Wilson loops from multicentre and rotating branes, mass gaps and phase structure in gauge theories

Abstract

Within the AdS/CFT correspondence we use multicentre D3-brane metrics to investigate Wilson loops and compute the associated heavy quark–antiquark potentials for the strongly coupled SU(N) super-Yang–Mills gauge theory, when the gauge symmetry is broken by the expectation values of the scalar fields. For the case of a uniform distribution of D3-branes over a disc, we find that there exists a maximum separation beyond which there is no force between the quark and the antiquark, i.e. the screening is complete. We associate this phenomenon with the possible existence of a mass gap in the strongly coupled gauge theory. In the finite-temperature case, when the corresponding supergravity solution is a rotating D3-brane solution, there is a class of potentials interpolating between a Coulombic and a confining behaviour. However, above a certain critical value of the mass parameter, the potentials exhibit a behaviour characteristic of statistical systems undergoing phase transitions. The physical path preserves the concavity property of the potential and minimizes the energy. Using the same rotating-brane solutions, we also compute spatial Wilson loops, associated with the quark–antiquark potential in models of three-dimensional gauge theories at zero temperature, with similar results.