Effective long distance $q\bar{q}$ potential in holographic RG flows

Abstract

We study the $q\bar{q}$ potential in strongly coupled non-conformal field theories with a non-trivial renormalization group flow via holography. We focus on the properties of this potential at an inter-quark separation $L$ large compared to the characteristic scale of the field theory. These are determined by the leading order IR physics plus a series of corrections, sensitive to the properties of the RG-flow. To determine those corrections, we propose a general method applying holographic Wilsonian renormalization to a dual string. We apply this method to examine in detail two sets of examples, $3+1$-dimensional theories with an RG flow ending in an IR fixed point; and theories that are confining in the IR, in particular, the Witten QCD and Klebanov-Strassler models. In both cases, we find corrections with a universal dependence on the inter-quark separation. When there is an IR fixed point, that correction decays as a power $\sim 1/L^4$. We explain that dependence in terms of a double-trace deformation in a one-dimensional defect theory. For a confining theory, the decay is exponential $\sim e^{-ML}$, with $M$ a scale of the order of the glueball mass. We interpret this correction using an effective flux tube description as produced by a background internal mode excitation induced by sources localized at the endpoints of the flux tube. We discuss how these results could be confronted with lattice QCD data to test whether the description of confinement via the gauge/gravity is qualitatively correct.

34 pages, 1 figure, new appendix with RG flow equation for the action and next order correction, references added, published version

References in corpus (16)

• Nonlinear Fluid Dynamics from Gravity
• Effective Holographic Theories for low-temperature condensed matter systems
• Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm
• Hidden supersymmetry of domain walls and cosmologies
• Effective String Theory Revisited
• Deconstructing holographic liquids
• Corrections to Nambu-Goto energy levels from the effective string action
• Closed flux tubes and their string description in D=3+1 SU(N) gauge theories
• On the effective theory of long open strings
• Flux Tube Spectra from Approximate Integrability at Low Energies
• Fluctuating Heavy Quark Energy Loss in Strongly-Coupled Quark-Gluon Plasma
• A different kind of string
• Probing boundary-corrections to Nambu-Goto open string energy levels in 3d SU(2) gauge theory
• Effective string theory and the long-range relativistic corrections to the quark-antiquark potential
• Dirichlet sigma models and mean curvature flow
• Spectrum of the open QCD flux tube and its effective string description I: 3d static potential in SU(N=2,3)

Cited by in corpus (1)

• Holographic RG flow and reparametrization invariance of Wilson Loops