Bulk dynamics in confining gauge theories

Abstract

We consider gauge/string duality (in the supergravity approximation) for confining gauge theories. The system under scrutiny is a 5-dimensional consistent truncation of type IIB supergravity obtained using the Papadopoulos-Tseytlin ansatz with boundary momentum added. We develop a gauge-invariant and sigma-modelcovariant approach to the dynamics of 5-dimensional bulk fluctuations. For the Maldacena-Nunez subsystem, we study glueball mass spectra. For the KlebanovStrassler subsystem, we compute the linearized equations of motion for the 7-scalar system, and show that a 3-scalar sector containing the scalar dual to the gluino bilinear decouples in the UV. We solve the fluctuation equations exactly in the "moderate UV" approximation and check this approximation numerically. Our results demonstrate the feasibility of analyzing the generally coupled equations for scalar bulk fluctuations, and constitute a step on the way towards computing correlators in confining gauge theories.

Large mass hierarchies from strongly-coupled dynamics

“…There exists a fully algorithmic procedure for computing glueball spectra, at leading order in the large-N and large 't Hooft coupling limits. It uses the action of a sigma-model coupled to gravity in five dimensions, that in the top-down approach may be obtained as a consistent truncation of the dimensional reduction of a more fundamental gravity theory in higher dimensions [61][62][63][64][65].…”

“…These techniques have been applied successfully to the dual of confining gauge theories, such as the Witten model [66][67][68], the Klebanov-Strassler model [61][62][63]69], the MaldacenaNunez model [61-63, 70, 71] and several generalisations, including cases in which the mass of the continuum massless theory. In this paper we collectively call lattice artefacts all effects that are not present in the continuum massless field theory, inclusive of finite volume, finite spacing and finite fermion mass effects.…”

“…We compute the spectrum of scalar and tensor fluctuations, that we interpret in terms of the glueballs of the (putative) dual field theory, by deriving the linearised equations of motions around the background solution, and by constructing explicitly gauge-invariant combinations of the fluctuations [61][62][63][64].…”

Multiscale confining dynamics from holographic RG flows

“…In order to proceed, it is convenient to use the gauge-invariant formalism developed in [107][108][109], and extended in [110] to the general case in which the σ-model does not admit a superpotential. We apply at r I and r U the boundary conditions discussed in [106], taking the special limit in which divergent boundary masses are added for all the σ-model scalars.…”

“…The crucial observation we start with is that the gauge-invariant variables a a are defined by [107][108][109]:…”