Remarks on the Heavy Quark Potential in the Supergravity Approach

Abstract

We point out certain unexpected features of the planar QCD3 confining potential, as computed from a classical worldsheet action in an AdS metric via the Maldacena conjecture. We show that there is no Luscher c/R term in the static-quark potential, which is contrary to both the prediction of various effective string models, and the results of some recent lattice Monte Carlo studies. It is also noted that the glueball masses extracted from classical supergravity tend to finite, coupling-independent constants in the strong coupling limit, even as the string tension tends to infinity in the same limit; this is a counter-intuitive result.

Figures (2)

• Figure 1: Heavy-quark potential determined from supergravity. At short distances $L<<1$, the potential is that of ${\cal N}=4$ super Yang-Mills theory in D=4 dimensions, while for $L>1$ it should match that of planar $QCD_3$ at strong coupling.
• Figure 2: Searching for a Lüscher term where there is no Lüscher term: Calculation of $c_{eff}$ in the heavy-quark potential obtained from supergravity.