## Advances in Theoretical and Mathematical Physics

- Adv. Theor. Math. Phys.
- Volume 13, Number 6 (2009), 1941-1981.

### Quantum 't Hooft operators and $S$-duality in $N=4$ super Yang-Mills

Jaume Gomis, Takuya Okuda, and Diego Trancanelli

#### Abstract

We provide a quantum path integral definition of an ’t Hooft loop operator, which inserts a point-like monopole in a four-dimensional gauge theory. We explicitly compute the expectation value of the circular ’t Hooft operators in $N = 4$ super Yang–Mills with arbitrary gauge group $G$ up to next to leading order in perturbation theory. We also compute in the strong coupling expansion the expectation value of the circular Wilson loop operators. The result of the computation of an ’t Hooft loop operator in the weak coupling expansion exactly reproduces the strong coupling result of the conjectured dual Wilson loop operator under the action of $S$-duality. This paper demonstrates — for the first time — that correlation functions in $N = 4$ super Yang–Mills admit the action of $S$-duality.

#### Article information

**Source**

Adv. Theor. Math. Phys., Volume 13, Number 6 (2009), 1941-1981.

**Dates**

First available in Project Euclid: 17 August 2010

**Permanent link to this document**

https://projecteuclid.org/euclid.atmp/1282054381

**Mathematical Reviews number (MathSciNet)**

MR2679001

**Zentralblatt MATH identifier**

1200.81109

#### Citation

Gomis, Jaume; Okuda, Takuya; Trancanelli, Diego. Quantum 't Hooft operators and $S$-duality in $N=4$ super Yang-Mills. Adv. Theor. Math. Phys. 13 (2009), no. 6, 1941--1981. https://projecteuclid.org/euclid.atmp/1282054381