Related papers: Ward identity violation for melonic $T^4$-truncati…
I give an overview over some work on rigorous renormalization theory based on the differential flow equations of the Wilson-Wegner renormalization group. I first consider massive Euclidean $\phi_4^4$-theory. The renormalization proofs are…
We continue the constructive program about tensor field theory through the next natural model, namely the rank five tensor theory with quartic melonic interactions and propagator inverse of the Laplacian on $U(1)^5$. We make a first step…
Using covariant methods, we construct and explore the Wetterich equation for a non-minimal coupling $F(\phi)R$ of a quantized scalar field to the Ricci scalar of a prescribed curved space. This includes the often considered non-minimal…
We present a Ward identity for nonlinear sigma models using generalized nonlinear shift symmetries, without introducing current algebra or coset space. The Ward identity constrains correlation functions of the sigma model such that the…
The interplay of mesonic fluctuations with an axial $U(1)_A$-symmetry breaking and resulting effects on the location of a possibly existing critical endpoint in the QCD phase diagram are investigated in a framework of the functional…
We investigate non-Abelian gauge theories within a Wilsonian Renormalisation Group approach. The cut-off term inherent in this approach leads to a modified Ward identity (mWI). It is shown that this mWI is compatible with the flow and that…
We discuss to what extent the full set of Ward Identities constrain the four-point function of the stress-energy tensors or conserved currents in a conformal field theory. We calculate the number of kinematically unrestricted functional…
We derive Ward identities for the Standard Model Effective Field Theory using the background field method. The resulting symmetry constraints on the Standard Model Effective Field Theory are basis independent, and constrain the perturbative…
We use holographic renormalization of minimal $\mathcal{N}=2$ gauged supergravity in order to derive the general form of the quantum Ward identities for 3d $\mathcal{N}=2$ and 4d $\mathcal{N}=1$ superconformal theories on general curved…
The melonic limit is a relatively new type of large-$N$ limit, differing from the much older and well-known large-$N$ limits of vector and matrix field theories, which are dominated by cactus and planar Feynman diagrams, respectively. The…
Euclidean field theories admit more general deformations than usually discussed in quantum field theories because of mixing between rotational symmetry and internal symmetry (a.k.a topological twist). Such deformations may be relevant, and…
We propose a new application of random tensor theory to studies of non-linear random flows in many variables. Our focus is on non-linear resonant systems which often emerge as weakly non-linear approximations to problems whose linearized…
In this paper we consider the complete momentum-independent quartic order truncation for the effective average action of a real Abelian rank 3 tensorial group field theory. This complete truncation includes non-melonic as well as…
We study the possible IR and UV asymptotics of 4D Lorentz invariant unitary quantum field theory. Our main tool is a generalization of the Komargodski-Schwimmer proof for the $a$-theorem. We use this to rule out a large class of…
The tensor track is a background-independent discretization of quantum gravity which includes a sum over all topologies. We discuss how to define a functional renormalization group flow and the Wetterich equation in the corresponding theory…
Systems of interacting non relativistic fermions in $d=1$, as well as spin chains or interacting bidimensional Ising models, verify an hidden approximate Gauge invariance which can be used to derive suitable Ward identities. Despite the…
We investigate the Ward-Takahashi identity at one-loop in the light-front (LF) formalism for a bound state of fermions. We consider a spinless bound state made up of two fermions in which the Ward-Takahashi identity is satisfied in the…
We derive Ward identities for fermionic systems exhibiting a gauge symmetry that gets globally broken. In particular, we focus on the relation that connects the gauge field response functions to the transverse susceptibilities of the order…
It is recalled why, as already stated in a previous paper, there seems to be an inconsistency in identifying the non perturbative ZA,MOM as the renormalisation of the axial current, or equivalently, in setting as normalisation condition…
We find the Holographic Renormalization Group equations for the holographic duals of generic gravity theories coupled to form fields and spin-1/2 fermions. Using Hamilton-Jacobi theory we discuss the structure of Ward identities, anomalies,…