相关论文: Geometric Holography, the Renormalization Group an…

I present a method of quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UCT). I also show that by using this method new features of…

In many instances of holographic correspondences between a d dimensional boundary theory and a d+1 dimensional bulk, a direct argument in the boundary theory implies that there must exist a simple and precise relation between the Euclidean…

We explore the notion of $c$-functions in renormalization group flows between theories in different spacetime dimensions. We discuss functions connecting central charges of the UV and IR fixed point theories on the one hand, and functions…

We prove a holographic c-theorem for the a central charge in AdS/CFT where the bulk is described by a gravitational action built out of an arbitrary function f(R^{ab}_{cd}) of the Riemann tensor coupled to bulk matter. This theorem holds…

Representations of $C^*$-algebras are realized on section spaces of holomorphic homogeneous vector bundles. The corresponding section spaces are investigated by means of a new notion of reproducing kernel, suitable for dealing with…

The renormalization group flow of unimodular quantum gravity is computed by taking into account the graviton and Faddeev-Popov ghosts anomalous dimensions. In this setting, a ultraviolet attractive fixed point is found. Symmetry-breaking…

We provide rigorous evidence of the fact that the modified Constantin-Lax-Majda equation modeling vortex and quasi-geostrophic dynamics describes the geodesic flow on the subgroup of orientation-preserving diffeomorphisms fixing one point,…

The integration of high-energy degrees of freedom along the renormalization group (RG) flow in Poincar\'e-invariant theories can be captured by a monotonic c-function. For such theories, holographic monotonic c-functions have been…

The Weyl anomaly in the Holographic Renormalisation Group as implemented using Hamilton-Jacobi language is studied in detail. We investigate the breakdown of the descent equations in order to isolate the Weyl anomaly of the dual field…

We discuss some general aspects of renormalization group flows in four dimensions. Every such flow can be reinterpreted in terms of a spontaneously broken conformal symmetry. We analyze in detail the consequences of trace anomalies for the…

We initiate a non-perturbative study of anisotropic, non-conformal and confining gauge theories that are holographically realized in gravity by generic Einstein-Axion-Dilaton systems. In the vacuum our solutions describe RG flows from a…

Hole-ography is a prescription relating the areas of surfaces in an AdS bulk to the differential entropy of a family of intervals in the dual CFT. In (2+1) bulk dimensions, or in higher dimensions when the bulk features a sufficient degree…

We revisit a study of local renormalization group (RG) with background gauge fields incorporated using the AdS/CFT correspondence. Starting with a $(d+1)$-dimensional bulk gravity coupled to scalars and gauge fields, we derive a local RG…

We discuss the holographic c-function and describe an algorithm for the practical computation of the changing central charge in arbitrary RG-flows. One example is worked out in detail. The renormalisation procedure of…

We investigate the geometry of holomorphic curves and complex surfaces from the perspective of singularity theory. We show that, with a suitable choice of a complex bilinear symmetric form, the families of functions and mappings that…

We consider holography for d-dimensional scale invariant but non-Lorentz invariant field theories, which do not admit the full Schrodinger symmetry group. We find new realizations of the corresponding (d+1)-dimensional gravity duals,…

We investigate relevant deformation and the renormalization group flow in a defect conformal field theory from the point of view of the holography. We propose a candidate of g-function in the context of the holography, and prove the…

An example of the holographic correspondence between 2d, N=2 quantum field theories and classical 4d, N=2 supergravity theories is found. The constraints on the target space geometry of the 4d, N=2 non-linear sigma-models in N=2…

We review the issue of gauge and gravitational anomalies with backgrounds, maybe offering a new outlook on some aspects of these questions. We compute the holographic anomalies of hypothetical theories dual, in the sense of the AdS-CFT…

In this work, we present a holographic renormalization scheme for asymptotically anti-de Sitter spacetimes in which the dual renormalization scheme of the boundary field theory is dimensional regularization. This constitutes a new level of…