Spectrum of large N glueballs: holography vs lattice

Abstract

Recently there has been a notable progress in the study of glueball states in lattice gauge theories, in particular extrapolating their spectrum to the limit of large number of colors N. In this note we compare the large N lattice results with the holographic predictions, focusing on the Klebanov-Strassler model, which describes a gauge theory with $$ \mathcal{N} $$ N = 1 supersymmetry. We note that glueball spectrum demonstrates approximate universality across a range of gauge theory models. Because of this universality the holographic models can give reliable predictions for the spectrum of pure SU(N) Yang-Mills theories with and without supersymmetry. This is especially important for the supersymmetric theories, for which no firm lattice predictions exist yet, and the holographic models remain the most tractable approach. For SU(N) theories with large N the lattice non-supersymmetric and holographic supersymmetric predictions for the mass ratios of the lightest states in various sectors agree up to 5–8%, supporting the proposed universality. In particular, both lattice and holography give predictions for the 2++ and 1−− mass ratio, consistent with the known constraints on the pomeron and odderon Regge trajectories.

Phases of a 10-D holographic hard wall model

“…The graviton field is related to a spin two color-neutral operator in the boundary theory and by the spectral theorem, the two point function of such an operator will have a pole at the mass of the lightest particle state that can be created by such an operator. This was studied by [54] in a recent paper where the author attempted to fit the known glueball spectrum to hardwall AdS computations in five dimensions (a recent review comparing holographic results to lattice can be found in [62]). Using linearized Einstein's equations in thermal AdS, the author fit the computed glueball masses to lattice data which fixed the IR-cutoff z g in physical units.…”