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We derive an effective dual holographic Einstein-Maxwell theory, applying renormalization group transformations to interacting Dirac fermions in a recursive way. In particular, we show how both background metric tensor and U(1) gauge fields…
The holographic correspondence between 2d, N=2 quantum field theories and classical 4d, N=2 supergravity coupled to hypermultiplet matter is proposed. The geometrical constraints on the target space of the 4d, N=2 non-linear sigma-models in…
We study five-dimensional $N=4$ gauged supergravity coupled to five vector multiplets with compact and non-compact gauge groups $U(1)\times SU(2)\times SU(2)$ and $U(1)\times SO(3,1)$. For $U(1)\times SU(2)\times SU(2)$ gauge group, we…
We study general correlation functions of various quantum field theories in the holographic setup. Following the holographic proposal, we investigate correlation functions via a geodesic length connecting boundary operators. We show that…
We investigate the holographic renormalization group flows and the classical phase transitions that occur in two dimensional QFT model dual to the New Massive 3D Gravity coupled to scalar matter. Specific matter self-interactions generated…
We introduce the gauge/gravity, or AdS/CFT, correspondence with an eye towards its application to strongly coupled systems. We provide an overview of the duality, including the AdS/CFT dictionary and holographic renormalization. We then…
Models of geometric flows pertaining to $\mathcal{R}^2$ scale invariant (super) gravity theories coupled to conformally invariant matter fields are investigated. Related to this work are supersymmetric scalar manifolds that are isomorphic…
We use the holographic method to investigate an RG flow and IR physics of a two-dimensional conformal field theory (CFT) deformed by a relevant scalar operator. On the dual gravity side, a renormalization group (RG) flow from a UV to IR CFT…
We study holographic RG flows in a 3d supergravity model from the side of the dynamical system theory. The gravity equations of motion are reduced to an autonomous dynamical system. Then we find equilibrium points of the system and analyze…
Quantum Chromodynamics in two spacetime dimensions is investigated with the Functional Renormalization Group. We use a functional formulation with covariant gauge fixing and derive Renormalization Group flow equations for the gauge…
Using the precursor map in AdS/CFT, the renormalization group cutoff function is mapped to the dual theory. The resulting flow equations on the two sides of the duality are compared.
Field theoretical renormalization group methods are applied to a simple model of a passive scalar quantity advected by the Gaussian non-solenoidal (``compressible'') velocity field with the covariance $\propto\delta(t-t')|…
The scalar normal modes of higher dimensional gravitating kink solutions are derived. By perturbing to second order the gravity and matter parts of the action in the background of a five-dimensional kink, the effective Lagrangian of the…
An approach to the Holographic Renormalization Group in the context of Rehren duality - a structural form of the AdS-CFT correspondence, in the context of Local Quantum Physics (Algebraic QFT) - is proposed. Special attention to the issue…
The one-loop renormalization of the action for a set Dirac fermions and a set of scalars spanning an arbitrary manifold coupled via Yukawa-like and gauge interactions is presented. The computation is performed with functional methods and in…
We study the renormalization group flow equations for correlation functions of weakly coupled quantum field theories in AdS. Taking the limit where the external points approach the conformal boundary, we obtain a flow of conformally…
We employ the functional renormalization group approach formulated on the Schwinger-Keldysh contour to calculate real-time correlation functions in scalar field theories. We provide a detailed description of the formalism, discuss suitable…
The AdS/CFT correspondence has developed over the last years into a very useful and powerful tool for studying strongly coupled field theories at finite temperature and density. Of particular interest is the regime of near equilibrium real…
We adapt the Hamilton-Jacobi method of holographic renormalization to scalar field theories in Minkowski spacetime with scattering boundary conditions. The approach yields a flat-space holographic dictionary in which the expectation value…
This thesis is based on the publications arXiv:1106.4253, arXiv:1206.2920, arXiv:1210.2590. We construct warped "AdS_4 x S^2 x S^2 x \Sigma" type IIB supergravity solutions dual to the infrared fixed points of all 3d N=4 linear and circular…