Fuzzy bags, Polyakov loop and gauge/string duality

TL;DR

This paper investigates quadratic corrections in gauge theories' thermal quantities and Polyakov loop using gauge/string duality, highlighting their possible non-local bulk spacetime origins and relation to confinement.

Contribution

It systematically analyzes quadratic corrections in both confined and deconfined phases via gauge/string duality, emphasizing their non-local bulk spacetime origins and limitations of local dilaton models.

Findings

Quadratic corrections appear in deconfined phase lattice data.

Such corrections are consistent with global or non-local effects in the bulk.

Local dilaton models cannot generate these quadratic contributions.

Abstract

Confinement in SU($N$) gauge theory is due to the linear potential between colored objects. At short distances, the linear contribution could be considered as the quadratic correction to the leading Coulomb term. Recent lattice data show that such quadratic corrections also appear in the deconfined phase, in both the thermal quantities and the Polyakov loop. These contributions are studied systematically employing the gauge/string duality. "Confinement" in ${\mathcal N}=4$ SU($N$) Super Yang-Mills (SYM) theory could be achieved kinematically when the theory is defined on a compact space manifold. In the large-$N$ limit, deconfinement of ${\mathcal N}=4$ SYM on $\mathbb{S}^3$ at strong coupling is dual to the Hawking-Page phase transition in the global Anti-de Sitter spacetime. Meantime, all the thermal quantities and the Polyakov loop achieve significant quadratic contributions. Similar results can also be obtained at weak coupling. However, when confinement is induced dynamically through the local dilaton field in the gravity-dilaton system, these contributions can not be generated consistently. This is in accordance with the fact that there is no dimension-2 gauge-invariant operator in the boundary gauge theory. Based on these results, we suspect that quadratic corrections, and also confinement, should be due to global or non-local effects in the bulk spacetime.