Evaluation Of Glueball Masses From Supergravity

TL;DR

The work addresses nonperturbative glueball spectra in large $N$ gauge theories by leveraging Witten’s finite‑temperature AdS black hole framework. It formulates a scalar eigenvalue problem in AdS backgrounds, deriving exact expansions near the horizon and at infinity, and shows that enforcing horizon regularity together with normalizability yields a discrete, horizon‑consistent spectrum; Neumann horizon boundary conditions are ruled out for smooth solutions. The leading dilaton fluctuation yields $m_0^{2}$ eigenvalues for $O^{++}$ in $QCD_3$ and $QCD_4$, and for $O^{--}$ in $QCD_3$, with string corrections $m_1^{2}$ agreeing with prior results. The approach confirms consistency with COOT lattice results and Csaki et al., providing high‑precision glueball masses and clarifying the critical role of horizon boundary conditions in holographic mass spectra.

Abstract

In the framework of the conjectured duality relation between large $N$ gauge theory and supergravity the spectra of masses in large $N$ gauge theory can be determined by solving certain eigenvalue problems in supergravity. In this paper we study the eigenmass problem given by Witten as a possible approximation for masses in QCD without supersymmetry. We place a particular emphasis on the treatment of the horizon and related boundary conditions. We construct exact expressions for the analytic expansions of the wave functions both at the horizon and at infinity and show that requiring smoothness at the horizon and normalizability gives a well defined eigenvalue problem. We show for example that there are no smooth solutions with vanishing derivative at the horizon. The mass eigenvalues up to $m^{2}=1000$ corresponding to smooth normalizable wave functions are presented. We comment on the relation of our work with the results found in a recent paper by Csáki et al., hep-th/9806021, which addresses the same problem.

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