Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-03-28
Nucl.Phys.B809:452-518,2009
Physics
High Energy Physics
High Energy Physics - Theory
65 pages, 1 figure; v2: References added; v3: Definitions of moduli spaces clarified, references added; Final version to be pu
Scientific paper
10.1016/j.nuclphysb.2008.09.024
We study the relation between Donaldson-Thomas theory of Calabi-Yau threefolds and a six-dimensional topological Yang-Mills theory. Our main example is the topological U(N) gauge theory on flat space in its Coulomb branch. To evaluate its partition function we use equivariant localization techniques on its noncommutative deformation. As a result the gauge theory localizes on noncommutative instantons which can be classified in terms of N-coloured three-dimensional Young diagrams. We give to these noncommutative instantons a geometrical description in terms of certain stable framed coherent sheaves on projective space by using a higher-dimensional generalization of the ADHM formalism. From this formalism we construct a topological matrix quantum mechanics which computes an index of BPS states and provides an alternative approach to the six-dimensional gauge theory.
Cirafici Michele
Sinkovics Annamaria
Szabo Richard J.
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