In the context of gauge-gravity duality, we try to understand better the proposed duality between the fractional D2-brane supergravity solutions of Cvetič, Gibbons, Lü, and Pope [Nucl. Phys. $\mathbf{B}606\mathrm{},$ 18 (2001)] and a confining $\mathrm{}(2+1)\mathrm{}$-dimensional gauge theory. Based on the similarities between this fractional D2-brane solution and D3-brane supergravity solutions with more firmly established gauge theory duals, we conjecture that a confining q string in the $\mathrm{}(2+1)\mathrm{}$-dimensional gauge theory is dual to a wrapped D4-brane. In particular, the D4-brane looks like a string in the gauge theory directions but wraps an ${\mathbf{S}}^3\subset {\mathbf{S}}^4$ in the transverse geometry. For one of the supergravity solutions, we find a near quadratic scaling law for the tension: $T\sim q\left(N-q\right).\mathrm{}$ Based on the tension, we conjecture that the gauge theory dual is $\mathrm{SU}\left(N\right)\mathrm{}$ far in the infrared. We also conjecture that a quadratic or near quadratic scaling is a generic feature of confining $\mathrm{}(2+1)\mathrm{}$-dimensional $\mathrm{SU}\left(N\right)\mathrm{}$ gauge theories.

• Received 20 June 2002

DOI:https://doi.org/10.1103/PhysRevD.66.065009