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

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) D3 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−+ = 2.5GeV and m * −+ = 3.8GeV 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 186MeV.

Confinement and Pseudoscalar Glueball Spectrum from Anisotropic Non-susy D$2$ Brane under Hawking-Page transition

“…The masses have been found to maintain almost a constant value up to (−δ) 1/5 ≈ 0.7 and shown an abrupt variation as it goes very close to the transition point (−δ) 1/5 ≈ 1. These are similar to the study of the anisotropic nonsusy D3 brane [40] where the same has been studied in 3 + 1 dimensional QCD-like theory. Therefore, from the holographic study of the 2 + 1 dimensional QCD-like theory under the deconfinement transition, we can have two important observations as follow.…”

“…Also the gravity background asymptotically reduces to the form AdS 4 ×S 6 . Therefore, following the Hawking-Page transition of the non-susy anisotropic D3 brane [40], we can assume an empirical definition of the temperature as…”

“…At a particular value of this anisotropy parameter, the anisotropic non-susy D2 brane reduces to the black D2 brane. Therefore varying that parameter we get the Hawking-Page transition and that parameter can be related to a temperature like quantity in the gauge theory [40]. Like the isotropic non-susy brane, other parameters of the gravity theory are related to the gluon condensate and the fixed mass scale of the corresponding gauge theory [4,29].…”

“…The complicated form of the potential (29) makes it harder to solve the WKB equation ( 30) analytically. However, following [40], one can find some analytical expressions of m or ω by using the Taylor series expansion of the integrand in (30) assuming large ω. Otherwise m can be solved using numerical technique, which is going to be used in this article.…”