Multi-Instantons, Three-Dimensional Gauge Theory, and the Gauss-Bonnet-Chern Theorem
arXiv:hep-th/9704197 · doi:10.1016/S0550-3213(97)00455-0
Abstract
We calculate multi-instanton effects in a three-dimensional gauge theory with N=8 supersymmetry and gauge group SU(2). The k-instanton contribution to an eight-fermion correlator is found to be proportional to the Gauss-Bonnet-Chern integral of the Gaussian curvature over the centered moduli-space of charge-k BPS monopoles, \tilde{M}_{k}. For k=2 the integral can be evaluated using the explicit metric on \tilde{M}_{2} found by Atiyah and Hitchin. In this case the integral is equal to the Euler character of the manifold. More generally the integral is the volume contribution to the index of the Euler operator on \tilde{M}_{k}, which may differ from the Euler character by a boundary term. We conjecture that the boundary terms vanish and evaluate the multi-instanton contributions using recent results for the cohomology of \tilde{M}_{k}. We comment briefly on the implications of our result for a recently proposed test of M(atrix) theory.
13 pages, LaTeX
References in corpus (7)
- Type IIB Superstrings, BPS Monopoles, And Three-Dimensional Gauge Dynamics
- Mirror Symmetry in Three-Dimensional Gauge Theories, SL(2,Z) and D-Brane Moduli Spaces
- Dynamics of N=2 Supersymmetric Gauge Theories in Three Dimensions
- Branes and Mirror Symmetry in N=2 Supersymmetric Gauge Theories in Three Dimensions
- Instantons, Three-Dimensional Gauge Theory, and the Atiyah-Hitchin Manifold
- Membrane Scattering with M-Momentum Transfer
- On Mass-Deformed N=4 Supersymmetric Yang-Mills Theory
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