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

TL;DR

The paper probes Maldacena's AdS/CFT framework by modeling heavy quarks as macroscopic strings ending on D3-branes, comparing bulk AdS5×S5 supergravity with D3-brane Born-Infeld dynamics. It derives boundary conditions from both perspectives, analyzes BPS and non-BPS quark–antiquark configurations, and computes static inter-quark potentials that reveal nonanalytic, square-root dependence on the 't Hooft coupling. A central theme is the geometric UV-IR duality linking directions parallel and perpendicular to the D3-brane, which helps explain how AdS5 geometry emerges at strong coupling. The work also explores θ-dependence, Wilson-loop dynamics, multi-prong string junctions, and finite-temperature extensions, offering a broad holographic portrait of heavy-quark physics at large N.

Abstract

We study some aspects of Maldacena's large $N$ correspondence between N=4 superconformal gauge theory on D3-brane and maximal supergravity on AdS_5xS_5 by introducing macroscopic strings as heavy (anti)-quark probes. The macroscopic strings are semi-infinite Type IIB strings ending on D3-brane world-volume. We first study deformation and fluctuation of D3-brane when a macroscopic BPS string is attached. We find that both dynamics and boundary conditions agree with those for macroscopic string in anti-de Sitter supergravity. As by-product we clarify how Polchinski's Dirichlet / Neumann open string boundary conditions arise dynamically. We then study non-BPS macroscopic string anti-string pair configuration as physical realization of heavy quark Wilson loop. We obtain quark-antiquark static potential from the supergravity side and find that the potential exhibits nonanalyticity of square-root branch cut in `t Hooft coupling parameter. We put forward the nonanalyticity as prediction for large-N gauge theory at strong `t Hooft coupling limit. By turning on Ramond-Ramond zero-form potential, we also study theta-vacuum angle dependence of the static potential. We finally discuss possible dynamical realization of heavy N-prong string junction and of large-N loop equation via local electric field and string recoil thereof. Throughout comparisons of the AdS-CFT correspondence, we find crucial role played by `geometric duality' between UV and IR scales on directions perpendicular to D3-brane and parallel ones, explaining how AdS5 spacetime geometry emerges out of four-dimensional gauge theory at strong coupling.

Figures (6)

• Figure 1: Macroscopic string as a BPS soliton on D3-brane worldvolume. Large-N corrections induced by branes at $U = 0$ in general gives rise to corrections to the shape and low-energy dynamics of the D3-brane.
• Figure 2: Non-BPS configuration of string anti-string pair as realization of heavy quark anti-quark pair. String corrections smooth out curvature at the two sharp corners.
• Figure 3: Heavy $(Q \overline{Q})$ realization via deformation of D3-brane world-volume. Highly non-BPS configuration (a) corresponds to two throats located at the same point on $\Omega_5$. For BPS configuration (b), two throats are at anti-podal points on $\Omega_5$. By continuous rotation on $\Omega_5$, (b) can be turned into (a) and vice versa.
• Figure 4: Non-BPS configuration of quark anti-quark pair on D-string.
• Figure 5: Conformal transformation cause local recoil of timelike loop. Back tracking at large $N$ is equivalent to pair creation process.