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2008•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsOpen access

Wilson loops: From 4D supersymmetric Yang-Mills theory to 2D Yang-Mills theory

Nadav Drukker, Simone Giombi, Riccardo Ricci, Diego Trancanelli

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Abstract

In this paper we study supersymmetric Wilson loops restricted to an ${S}^{2}$ submanifold of four-dimensional space in $\mathcal{N}=4$ super Yang-Mills theory. We provide evidence from both perturbation theory and the AdS dual that those loops are equal to the analogous observables in two-dimensional Yang-Mills on ${S}^{2}$ (excluding nonperturbative contributions). This relates a subsector of $\mathcal{N}=4$ SYM to a low-dimensional soluble model and also suggests that this subsector of $\mathcal{N}=4$ SYM is invariant under area preserving diffeomorphisms.

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In this paper we study supersymmetric Wilson loops restricted to an ${S}^{2}$ submanifold of four-dimensional space in $\mathcal{N}=4$ super Yang-Mills theory. We provide evidence from both perturbation theory and the AdS dual that those loops are equal to the analogous observables in two-dimensional Yang-Mills on ${S}^{2}$ (excluding nonperturbative contributions). This relates a subsector of $\mathcal{N}=4$ SYM to a low-dimensional soluble model and also suggests that this subsector of $\mathcal{N}=4$ SYM is invariant under area preserving diffeomorphisms.

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Available abstract

In this paper we study supersymmetric Wilson loops restricted to an ${S}^{2}$ submanifold of four-dimensional space in $\mathcal{N}=4$ super Yang-Mills theory. We provide evidence from both perturbation theory and the AdS dual that those loops are equal to the analogous observables in two-dimensional Yang-Mills on ${S}^{2}$ (excluding nonperturbative contributions). This relates a subsector of $\mathcal{N}=4$ SYM to a low-dimensional soluble model and also suggests that this subsector of $\mathcal{N}=4$ SYM is invariant under area preserving diffeomorphisms.

Key concepts: Yang–Mills existence and mass gap, Yang–Mills theory, Submanifold, Mathematical physics, Physics, Observable, Wilson loop, Perturbation theory (quantum mechanics)

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