3213(97)00544-0

The overlap formalism of chiral fermions provides a tool to measure the index, Q, of the chiral Dirac operator in a fixed gauge field background on the lattice. This enables a numerical measurement of the probability distribution, p(Q), in Yang-Mills theories. We have obtained an estimate for p(Q) in pure SU(2) gauge theory by measuring Q on 140 independent gauge field configurations generated on a 12^4 lattice using the standard single plaquette Wilson action at a coupling of beta=2.4. This distribution is in good agreement with a recent measurement [8] of the distribution of the topological charge on the same lattice using the same coupling and the same lattice gauge action. In particular we find =3.3(4) to be compared with = 3.9(5) found in [8]. The good agreement between the two distributions is an indication that the continuum index theorem can be carried over in a probabilistic sense on to the lattice.

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