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Non-compact Conformal Field Theories (CFTs) are central to several aspects of string theory and condensed matter physics. They are characterised, in particular, by the appearance of a continuum of conformal dimensions. Surprisingly, such…

We revisit the question of conformal boundary conditions in the compact free boson CFT in two dimensions. Besides the well-known Neumann and Dirichlet cases, there is an additional proposed one-parameter family of boundary states when the…

The AdS/CFT correspondence has led to important insights into the properties of quantum chromodynamics even though QCD is a broken conformal theory. A holographic model based on a truncated AdS space can be used to obtain the hadronic…

In addition to describing our universe, gravitational theories profoundly inspire the study of emergent properties of exotic phases of matter. While the Anti-de Sitter/conformal field theory (AdS/CFT) correspondence is one of the most…

We review an explicit regularization of the AdS$_2$/CFT$_1$ correspondence, that preserves all isometries of bulk and boundary degrees of freedom. This scheme is useful to characterize the space of the unitary evolution operators that…

We develop further the theory of Rational Conformal Field Theories (RCFTs) on a cylinder with specified boundary conditions emphasizing the role of a triplet of algebras: the Verlinde, graph fusion and Pasquier algebras. We show that…

We follow to Witten proposal in the calculation of conformal anomaly from d+1-dimensional higher derivative gravity via AdS/CFT correspondence. It is assumed that some d-dimensional conformal field theories have a description in terms of…

We present a detailed analysis of a scalar conformal four-point function obtained from AdS/CFT correspondence. We study the scalar exchange graphs in AdS and discuss their analytic properties. Using methods of conformal partial wave…

Moving from the mirror theory Bethe-Yang equations proposed by Arutyunov and Frolov, we derive the thermodynamic Bethe Ansatz equations which should control the spectrum of the planar $\text{AdS}_5/\text{CFT}_4$ correspondence. The…

We resolve the entropy problem in the AdS$_3$/CFT correspondence by introducing both the normalizable and non-normalizable bulk modes. On the boundary, the normalizable Liouville states gives us $c=1$ conformal field theory(CFT), whereas…

This thesis contains original research on the conjectured AdS/CFT correspondence. Known are the holographic correlators resulting from this correspondence under its classical approximation, confirming the conjecture at this level. In this…

We revisit AdS/CFT at finite radial cut-off, specifically in the context of double trace perturbations, $\mathbb{O}_n$= $\mathbb{O}(x) (\partial^2)^{n} {\mathcal O}(x)$, with arbitrary $n$. As well-known, the standard GKPW prescription,…

The AdS/CFT correspondence is employed to derive logarithmic corrections to the Cardy-Verlinde formula when thermal fluctuations in the Anti-de Sitter black hole are accounted for. The qualitative effect of these corrections on the…

In the framework of gauge invariant approach involving Stueckelberg and auxiliary fields, totally symmetric arbitrary spin anomalous conformal current and shadow field in flat space-time of dimension greater than or equal to four are…

The issue of holographic principle in the PP-wave limit of the AdS/CFT correspondence is discussed, in the hope of clarifying some confusions in the literature. We show that, in the plane-wave limit, the relation between the partition…

We analyze the conformal invariance of submanifold observables associated with $k$-branes in the AdS/CFT correspondence. For odd $k$, the resulting observables are conformally invariant, and for even $k$, they transform with a conformal…

It is a long-standing conjecture that any CFT with a large central charge and a large gap $\Delta_{\text{gap}}$ in the spectrum of higher-spin single-trace operators must be dual to a local effective field theory in AdS. We prove a sharp…

We explicitly calculate a Witten diagram with general spinor field exchange on $(d+1)$-dimensional Euclidean Anti-de Sitter space, which is necessary to evaluate four-point correlation functions with spinor fields when we make use of the…

The Witten-Yau theorem in the AdS/CFT correspondence conjectures that the conformal boundary to AdS space must possess a metric of non-negative scalar curvature for the conformal field theory defined thereon to be free of pathologies. By…

Motivated by the recent work on $T\bar{T}$-type deformations of 2D CFTs, a especial class of single-trace deformations of AdS$_3$/CFT$_2$ correspondence has been investigated. From the worldsheet perspective, this corresponds to a marginal…