Zero Modes and the Atiyah-Singer Index in Noncommutative Instantons
Abstract
We study the bosonic and fermionic zero modes in noncommutative instanton backgrounds based on the ADHM construction. In k instanton background in U(N) gauge theory, we show how to explicitly construct 4Nk (2Nk) bosonic (fermionic) zero modes in the adjoint representation and 2k (k) bosonic (fermionic) zero modes in the fundamental representation from the ADHM construction. The number of fermionic zero modes is also shown to be exactly equal to the Atiyah-Singer index of the Dirac operator in the noncommutative instanton background. We point out that (super)conformal zero modes in non-BPS instantons are affected by the noncommutativity. The role of Lorentz symmetry breaking by the noncommutativity is also briefly discussed to figure out the structure of U(1) instantons.
Keywords
Cite
@article{arxiv.hep-th/0205010,
title = {Zero Modes and the Atiyah-Singer Index in Noncommutative Instantons},
author = {Keun-Young Kim and Bum-Hoon Lee and Hyun Seok Yang},
journal= {arXiv preprint arXiv:hep-th/0205010},
year = {2009}
}
Comments
v3: 24 pages, Latex, corrected typos, references added, to appear in Phys. Rev. D