Mišković, O.Olea, R.2023-07-312023-07-312012Journal of Physics: Conference Series, Volume 343, 2012, Article number 012077, 7th International Conference on Quantum Theory and Symmetries, QTS7, 7 August 2011, through 13 August 2011, Code 888981742-6588https://repositorio.unab.cl/xmlui/handle/ria/52101Indexación: Scopus.In an arbitrary dimension D, we study quadratic corrections to Einstein-Hilbert action described by the Gauss-Bonnet term. We consider charged black hole solutions with anti-de Sitter (AdS) asymptotics, of interest in the context of gravity/gauge theory dualities (AdS/CFT). The electric charge here is due to the addition of an arbitrary nonlinear electrodynamics (NED) Lagrangian. Due to the existence of a vacuum energy for global AdS spacetime in odd dimensions in the framework of AdS/CFT correspondence, we derive a Quantum Statistical Relation directly from the Euclidean action and not from the First Law of thermodynamics. To this end, we employ a background-independent regularization scheme which consists in supplementing the bulk action with counterterms that depend both on the extrinsic and intrinsic curvatures of the boundary (also known as Kounterterms). This procedure results in a consistent inclusion of the vacuum energy in the thermodynamic description for Einstein-Gauss-Bonnet AdS gravity regardless the explicit form of the NED Lagrangian.enElectrodynamicsGravitationLagrange multipliersQuantum theoryStarsThermodynamicsArtículoAttribution-NonCommercial 4.0 International (CC BY-NC 4.0)10.1088/1742-6596/343/1/012077