Finite temperature $0^{-+}$ glueball spectrum from non-susy D3 brane of Type IIB string theory

TL;DR

This paper computes the finite-temperature pseudo-scalar glueball spectrum in holographic QCD using non-susy D3 brane backgrounds, revealing temperature-dependent mass behavior consistent with deconfinement transition.

Contribution

It provides an analytical and numerical calculation of the $0^{-+}$ glueball masses at finite temperature from a holographic dual of QCD, incorporating WKB approximation methods.

Findings

Glueball masses decrease with temperature and vanish at the deconfinement point.

The deconfinement transition temperature is estimated at about 186 MeV.

Results align with recent lattice QCD findings.

Abstract

Here, we calculate the pseudo-scalar glueball mass at finite temperature from the holographic QCD in $3+1$ dimensions. The decoupled geometry of the non-supersymmetric (non-susy) D$3$ brane at the finite temperature which is the solution of the type-II supergravity is considered as the dual theory of QCD. We calculate the mass spectrum from the axion fluctuation in this gravity background using WKB approximations. Approximating the WKB equation for various orders of mass, we derive the analytical expressions of the mass spectrum of $0^{-+}$ at the finite temperature. Finally we evaluate the masses numerically as $m_{-+}=2.5$GeV and $m_{-+}^*=3.8$GeV from the complete WKB equation. The mass of a given state is found to decrease with increasing temperature and becomes zero at confinement -deconfinement transition temperature which is consistent with the idea of deconfinement and also matches with some recent lattice results. From this temperature variation, the QCD transition point is found to be about $186$MeV.