String Theory Corrections to Holographic Black Hole Chemistry

TL;DR

This paper investigates how string theory corrections, involving higher derivative terms, modify the thermodynamics of holographic black holes and their boundary duals, emphasizing the role of the string parameter ' in the first law.

Contribution

It demonstrates that including ' variations is essential for matching bulk and boundary thermodynamics in higher derivative gravity theories.

Findings

String corrections modify the first law and Smarr relation in holographic thermodynamics.

Including ' variations accounts for changes in boundary central charges and chemical potentials.

Results are supported by explicit calculations with four, six, and '^4 terms in the bulk.

Abstract

The connection between the bulk and the boundary first law of thermodynamics in adS space has been discussed in generic higher derivative gravity. String theory corrections to the supergravity render higher derivative terms in the bulk action, proportional to different powers of string theory parameter $\alpha'$. A variation in the cosmological constant induces a variation in the 't Hooft coupling in the boundary theory. We show that in order to match the bulk first law and Smarr relation with the boundary side one needs to include the variation of $\alpha'$ in the bulk thermodynamics as a book keeping device. Accordingly, the boundary first law and Euler relation are modified with the inclusion of two central charges ($a$, $c$) and/or other chemical potentials as thermodynamic variables. We consider four and six derivative terms as well as the $\text{Weyl}^4$ terms (in type IIB) in bulk in support of our generic result.