We carry out field redefinitions in ten-dimensional Type IIB supergravity and show that they do not give rise to any physical corrections to the holographic renormalization group structure in the AdS/CFT correspondence. We in particular show that the holographic Weyl anomaly of the N = 4 SU(N) super Yang-Mills theory does not change under the field redefinition of the ten-dimensional metric of ...

Sequences of nodal counts store information on the geometry (metric) of the domain where the wave equation is considered. To demonstrate this statement, we consider the eigenfunctions of the Laplace-Beltrami operator on surfaces of revolution. Arranging the wave functions by increasing values of the eigenvalues, and counting the number of their nodal domains, we obtain the nodal sequence whose ...

In this talk I will briefly outline work in progress in two different contexts in astrophysical relativity, i.e. the study of rotating star spacetimes and the problem of reliably extracting gravitational wave templates in numerical relativity. In both cases the use of Weyl scalars and curvature invariants helps to clarify important issues. INTRODUCTION The Weyl scalars the components of the Wey...

Abstract We present new rotating vacuum configurations endowed with both dynamical torsion and nonmetricity fields in the framework of Metric-Affine gauge theory gravity. For this task, we consider scalar-flat Weyl-Cartan geometries obtain an axisymmetric Kerr-Newman solution decoupling limit between orbital spin angular momentum. The corresponding Kerr-Newman-de Sitter is also compatible a cos...

Gravitational decoupling via the Minimal Geometric Deformation (MGD) approach has been used extensively in General Relativity (GR), mainly as a simple method for generating exact anisotropic solutions from perfect fluid seed solutions. Recently this also to generate spherically symmetric of Einstein-scalar system Schwarzschild vacuum metric. This was then investigate effect scalar fields on bla...

Weyl semimetals are of great interest because they provide the first realization of the Weyl fermion, exhibit exotic quantum anomalies, and host Fermi arc surface states. The separation between Weyl nodes of opposite chirality gives a measure of the robustness of the Weyl semimetal state. To exploit the novel phenomena that arise from Weyl fermions in applications, it is crucially important to ...

We discuss a quantum extension of the holographic RG flow equation obtained previously from the classical Hamiltonian constraint in the bulk AdS supergravity. The WheelerDeWitt equation is proposed to generate the extended RG flow and to produce 1/N subleading corrections systematically. Our formulation in five dimensions is applied to the derivation of the Weyl anomaly of boundary N = 4 SU(N) ...

Abstract Spin foams arise from a quantization of classical gravity expressed via the Plebanski action. Key open questions related to continuum limit spin are whether general relativity is reproduced and what type corrections could emerge. As central component for foam dynamics, recent results on Area Regge action suggest close relation with actions area metrics instead length metric. Inspired b...

Stability and chaoticity in conservative Hamiltonian systems are analyzed using an indicator based on a generalization of the virtual work principle (VWP) for Riemannian manifolds. The geometrodynamic formalism obtained this way is applied to define mechanical manifold Jacobi metric, where system trajectories geodesics. VWP static equilibrium Euclidean spaces generalized through geodesic equati...

Semiclassical Einstein-Langevin equations for arbitrary small metric perturbations conformally coupled to a massless quantum scalar eld in a spatially at cosmological background are derived. Use is made of the fact that for this problem the in-in or closed time path e ective action is simply related to the Feynman and Vernon in uence functional which describes the e ect of the \environment", th...