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Register a new userUniversal criticality of thermodynamic geometry for boundary conformal field theories in gauge/gravity duality
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Added by
Seyed Ali Hosseini Mansoori
Publication date
2021
fields
Physics
and research's language is
English
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According to more recent AdS/CFT interpretation cite{Karch:2015rpa}, in which varying cosmological constant $Lambda$ in the bulk corresponds to varying the curvature radius governing the space on which the field theory resides, we study the criticality of thermodynamic curvatures for thermal boundary conformal field theories (CFT) that are dual to $d$-dimensional charged anti-de Sitter (AdS) black holes, embedded in $D$-dimensional M-theory/superstring inspired models having $AdS_{d}times mathbb{S}^{d+k}$ spacetime with $D=2d+k$. Analogous with criticality features acquired for charged AdS black holes in the bulk cite{HosseiniMansoori:2020jrx}, the normalized intrinsic curvature $R_N$ and extrinsic curvature $K_N$ of the boundary CFT has critical exponents 2 and 1, respectively. In this respect, the universal amplitude of $R_Nt^2$ is $frac{1}{2}$ and $K_Nt$ is $-frac{1}{2}$ when $trightarrow0^-$, whereas $R_Nt^2approx frac{1}{8}$ and $K_Ntapproxfrac{1}{4}$ in the limit $trightarrow0^+$ in which $t=T/T_c-1$ is the temperature parameter with the critical temperature, $T_{c}$. Interestingly, these critical amplitudes are independent of the number of thermal CFT dimensions and are remarkably similar to one given for higher dimensional charged AdS black holes in the bulk.
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In this letter, we first redefine our formalism of the thermodynamic geometry introduced in [1,2] by changing coordinates of the thermodynamic space by means of Jacobian matrices. We then show that the geometrothermodynamics (GTD) is conformally related to this new formalism of the thermodynamic geometry. This conformal transformation is singular at unphysical points were generated in GTD metric. Therefore, working with our metric neatly excludes all unphysical points without imposing any constraints.
We use gauge/gravity duality to study the thermodynamics of a generic almost conformal theory, specified by its beta function. Three different phases are identified, a high temperature phase of massless partons, an intermediate quasi-conformal phase and a low temperature confining phase. The limit of a theory with infrared fixed point, in which the coupling does not run to infinity, is also studied. The transitions between the phases are of first order or continuous, depending on the parameters of the beta function. The results presented follow from gauge/gravity duality; no specific boundary theory is assumed, only its beta function.
We explore how far one can go in constructing $d$-dimensional static black holes coupled to $p$-form and scalar fields before actually specifying the gravity and electrodynamics theory one wants to solve. At the same time, we study to what extent one can enlarge the space of black hole solutions by allowing for horizon geometries more general than spaces of constant curvature. We prove that a generalized Schwarzschild-like ansatz with an arbitrary isotropy-irreducible homogeneous base space (IHS) provides an answer to both questions, up to naturally adapting the gauge fields to the spacetime geometry. In particular, an IHS-Kahler base space enables one to construct magnetic and dyonic 2-form solutions in a large class of theories, including non-minimally couplings. We exemplify our results by constructing simple solutions to particular theories such as $R^2$, Gauss-Bonnet and (a sector of) Einstein-Horndeski gravity coupled to certain $p$-form and conformally invariant electrodynamics.
We use gauge/gravity duality to study simultaneously the mass spectrum and the thermodynamics of a generic quasi-conformal gauge theory, specified by its beta function. The beta function of a quasi-conformal theory almost vanishes, and the coupling is almost constant between two widely separated energy scales. Depending on whether the gravity dual has a black hole or not, the mass spectrum is either a spectrum of quasinormal oscillations or a normal T=0 mass spectrum. The mass spectrum is quantitatively correlated with the thermal properties of the system. As the theory approaches conformality, the masses have to vanish. We show that in this limit, the masses calculated via gauge/gravity duality satisfy expected scaling properties.
In this work, a correspondence between black hole solutions of conformal and massive theories of gravity is found. It is seen that this correspondence imposes some constraints on parameters of these theories. What is more, a relation between the mass of black holes and the parameters of massive gravity is found. Indeed, the acceptable ranges of massive gravity parameters ($c_{1}$ and $c_{2}$) are found. It is shown that by considering the positive mass of black holes, some ranges of $c_{1}$ and $c_{2}$ are acceptable.
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