Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity

Abstract.

We study some aspects of Maldacena's large-N correspondence between ${\cal N}=4$ superconformal gauge theory on the D3-brane and maximal supergravity on AdS$_5 \times S_5$ by introducing macroscopic strings as heavy (anti-) quark probes. The macroscopic strings are semi-infinite Type IIB strings ending on a D3-brane world-volume. We first study deformation and fluctuation of D3-branes when a macroscopic BPS string is attached. We find that both dynamics and boundary conditions agree with those for the macroscopic string in anti-de Sitter supergravity. As a by-product we clarify how Polchinski's Dirichlet and Neumann open string boundary conditions arise dynamically. We then study the non-BPS macroscopic string–anti-string pair configuration as a physical realization of a heavy quark Wilson loop. We obtain the $Q \bar Q$ static potential from the supergravity side and find that the potential exhibits non-analyticity of the square-root branch cut in the 't Hooft coupling parameter. We put forward non-analyticity as a prediction for large-N gauge theory in the strong 't Hooft coupling limit. By turning on the Ramond–Ramond zero-form potential, we also study the $\theta$ vacuum angle dependence of the static potential. We finally discuss the possible dynamical realization of the heavy N-prong string junction and of the large-N loop equation via a local electric field and string recoil thereof. Throughout comparisons of the AdS–CFT correspondence, we find that a crucial role is played by “geometric duality” between the UV and IR scales in directions perpendicular to the D3-brane and parallel ones, explaining how the AdS$_5$ spacetime geometry emerges out of four-dimensional gauge theory at strong coupling.