Instanton calculus and chiral one-point functions in supersymmetric gauge theories

Details Instanton calculus and chiral one-point functions in supersymmetric gauge theories Instanton calculus and chiral one-point functions in supersymmetric gauge theories

2007-02-16

arxiv.org/abs/hep-th/0702125v4

Adv.Theor.Math.Phys.12:1401-1428,2008

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, no figure; (v2) substantially revised: a few mistakes corrected, a new result (section 6) and references added; (v3)

Scientific paper

We compute topological one-point functions of the chiral operator Tr \phi^k in the maximally confining phase of U(N) supersymmetric gauge theory. These one-point functions are polynomials in the equivariant parameter \hbar and the parameter of instanton expansion q=\Lambda^{2N} and are of particular interest from gauge/string theory correspondence, since they are related to the Gromov-Witten theory of P^1. Based on a combinatorial identity that gives summation formula over Young diagrams of relevant functions, we find a relation among chiral one-point functions, which recursively determines the \hbar expansion of the generating function of one-point functions. Using a result from the operator formalism of the Gromov-Witten theory, we also present a vacuum expectation value of the loop operator Tr e^{it\phi}.

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