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Register a new userConceptual Aspects of Gauge/Gravity Duality
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We give an introductory review of gauge/gravity duality, and associated ideas of holography, emphasising the conceptual aspects. The opening Sections gather the ingredients, viz. anti-de Sitter spacetime, conformal field theory and string theory, that we need for presenting, in Section 5, the central and original example: Maldacenas AdS/CFT correspondence. Sections 6 and 7 develop the ideas of this example, also in applications to condensed matter systems, QCD, and hydrodynamics. Sections 8 and 9 discuss the possible extensions of holographic ideas to de Sitter spacetime and to black holes. Section 10 discusses the bearing of gauge/gravity duality on two philosophical topics: the equivalence of physical theories, and the idea that spacetime, or some features of it, are emergent.
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Recently we provided a microscopic derivation of the exact supergravity profile for the twisted scalar field emitted by systems of fractional D3-branes at a Z2 orbifold singularity. In this contribution we focus on a set-up supporting an N = 2 SYM theory with SU(2) gauge group and Nf=4. We take into account the tower of D-instanton corrections to the source terms for the twisted scalar and find that its profile can be expressed in terms of the chiral ring elements of the gauge theory. We show how the twisted scalar, which at the perturbative level represents the gravity counterpart of the gauge coupling, at the non-perturbative level is related to the effective gauge coupling in an interestingly modified way.
We study a gauge/gravity model for the thermodynamics of a gauge theory with one running coupling. The gravity side contains an ansatz for the metric and a scalar field, on the field theory side one starts by giving an ansatz for the beta function describing the scale dependence of the coupling. The model is based on relating the scale to the extra dimensional coordinate and the beta function to the gravity fields, thereby also determining the scalar field potential. We study three different forms of beta functions of increasing complexity and give semianalytic solutions describing first order or continuous transitions.
We propose a new doorway to study the interplay between equations of state of dense matter and compact stars in gauge/gravity correspondence. For this we construct a bulk geometry near the boundary of five-dimensional spacetime. By solving a constraint equation derived from the bulk equation of motion together with the Tolman-Oppenheimer-Volkoff equation, we determine the equations of state for compact stars. The input parameters in this study are the energy density and pressure at the center of the compact objects. We also study how the equation of state depends on the parameters.
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.
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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