AdS-CFT Correspondence in Noncommutative background, related thermodynamics and Holographic Superconductor in Magnetic Field

TL;DR

This paper develops a noncommutative extension of the AdS-CFT correspondence, analyzing its effects on holographic superconductors and thermodynamics, revealing that noncommutativity weakens the superconducting phase and alters black hole properties.

Contribution

It introduces a noncommutative framework into AdS-CFT, studying its impact on black hole thermodynamics and holographic superconductors, highlighting the fragility of superconductivity under noncommutative effects.

Findings

Noncommutativity reduces the critical temperature and magnetic field for superconductivity.

Noncommutative effects oppose black hole hair formation.

Qualitative agreement with noncommutative condensed matter superconductors.

Abstract

In this work, we formulate a Non-Commutative (NC) extension of AdS-CFT correspondence that is manifested in the modification of behavior of a holographic superconductor. The noncommutativity is introduced in the model through the NC corrected AdS charged black hole metric developed by Nicolini, Smailagic and Spallucci. First of all we discuss thermodynamic properties of this black hole in Euclidean formalism. In particular, we compute trace of the boundary energy-momentum tensor which, as expected, is non-zero due to the NC scale introduced in the model. Our findings indicate that the non-commutative effects tend to work against the black hole hair formation. This, in turn, has an adverse effect on the holographic superconductor by making the superconducting phase more fragile. This is reflected in the reduced value of the critical magnetic field and critical temperature. Finally, we comment on a qualitative agreement between our (holographic superconductor) result and that obtained for a conventional superconductor in NC space in a purely condensed matter scenario. In both cases noncommutativity tends to oppose the superconducting phase.