Holographic observables at large d

Abstract

We study holographically nonlocal observables in field theories at finite temperature and in the large d limit. These include the Wilson loop, the entanglement entropy, as well as an extension to various dual extremal surfaces of arbitrary codimension. The large d limit creates a localized potential in the near horizon regime resulting in a simplification of the analysis for the nonlocal observables, while at the same time retaining their qualitative physical properties. Moreover, we study the monotonicity of the coefficient α of the entanglement's area term, the so-called area theorem. We find that the difference between the UV and IR of the α values, normalized with the thermal entropy, converges at large d to a constant value which is obtained analytically. Therefore, the large d limit may be used as a tool for the study and (in)validation of the renormalization group monotonicity theorems. All the expectation values of the observables under study show rapid convergence to certain values as d increases. The extrapolation of the large d limit to low and intermediate dimensions shows good quantitative agreement with the numerical analysis of the observables.