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In this paper, we delve into the study of thermodynamics and phase transition of charged Gauss–Bonnet black holes within the context of anti-de Sitter space, with particular emphasis on the central charge's role within the dual conformal field theory (CFT). We employ a holographic methodology that interprets the cosmological constant and the Newton constant as thermodynamic variables, leading to the derivation of a modified first law of thermodynamics that incorporates the thermodynamic volume and pressure. Our findings reveal that the central charge of the CFT is intrinsically linked to the variation of these constants, and its stability can be ensured by simultaneous adjustment of these constants. We further explore the phase structures of the black holes, utilizing the free energy. Our research uncovers the existence of a critical value of the central charge, beyond which the phase diagram displays a first-order phase transition between small and large black holes. We also delve into the implications of our findings on the complexity of the CFT. Our conclusions underscore the significant role of the central charge in the holographic thermodynamics and phase transition of charged Gauss–Bonnet black holes. Furthermore, we conclude that while the central charge considered provides suitable and satisfactory solutions for this black hole in 4 and 5 dimensions, it becomes necessary to introduce a unique central charge for this structure of modified gravity. In essence, the central charge in holographic thermodynamics is not a universal value and requires modification in accordance with different modified gravities. Consequently, the physics of the problem will significantly deviate from the one discussed in this article, indicating a rich and complex landscape for future work. [ABSTRACT FROM AUTHOR]

This paper performed an investigation into the s-embedding of the Lie superalgebra (→ S 1 ∣ 1 ) , a representation of smooth vector fields on a (1,1)-dimensional super-circle. Our primary objective was to establish a precise definition of the s-embedding, effectively dissecting the Lie superalgebra into the superalgebra of super-pseudodifferential operators ( S ψ D ⊙ ) residing on the super-circle S 1 | 1 . We also introduce and rigorously define the central charge within the framework of (→ S 1 ∣ 1 ) , leveraging the canonical central extension of S ψ D ⊙ . Moreover, we expanded the scope of our inquiry to encompass the domain of fuzzy Lie algebras, seeking to elucidate potential connections and parallels between these ostensibly distinct mathematical constructs. Our exploration spanned various facets, including non-commutative structures, representation theory, central extensions, and central charges, as we aimed to bridge the gap between Lie superalgebras and fuzzy Lie algebras. To summarize, this paper is a pioneering work with two pivotal contributions. Initially, a meticulous definition of the s-embedding of the Lie superalgebra (→ S 1 | 1 ) is provided, emphasizing the representationof smooth vector fields on the (1,1)-dimensional super-circle, thereby enriching a fundamental comprehension of the topic. Moreover, an investigation of the realm of fuzzy Lie algebras was undertaken, probing associations with conventional Lie superalgebras. Capitalizing on these discoveries, we expound upon the nexus between central extensions and provide a novel deformed representation of the central charge. [ABSTRACT FROM AUTHOR]

The partition function of three-dimensional gravity in the quantum regime is dual to the Ising model when the central charge c = 1/2. Mathematically, we show that the three-dimensional gravity can be described by Schramm–Loewner evolution (SLE) with certain κ. In fact, SLE depends on the parameter κ, which controls the diffusion of the Brownian motion. Each value of c < 1 corresponds to two values of κ, which may hint that the three-dimensional gravity has two different phases at certain central charge c. Moreover, phase transition is also discussed in AdS and Ising model. [ABSTRACT FROM AUTHOR]

Liouville first passage percolation (LFPP) with parameter ξ>0 is the family of random distance functions {Dϵh}ϵ>0 on the plane obtained by integrating eξhϵ along paths, where hϵ for ϵ>0 is a smooth mollification of the planar Gaussian free field. Previous work by Ding-Dubédat-Dunlap-Falconet and Gwynne-Miller has shown that there is a critical value ξcrit>0 such that for ξ<ξcrit, LFPP converges under appropriate re-scaling to a random metric on the plane which induces the same topology as the Euclidean metric (the so-called γ-\emph{Liouville quantum gravity metric} for γ=γ(ξ)∈(0,2)). We show that for all ξ>0, the LFPP metrics are tight with respect to the topology on lower semicontinuous functions. For ξ>ξcrit, every possible subsequential limit Dh is a metric on the plane which does\emph{not} induce the Euclidean topology: rather, there is an uncountable, dense, Lebesgue measure-zero set of points z∈C such that Dh(z,w)=∞ for every w∈C∖{z}. We expect that these subsequential limiting metrics are related to Liouville quantum gravity with matter central charge in (1,25). [ABSTRACT FROM AUTHOR]

This paper performed an investigation into the s-embedding of the Lie superalgebra (→S1∣1), a representation of smooth vector fields on a (1,1)-dimensional super-circle. Our primary objective was to establish a precise definition of the s-embedding, effectively dissecting the Lie superalgebra into the superalgebra of super-pseudodifferential operators ( SψD⊙) residing on the super-circle S1|1. We also introduce and rigorously define the central charge within the framework of (→S1∣1), leveraging the canonical central extension of SψD⊙. Moreover, we expanded the scope of our inquiry to encompass the domain of fuzzy Lie algebras, seeking to elucidate potential connections and parallels between these ostensibly distinct mathematical constructs. Our exploration spanned various facets, including non-commutative structures, representation theory, central extensions, and central charges, as we aimed to bridge the gap between Lie superalgebras and fuzzy Lie algebras. To summarize, this paper is a pioneering work with two pivotal contributions. Initially, a meticulous definition of the s-embedding of the Lie superalgebra (→S1|1) is provided, emphasizing the representationof smooth vector fields on the (1,1)-dimensional super-circle, thereby enriching a fundamental comprehension of the topic. Moreover, an investigation of the realm of fuzzy Lie algebras was undertaken, probing associations with conventional Lie superalgebras. Capitalizing on these discoveries, we expound upon the nexus between central extensions and provide a novel deformed representation of the central charge.

