We study the thermodynamic properties of a warped ${\mathrm{AdS}}_3$ black hole within the framework of thermodynamic information geometry. Our analysis focuses on finding the set of proper thermodynamic Riemannian metrics on the space of equilibrium states, together with the conditions for local and global thermodynamic stability. We use our findings to constrain the values of left and right central charges from the dual conformal field theory and the parameters of the bulk gravitational theory.

We review a recent investigation of the effect of magnetic catalysis of mass generation in holographic Yang‐Mills theories. We aim at a self‐contained and pedagogical form of the review. We provide a brief field theory background and review the basics of holographic flavordynamics. The main part of the paper investigates the influence of external magnetic field to holographic gauge theories dual to the D3/D5‐ and D3/D7‐brane intersections. Among the observed phenomena are the spontaneous breaking of a global internal symmetry, Zeeman splitting of the energy levels, and the existence of pseudo, Goldstone modes. An analytic derivation of the Gell‐Mann‐Oaks‐Renner relation for the D3/D7 set up is reviewed. In the D3/D5 case, the pseudo‐Goldstone modes satisfy nonrelativistic dispersion relation. The studies reviewed confirm the universal nature of the magnetic catalysis of mass generation.

In the recent study of Virasoro action on characters, we discovered that it gets especially simple for peculiar linear combinations of the Virasoro operators: particular harmonics of $${\hat{w}}$$w ^ -operators. In this letter, we demonstrate that even more is true: a singlew-constraint is sufficient to uniquely specify the partition functions provided one assumes that it is a power series in time-variables. This substitutes the previous specifications in terms of two requirements: either a string equation imposed on the KP/Toda $$\tau $$τ -function or a pair of Virasoro generators. This mysterious single-entry definition holds for a variety of theories, including Hermitian and complex matrix models, and also matrix models with external matrix: the unitary and cubic Kontsevich models. In these cases, it is equivalent to W-representation and is closely related to super integrability. However, a similar single equation that completely determines the partition function exists also in the case of the generalized Kontsevich model (GKM) with potential of higher degree, when the constraint algebra is a larger W-algebra, and neither W-representation, nor superintegrability are understood well enough.

In this paper we consider a simple generalization of the method of Lunin and Maldacena for generating new string backgrounds based on TsT transformations. We study multishift $Ts\cdots sT$ transformations applied to backgrounds with at least two U(1) isometries. We prove that the string currents in any two backgrounds related by $Ts\cdots sT$ transformations are equal. Applying this procedure to the $Ad{S}_5\times S^5$, we find a new background and study some properties of the semiclassical strings.

We revisit the classical thermodynamic stability of the standard black hole solutions by implementing the intrinsic necessary and sufficient conditions for stable global and local thermodynamic equilibrium. The criteria for such equilibria are quite generic and well-established in classical thermodynamics, but they have not been fully utilized in black hole physics. We show how weaker or incomplete conditions could lead to misleading or incorrect results for the thermodynamic stability of the system. We also stress the importance of finding all possible local heat capacities in order to fully describe the classical equilibrium picture of black holes. Finally, we thoroughly investigate the critical and phase transition curves and the limits of the classical analysis. This paper is the first in the line of intended works on thermodynamic stability of black holes in modified theories of gravity and holography.

We derive the extended renormalized entanglement entropy and the Fisher information metric in the case of closed bosonic strings in a homogeneous plane wave background. Our investigations are conducted within the framework of thermo field dynamics. The formalism is also illustrated in the example of some particular models in condensed matter physics and the nonequilibrium case for a system with dissipations.