## Advanced Studies in Pure Mathematics

### Instanton counting and the chiral ring relations in supersymmetric gauge theories

Hiroaki Kanno

#### Abstract

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.

#### Article information

Dates
First available in Project Euclid: 28 November 2018

https://projecteuclid.org/ euclid.aspm/1543447901

Digital Object Identifier
doi:10.2969/aspm/05510051

Mathematical Reviews number (MathSciNet)
MR2463490

Zentralblatt MATH identifier
1206.05101

#### Citation

Kanno, Hiroaki. Instanton counting and the chiral ring relations in supersymmetric gauge theories. Noncommutativity and Singularities: Proceedings of French–Japanese symposia held at IHÉS in 2006, 51--67, Mathematical Society of Japan, Tokyo, Japan, 2009. doi:10.2969/aspm/05510051. https://projecteuclid.org/euclid.aspm/1543447901