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 $\alpha$ of the entanglement’s area term, the so-called area theorem. We find that the difference between the UV and IR of the $\alpha$ 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.

• Received 6 November 2021
• Accepted 4 January 2022

DOI:https://doi.org/10.1103/PhysRevD.105.026016

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Published by the American Physical Society