String Theory Corrections to Holographic Black Hole Chemistry

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 ${\alpha }^{\prime }$. 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 ${\alpha }^{\prime }$ 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.

20+6+3 pages, Comments are welcome

References in corpus (9)

• Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume
• Smarr Formula and an Extended First Law for Lovelock Gravity
• Thermodynamics of AdS Black Holes: Central Charge Criticality
• R^4, purified
• On Euclidean and Noetherian Entropies in AdS Space
• Higher Order Corrections to Holographic Black Hole Chemistry
• Shear Viscosity to Entropy Density Ratio in Six Derivative Gravity
• Killing Symmetries and Smarr Formula for Black Holes in Arbitrary Dimensions
• Interaction Between AdS Black Hole Molecules

Cited by in corpus (1)

• Thermodynamics and phase transition in central charge criticality of charged Gauss-Bonnet AdS black holes