Multiinstantons, threedimensional gauge theory, and the GaussBonnetChern theorem
Abstract
We calculate multiinstanton effects in a threedimensional gauge theory with N = 8 supersymmetry and gauge group SU(2). The kinstanton contribution to an eightfermion correlator is found to be proportional to the GaussBonnetChem integral of the Gaussian curvature over the centered moduli space of charge k BPS monopoles, M¯ _{k}. For k = 2 the integral can be evaluated using the explicit metric on 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 M¯ _{k} which may differ from the Euler character by a boundary term. We conjecture that the boundary terms vanish and evaluate the multiinstanton contributions using recent results for the cohomology of M¯ _{k} We comment briefly on the implications of our result for a recently proposed test of M(atrix) theory.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1997
 DOI:
 10.1016/S05503213(97)004550
 arXiv:
 arXiv:hepth/9704197
 Bibcode:
 1997NuPhB.502...94D
 Keywords:

 High Energy Physics  Theory
 EPrint:
 13 pages, LaTeX