String theory corrections to holographic black hole chemistry

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