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The gradient flow bears a close resemblance to the coarse graining, the guiding principle of the renormalization group (RG). In the case of scalar field theory, a precise connection has been made between the gradient flow and the RG flow of…

We combine old ideas about exact renormalization-group-flow (RGF) equations with the Vilkovisky-De Witt (VDW) approach to reparametrization invariant effective actions and arrive at a new, exact, gauge-invariant RGF equation. The price to…

The cutoff scheme dependence in the several formulations of the Exact Renormalization Group (ERG) is investigated. It is shown that the cutoff scheme dependence of the Wilsonian effective action is regarded as a certain coordinate…

In this note we investigate the proposal of Ellwood and one of the authors et al. to construct a string field theory solution describing the endpoint of an RG flow from a reference BCFT to a target BCFT*. We show that the proposed class of…

We derive a system of coupled flow equations for the proper-vertices of the background effective average action and we give an explicit representation of these by means of diagrammatic and momentum space techniques. This explicit…

We sketch the construction of a gauge invariant Exact Renormalization Group (ERG). Starting from Polchinski's equation, the emphasis is on how a series of ideas have combined to yield the gauge invariant formalism. A novel symmetry of the…

One-dimensional strongly correlated electron systems coupled via transverse hopping and presence of interband interactions can converge to a Luttinger liquid state or diverge to an even more intricate behavior, as a Mott state. Explicit…

We adapt the precise definition of the flowing effective action in order to obtain a functional flow equation with simple properties close to physical intuition. The simplified flow equation is invariant under local gauge transformations…

Theoretical developments in the field of Lagrangian turbulence are made difficult by the fact that equations governing the evolution of lagrangian flows are implicit contrary to eulerian flows. In this article, an {\it exact} explicit…

Gradient Flow Exact Renormalization Group (GF-ERG) is a framework to define the renormalization group flow of Wilsonian effective action utilizing coarse-graining along the diffusion equations. We apply it for Scalar Quantum Electrodynamics…

The flow equations or exact RG equations for the Higgs Top System are solved to leading order in $1/N_c$. This allows to relate arbitrary bare actions with this field content continuously to effective low energy theories, and we find the…

We establish a concrete correspondence between a gradient flow and the renormalization group flow for a generic scalar field theory. We use the exact renormalization group formalism with a particular choice of the cutoff function.

We obtain the exact renormalization group (RG) flow equation for a self interacting real scalar field in an expanding cosmological background. The beta functional for the potential in the local potential approximation is determined in terms…

We write a Renormalization Group (RG) equation for the function f in a theory of gravity in the f(R) truncation. Our equation differs from previous ones due to the exponential parametrization of the quantum fluctuations and to the choice of…

The gradient flow exact renormalization group (GFERG) is a variant of the exact renormalization group (ERG) for gauge theory that is aimed at preserve gauge invariance as manifestly as possible. It achieves this goal by utilizing the…

We study the holographic renormalization group (RG) flow in the presence of higher-order curvature corrections to the $(d+1)$-dimensional Einstein-Hilbert (EH) action for an arbitrary interacting scalar matter field by using the…

Starting from the basic path integral in phase space we reconsider the functional approach to the RG flow of the one particle irreducible effective average action. On employing a balanced coarse-graining procedure for the canonical…

The Renormalization Group (RG) is a set of methods that have been instrumental in tackling problems involving an infinite number of degrees of freedom. What all these methods have in common -- which is what explains their success -- is that…

The calculation of the full (renormalized) holographic action is undertaken in general Einstein-scalar theories. The appropriate formalism is developed and the renormalized effective action is calculated up to two derivatives in the metric…

We study supersymmetric quantum mechanics with the functional RG formulated in terms of an exact and manifestly off-shell supersymmetric flow equation for the effective action. We solve the flow equation nonperturbatively in a systematic…