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VOL. 55 | 2009 Instanton counting and the chiral ring relations in supersymmetric gauge theories
Hiroaki Kanno

Editor(s) Jean-Pierre Bourguignon, Motoko Kotani, Yoshiaki Maeda, Nobuyuki Tose


We compute topological one-point functions of the chiral operator $\mathrm{Tr}\ \varphi^k$ in the maximally confining phase of $U(N)$ supersymmetric gauge theory. These chiral one-point functions are of particular interest from gauge/string theory correspondence, since they are related to the equivariant Gromov–Witten theory of $\mathbf{P}^1$. By considering the power sums of Jucys–Murphy elements in the class algebra of the symmetric group we can derive a combinatorial identity that leads the relations among chiral one-point functions. Using the operator formalism of free fermions, we also compute the vacuum expectation value of the loop operator $\langle \mathrm{Tr}\ e^{it\varphi}\rangle$ which gives the generating function of the one-point functions.


Published: 1 January 2009
First available in Project Euclid: 28 November 2018

zbMATH: 1206.05101
MathSciNet: MR2463490

Digital Object Identifier: 10.2969/aspm/05510051

Primary: 05E10, 81T45, 81T60

Rights: Copyright © 2009 Mathematical Society of Japan


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