Evaluation of glueball masses from supergravity

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.

The Pomeron and gauge/string duality

“…(3.5) 14 In order to keep equations uncluttered, we adopt simple overall normalizations in Eqs. (3.1), (3.6), but keep all later equations normalized with respect to these.…”

“…A better model would have a smooth minimum. For example, consider the variant 14) combined with an orbifolding u → −u. The potential has been designed to have the same large-u behavior and the same minimum as before.…”

“…The relevant tensor glueball state was first studied in [9,10,11] from an AdS/CFT duality perspective. For first attempts at calculating glueball masses using AdS/CFT, following work of [12], see [13,14].…”

A brief review of glueball masses from gauge/gravity duality

“…This study was pioneered by [9] and afterwards the spectrum was completed in [10]- [13]. As mentioned in the previous section, the computation of correlation functions amounts -using the gauge/gravity duality-to solving field equations for the corresponding fluctuation in the AdS background.…”

“…The spectrum is found to be discrete and exhibits a mass gap. In [9], [10] the authors found that the mass of the 0 ++ and its excited states is given by, …”