Rotating D3-branes and QCD in three dimensions

TL;DR

This work builds non-supersymmetric 2+1D SU(N) Yang–Mills models from a rotating D3-brane background with three angular momenta, deriving the geometry, thermodynamics, and field-theory limit. A unified WKB framework is developed to compute glueball and KK spectra, yielding analytic mass formulas that depend universally on two scales: ξ and TH. The results show that KK modes along the circle do not decouple in the supergravity regime, while sphere KK modes also remain non-decoupled, exposing qualitative differences from finite‑λ, finite‑N YM theories. The analysis highlights a residual U(1)^3 global symmetry and provides insight into how strong-coupling holographic models can approximate QCD-like spectra, with potential corrections as one moves toward weak coupling.

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/λand 1/N (where λis 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 λ, N) Yang-Mills theories.