Effective holographic models for QCD: Glueball spectrum and trace anomaly

Abstract

We investigate effective holographic models for QCD arising from five dimensional Dilaton-Gravity. The models are characterized by a dilaton with a mass term in the UV, dual to a CFT deformation by a relevant operator, and quadratic in the IR. The UV constraint leads to the explicit breaking of conformal symmetry whereas the IR constraint guarantees linear confinement. We propose semi-analytic interpolations between the UV and the IR and obtain a spectrum for scalar and tensor glueballs consistent with lattice QCD data. We use the glueball spectrum as a physical constraint to find the evolution of the model parameters as the mass term goes to zero. Finally, we reproduce the universal result for the trace anomaly of deformed CFTs and propose a dictionary between this result and the QCD trace anomaly. A nontrivial consequence of this dictionary is the emergence of a β function similar to the two-loop perturbative QCD result.

Conformal symmetry breaking in holographic QCD

“…Additionally, = ∆ − is related to the mass of the dilaton field through the relation M 2 Φ 2 = ( − 4) [24], where represents the AdS radius and M Φ the mass of the dilaton. The profile of the dilaton close to the boundary (6) guarantees the correct asymptotic behavior, in agreement with what is expected from the scalar operator O coupled to the source (for a discussion see for instance [40], see also [36]). On the other hand, in the deep IR region, the profile of the dilaton field guarantees confinement, because it satisfies the general criteria investigated in Ref.…”

“…The picture of the five-dimensional action (1) in the dual field theory was previously investigated in Refs. [37,38] (see also [36]). In the extreme UV, which is equivalent to be at the boundary in the bulk theory, the field theory has conformal symmetry when the dimension of the operator O is ∆ + = 4 (marginal operator).…”

“…For our convenience, the authors of Ref. [36] obtained the onepoint correlation functions using a minimal subtraction scheme, thus, the VEV of the scalar operator reads as…”

Melting of scalar mesons and black-hole quasinormal modes in a holographic QCD model

“…We now turn attention to the dilaton field Φ(z) and consider a functional dependency on z that is consistent with some aspects of QCD, namely, Φ(z) ∼ z 4 in the UV (to describe correctly the gluon condensate) [9], and Φ(z) ∼ z 2 in the IR (to guarantee confinement) [12]. To smoothly connect these regimes, we use an interpolation function in the form [27]…”

“…Hence, the solution that guarantees convergence of the wave function in this region is given by [27]…”