We study the thermodynamics of the Taub–NUT AdS black holes by Visser's holographic method using AdS radius as a constant parameter under the restricted phase space approach. Instead of the variables P and V, we deal with the central charge and also chemical potential as a unique couple of conjugate thermodynamic variables. We study some interesting properties of the Taub–NUT black holes e.g. supercritical phase equilibrium in the T - S processes, Q - Φ and the Hawking-Page phase transition in the μ - C processes. As a consequence, the consistency of the weak gravity conjecture of multi-charge for Taub–NUT-AdS black holes at critical points is proved. We conclude that in the presence of the central charge and assuming C = 3 8 ℓ 2 , weak gravity conjecture could be satisfied in the Taub–NUT-AdS black holes with n ^ ≪ 1 . [ABSTRACT FROM AUTHOR]

Generally speaking, entanglement entropy (EE) between two subregions of a gapped quantum many-body state is proportional to the area/length of their interface due to the short-range quantum correlation. However, the so-called area law is violated logarithmically in a quantum critical phase. Moreover, the subleading correction exists in long-range entangled topological phases. It is referred to as topological EE which is related to the quantum dimension of the collective excitation in the bulk. Furthermore, if a non-smooth sharp angle is in the presence of the subsystem boundary, a universal angle dependent geometric contribution is expected to appear in the subleading correction. In this work, we simultaneously explore the geometric and edge contributions in the integer quantum Hall (IQH) state and its edge reconstruction in a unified bipartite method. Their scaling is found to be consistent with conformal field theory (CFT) predictions and recent results of particle number fluctuation calculations.

For a quiver Q of Dynkin type A n , we give a set of n − 1 inequalities which are necessary and sufficient for a linear stability condition (a.k.a. central charge) Z : K 0 (Q) → ℂ to make all indecomposable representations stable. We furthermore show that these are a minimal set of inequalities defining the space T S (Q) of total stability conditions, considered as an open subset of ℝ Q 0 × (ℝ > 0) Q 0 . We then use these inequalities to show that each fiber of the projection of T S (Q) to (ℝ > 0) Q 0 is linearly equivalent to ℝ × ℝ > 0 Q 1 . [ABSTRACT FROM AUTHOR]

Nontrivial diffeomorphisms act on the horizon of a generic 4D black holes and create distinguishing features referred to as soft hair. Amongst these are a leftâ€"right pair of Virasoro algebras with associated charges that reproduce the Bekensteinâ€"Hawking entropy for Kerr black holes. In this paper we show that if one adds a negative cosmological constant, there is a similar set of infinitesimal diffeomorphisms that act non-trivially on the horizon. The algebra of these diffeomorphisms gives rise to a central charge. Adding a boundary counterterm, justified to achieve integrability, leads to well-defined central charges with c L = c R. The macroscopic area law for Kerr-AdS black holes follows from the assumption of a Cardy formula governing the black hole microstates. [ABSTRACT FROM AUTHOR]

In this article, we study the relationship among maximal green sequences, complete forward hom-orthogonal sequences and stability functions in abelian length categories. Mainly, we firstly give a one-to-one correspondence between maximal green sequences and complete forward hom-orthogonal sequences via mutual constructions, and then prove that a maximal green sequence can be induced by a central charge if and only if it satisfies crossing inequalities. As applications, we show that crossing inequalities can be computed by c -vectors for finite dimensional algebras; finally, we give the Rotation Lemma for finite dimensional Jacobian algebras. [ABSTRACT FROM AUTHOR]

We construct maximal green sequences of maximal length for any affine quiver of type A. We determine which sets of modules (equivalently c-vectors) can occur in such sequences and, among these, which are given by a linear stability condition (also called a central charge). There is always at least one such maximal set which is linear. The proofs use representation theory and three kinds of diagrams shown in Fig. 1. Background material is reviewed with details presented in two separate papers Igusa (2017a, b). [ABSTRACT FROM AUTHOR]

For modules over an artin algebra, a linear stability condition is given by a "central charge" and a nonlinear stability condition is given by the wall-crossing sequence of a "green path." Finite Harder-Narasimhan stratifications of the module category, maximal forward hom-orthogonal sequences and maximal green sequences, defined using Fomin-Zelevinsky quiver mutation are shown to be equivalent to finite nonlinear stability conditions when the algebra is hereditary. This is the first of a series of three papers whose purpose is to determine all maximal green sequences of maximal length for quivers of affine type A and determine which are linear. [ABSTRACT FROM AUTHOR]