String Theory Corrections to Holographic Black Hole Chemistry

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 $α'$. 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 $α'$ 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.

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