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arXiv · hep-lat/9702005

A numerical test of the continuum index theorem on the lattice

Rajamani Narayanan·Pavlos Vranas
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Abstract

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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Rajamani Narayanan, Pavlos Vranas. 1997-02-06. A numerical test of the continuum index theorem on the lattice. https://doi.org/10.1016/s0550-3213(97)00544-0

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