Related papers: Constraining Non-Relativistic RG Flows with Hologr…
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…
An interpolating function $\tilde F$ between the $a$-anomaly coefficient in even dimensions and the free energy on an odd-dimensional sphere has been proposed recently and is conjectured to monotonically decrease along any renormalization…
We construct the c-function whose gradient determines the RG flow of the conductivities (sigma_xy and sigma_xx) for a quantum Hall system, subject to two assumptions. (1) We take the flow to be invariant with respect to the infinite…
We study cosmological solutions of Einstein gravity with a positive cosmological constant in diverse dimensions. These include big-bang models that re-collapse, big-bang models that approach de Sitter acceleration at late times, and bounce…
B List has recently studied a geometric flow whose fixed points correspond to static Ricci flat spacetimes. It is now known that this flow is in fact Ricci flow modulo pullback by a certain diffeomorphism. We use this observation to…
Qualitatively new aspects of the (linear and non-linear) stability of sheared relativistic (slab) jets are analyzed. The linear problem has been solved for a wide range of jet models well inside the ultrarelativistic domain (flow Lorentz…
The holographic RG flow in AdS/CFT correspondence naturally defines a holographic scheme in which the central charge c and the beta function are related by a universal formula. We perform some checks of that formula and we compare it with…
Implementing the Wilsonian renormalization group (RG) transformation in a nonperturbative way, we construct an effective holographic dual description with an emergent extradimension identified with an RG scale. Taking the large$-N$ limit,…
We develop an approach to the theory of relativistic geometric flows and emergent gravity defined by entropy functionals and related statistical thermodynamics models. Nonholonomic deformations of G. Perelman's functionals and related…
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 Wetterich-equation to study the renormalization group flow of $f(R)$-gravity in a three-dimensional, conformally reduced setting. Building on the exact heat kernel for maximally symmetric spaces, we obtain a partial differential…
Causal horizons in pure Poincare $AdS$ are Killing horizons generated by dilatation vector. Renormalization group (RG) flow breaks the dilatation symmetry and makes the horizons dynamical. We propose that the boundary RG flow is dual to the…
The holographic renormalization group flows associated with marginally relevant operators are analyzed. The associated perturbative and non-perturbative beta-functions are calculated and the consistent scalar potentials are identified. The…
We construct a novel Wetterich-type functional renormalization group equation for gravity which encodes the gravitational degrees of freedom in terms of gauge-invariant fluctuation fields. Applying a linear-geometric approximation the…
Based on Son-Yamamoto relation obtained for transverse part of triangle axial anomaly in ${\rm QCD}_4$, we derive its analog in two-dimensional system. It connects the transverse part of mixed vector-axial current two-point function with…
A thermodynamic analysis of weakly nonlocal non-relativistic fluids is presented under the assumption that an additional scalar field also contributes to the dynamics. The most general evolution of this field and the constitutive relations…
A non-perturbative and continuous definition of RG transformations as stochastic processes is proposed, inspired by the observation that the functional RG equations for effective Boltzmann factors may be interpreted as Fokker-Planck…
We study the $q\bar{q}$ potential in strongly coupled non-conformal field theories with a non-trivial renormalization group flow via holography. We focus on the properties of this potential at an inter-quark separation $L$ large compared to…
We complete the reformulation of the holographic correspondence as a \emph{highly efficient RG flow} that can also determine the UV data in the field theory in the strong coupling and large $N$ limit. We introduce a special way to define…
We investigate the analogy between the renormalization group (RG) and deep neural networks, wherein subsequent layers of neurons are analogous to successive steps along the RG. In particular, we quantify the flow of information by…