Related papers: Higher dimensional higher derivative $\phi^4$ theo…
We study how universality classes of O(N)-symmetric models depend continuously on the dimension d and the number of field components N. We observe, from a renormalization group perspective, how the implications of the…
A discussion of the number of degrees of freedom, and their dynamical properties, in higher derivative gravitational theories is presented. The complete non-linear sigma model for these degrees of freedom is exhibited using the method of…
We renormalize the six dimensional cubic theory with an $O(N)$ $\times$ $O(m)$ symmetry at three loops in the modified minimal subtraction (MSbar) scheme. The theory lies in the same universality class as the four dimensional…
We calculate the critical exponents for Lorentz-violating O($N$) $\lambda\phi^{4}$ scalar field theories by using two independent methods. In the first situation we renormalize a massless theory by utilizing normalization conditions. An…
In 4D renormalisable theories, integrating out massive states generates in the low energy effective action higher dimensional operators (derivative or otherwise). Using a superfield language it is shown that a 4D N=1 supersymmetric theory…
In this paper we consider self interacting scalar quantum field theories over a $d$ dimensional Minkowski spacetime with various interaction Lagrangians which are suitable functions of the field. The interacting field observables are…
We study renormalization group (RG) fixed points of scalar field theories endowed with the discrete symmetry groups of regular polytopes. We employ the functional perturbative renormalization group (FPRG) approach and the…
We revisit the classic $O(N)$ symmetric scalar field theories in $d$ dimensions with interaction $(\phi^i \phi^i)^2$. For $2<d<4$ these theories flow to the Wilson-Fisher fixed points for any $N$. A standard large $N$ Hubbard-Stratonovich…
We review recent activity in the construction of the renormalization group functions for O(N) scalar and gauge theories in six and higher dimensions. The theories lie in their respective universality classes at the Wilson-Fisher fixed…
In a four-dimensional space, I shall construct all of the conformally invariant scalar-tensor field theories, which are flat space compatible; i.e., well-defined and differentiable when evaluated for a flat metric tensor and constant scalar…
We consider the family of renormalizable scalar QFTs with self-interacting potentials of highest monomial $\phi^{m}$ below their upper critical dimensions $d_c=\frac{2m}{m-2}$, and study them using a combination of CFT constraints,…
In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories.…
We discuss the approach of effective field theory on a d-dimensional Euclidean space in a scalar theory with two different mass scales in the presence of flat surfaces. Then considering Dirichlet and Neumann boundary conditions, we…
The multicritical generalizations of the Lee-Yang universality class arise as renormalization-group fixed points of scalar field theories with complex $i\varphi^{2n+1}$ interaction, $n\in\mathbb{N}$, just below their upper critical…
New reparametrisation invariant field equations are constructed which describe $d$-brane models in a space of $d+1$ dimensions. These equations, like the recently discovered scalar field equations in $d+1$ dimensions, are universal, in the…
Finite Euler hierarchies of field theory Lagrangians leading to universal equations of motion for new types of string and membrane theories and for {\it classical} topological field theories are constructed. The analysis uses two main…
We study the condition that the theory is unitary and stable in three-dimensional gravity with most general quadratic curvature, Lorentz-Chern-Simons and cosmological terms. We provide the complete classification of the unitary theories…
Non-Fermi liquids in $d>2$ remain poorly understood, particularly when relevant perturbations destabilize them. In one spatial dimension, chirally stabilized fixed points provide a rare class of analytically tractable non-Fermi-liquid…
There have been some speculations about the existence of critical unitary O(N)-invariant scalar field theories in dimensions 4<d<6 and for large N. Using the functional renormalization group equation, we show that in the lowest order of the…
The wave function in the quantum theory of the O(N) extended supersymmetric particle model describes a massless free field with spin N/2. This quantum theory is here exactly solved in terms of gauge fields in arbitrary even dimensions using…