Renormalization group flow, stability, and bulk viscosity in a large N thermal QCD model

Abstract

The ultraviolet completion of a large N QCD model requires introducing new degrees of freedom at certain scale so that the UV behavior may become asymptotically conformal with no Landau poles and no UV divergences of Wilson loops. These UV degrees of freedom are represented by certain anti-branes arranged on the blown-up sphere of a warped resolved conifold in a way that they are separated from the other set of branes that control the IR behavior of the theory. This separation of the branes and the anti-branes creates instability in the theory. Further complications arise from the curvature of the ambient space. We show that, despite these analytical hurdles, stability may still be achieved by switching on appropriate world-volume fluxes on the branes. The UV degrees of freedom, on the other hand, modify the RG flow in the model. We discuss this in details by evaluating the flow from IR confining to UV conformal. Finally we lay down a calculational scheme to study bulk viscosity which, in turn, would signal the inherent non-conformality in this model.

Bulk viscosity at extreme limits: from kinetic theory to strings

“…For the present case we will work out the equation satisfied by p 0x as this is the only component relevant for bulk viscosity. This will be explained soon (see also [84]). In fact what is required is not p 0x , rather p 0x , and therefore we will work out the equation for Y x (r, |ω|) ≡ p 0x .…”

“…One may also get these coefficients directly from the rt EOM. We expect these two ways of getting these coefficients to match because in the absence of the sources i.e for the conformal case, the extra rt equation did not over-constrain the system [84]. Motivated by the above discussions, one may now give similar arguments for the five-form EOM, where the constraint equation takes the following form:…”

“…From the type IIB side, the UV CFT may be easily described by allowing additional M anti-D5-branes distributed on the northern hemisphere of the resolved sphere parametrized by (θ 1 , φ 1 ). These anti-D5-branes are stabilized against collapse by using fluxes, details of which have appeared in [59,84]. The string connecting the branes and the anti-branes are heavy, and they are integrated out at low energies.…”

“…In [84] we made some preliminary study of bulk viscosity using the UV complete large N thermal QCD model of [58] with N f = 0. The metric that we took in [84] is of the form:…”

“…where D 1 , D 2 and D 1 are constants that may be fixed from the boundary conditions. This has been discussed in details in [84], and after the dust settles, the functional form for P (r) and Q(r) can be explicitly represented in the following way:…”