Fujii, Shigeyuki; Kanno, Hiroaki; Moriyama, Sanefumi; Okada, Soichi Instanton calculus and chiral one-point functions in supersymmetric gauge theories. (English) Zbl 1151.81359 Adv. Theor. Math. Phys. 12, No. 6, 1401-1428 (2008). Summary: We compute topological one-point functions of the chiral operator \(\text{Tr\,} \varphi^k\) 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 \(\mathbb{P}^1\). 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 \(\text{Tr}\, e^{it\varphi}\). Cited in 11 Documents MSC: 81T13 Yang-Mills and other gauge theories in quantum field theory 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81T60 Supersymmetric field theories in quantum mechanics 14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) PDFBibTeX XMLCite \textit{S. Fujii} et al., Adv. Theor. Math. Phys. 12, No. 6, 1401--1428 (2008; Zbl 1151.81359) Full Text: DOI arXiv Euclid