Rotating D3-branes and QCD in three dimensions

TL;DR

This paper explores rotating D3-brane solutions to model non-supersymmetric 2+1 dimensional SU(N) Yang-Mills theories, calculating glueball and Kaluza-Klein masses, and analyzing parameter regimes for state decoupling.

Contribution

It introduces a three-parameter class of non-supersymmetric D3-brane geometries to model 3D Yang-Mills theories and derives analytic expressions for glueball and Kaluza-Klein masses.

Findings

Glueball masses calculated using WKB approximation.

Identification of parameter regions where Kaluza-Klein states decouple.

Discovery of states with masses comparable to glueballs and a global U(1)^3 symmetry.

Abstract

We investigate the rotating D3-brane solution with maximum number of angular momentum parameters. After determining the angular velocities, Hawking temperature, ADM mass and entropy, we use this geometry to construct general three-parameter models of non-supersymmetric pure SU(N) Yang-Mills theories in 2+1 dimensions. We calculate glueball masses in the WKB approximation and obtain closed analytic expressions for generic values of the parameters. We also determine the masses of Kaluza--Klein states associated with internal parts of the ten-dimensional metric and investigate the parameter region where some of these states are decoupled. To leading order in 1/\lambda and 1/N (where \lambda is the 't Hooft coupling) we find a global U(1)^3 symmetry and states with masses comparable to glueball masses, which have no counterpart in the more familiar (finite \lambda, N) Yang-Mills theories.