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

S.-J. Rey; J.-T. Yee

doi:doi:10.1007/s100520100799

2021 Impact factor 4.991

Particles and Fields

Eur. Phys. J. C 22, 379-394 (2001)
DOI: 10.1007/s100520100799

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

S.-J. Rey and J.-T. Yee

School of Physics & Center for Theoretical Physics, Seoul National University, Seoul 151-747, Korea

(Received: 21 September 2001 / Published online: 12 November 2001 - © Springer-Verlag / Società Italiana di Fisica 2001 )

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 ${\mathrm {AdS}}_5 \times S_5$ 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 AdS₅ spacetime geometry emerges out of four-dimensional gauge theory at strong coupling.