String Tensions and Three Dimensional Confining Gauge Theories

TL;DR

This paper explores the gauge/gravity duality for 2+1 dimensional confining gauge theories, proposing a duality between fractional D2-branes and wrapped D4-branes, and finds a quadratic scaling law for string tension.

Contribution

It conjectures a duality between fractional D2-branes and confining q-strings as wrapped D4-branes, and suggests quadratic tension scaling as a generic feature.

Findings

Quadratic scaling law for string tension: T ~ q(N-q).

Conjecture that the dual gauge theory is SU(N) in the infrared.

Proposal that quadratic tension scaling is common in 2+1D SU(N) confining theories.

Abstract

In the context of gauge/gravity duality, we try to understand better the proposed duality between the fractional D2-brane supergravity solutions of (Nucl. Phys. B 606 (2001) 18, hep-th/0101096) and a confining 2+1 dimensional gauge theory. Based on the similarities between this fractional D2-brane solution and D3-brane supergravity solutions with more firmly established gauge theory duals, we conjecture that a confining q-string in the 2+1 dimensional gauge theory is dual to a wrapped D4-brane. In particular, the D4-brane looks like a string in the gauge theory directions but wraps a S**3 in S**4 in the transverse geometry. For one of the supergravity solutions, we find a near quadratic scaling law for the tension: $T \sim q (N-q)$. Based on the tension, we conjecture that the gauge theory dual is SU(N) far in the infrared. We also conjecture that a quadratic or near quadratic scaling is a generic feature of confining 2+1 dimensional SU(N) gauge theories.