A conjectured duality between supergravity and N=infinity gauge theories gives predictions for the glueball masses as eigenvalues for a supergravity wave equations in a black hole geometry, and describes a physics, most close to a high-temperature expansion of a lattice QCD. We present an analytical solution for eigenvalues and eigenfunctions, with eigenvalues given by zeroes of a certain well-computable function r(p), the zeroes of which signifies that two solutions with desired behaviour at two singular points become Linearly dependent. Our computation shows corrections to the WKB formula m(2) = 6n(n + 1) for eigenvalues corresponding to glueball masses in 3 dimensional QCD, and gives the first states with masses m(2) = 11.58766; 34.52698; 68.974962; 114.91044; 172.33171; 241.236607; 321.626549,.... In QCD(4), our computation gives squares of masses 37.169908; 81.354363; 138.473573; 208.859215; 292.583628; 389.671368 500.132850, 623.97315 ... for O + +. In both cases, we have a powerful method which allows to compute eigenvalues with an arbitrary precision, if so needed, which may provide quantitative tests for the duality conjecture. Our results matches well with the numerical computation of [3] with in precision reported there in both QCD(3) and QCD(4) cases. As an additional curiosity, we report that for eigenvalues of about 7000, the power series, although convergent, has coefficients of orders 10(34); and also the final answer gets small, of order 10(-6) in QCD(4). Tricks were used to get reliably the function r(p) above 7000. In principle we can go to infinitely high eigenvalues at an expense of computer sufferings; although eventually such computation will slow down to make it impractical, also as corrections may be expected for higher states, since fine cancellations of Very big terms is what produces higher eigenvalues. (C) 1998 Elsevier Science B.V. All rights reserved.
