Quantum corrections to the thermodynamics of R-charged D1-branes

We investigate the quantum thermodynamics of R-charged D1-branes by incorporating non-perturbative exponential corrections that arise naturally from D-instanton contributions in type IIB string theory. Our approach extends beyond classical supergravity solutions to capture the quantum gravitational regime where traditional thermodynamic descriptions break down. Through systematic analysis of the corrected entropy expression, we derive quantum-modified thermodynamic potentials including temperature, specific heat, internal energy, and Helmholtz free energy, revealing profound deviations from classical behavior in the small-horizon limit where quantum effects dominate. The exponential corrections induce thermodynamic instabilities characterized by negative specific heat and modify the brane’s phase structure, while breaking fundamental scaling relations such as the Smarr formula through quantum deviations that encode the breakdown of classical symmetries. We extend our analysis to quantum work and thermodynamic geometry, demonstrating that these corrections reveal strong attractive microstructural interactions and potential phase transitions near extremality. The thermodynamic curvature diverges negatively in the quantum regime, signaling enhanced correlations among underlying degrees of freedom. Through the AdS/CFT correspondence, we interpret these bulk quantum effects within the dual (1 + 1)-dimensional supersymmetric Yang–Mills theory, identifying suppressed degrees of freedom, anomalous scaling behavior, and quantum-induced trace anomalies in the boundary stress tensor. Our holographic renormalization analysis reveals that quantum corrections effectively reduce the central charge and introduce conformal symmetry breaking, reflecting the deep influence of quantum gravity on strongly coupled gauge theories. These findings establish the critical importance of quantum corrections in black brane thermodynamics and provide new insights into the holographic structure of gauge theories under quantum gravitational influence.