Related papers: The F-theorem in the melonic limit
The conclusion of the original paper was wrong, due to the incorrect assumption that the low-energy limit at the strongly-coupled point consists of a single, coupled SCFT. By taking into account the fact that the low-energy limit consists…
It is argued that universality is severely limited for models with multiple fixed points. As a demonstration the renormalization group equations are presented for the potential and the wave function renormalization constants in the $O(N)$…
The matrix model of Kapustin, Willett, and Yaakov is a powerful tool for exploring the properties of strongly interacting superconformal Chern-Simons theories in 2+1 dimensions. In this paper, we use this matrix model to study necklace…
The fundamental theorem in renormalization group flows in two dimensions is the $c$-theorem, which dictates that the number of degrees of freedom must decrease monotonically along the renormalization group flow. The $k$-theorem claims that…
The three dimensional nonlinear sigma model is unrenormalizable in perturbative method. By using the $\beta$ function in the nonperturbative Wilsonian renormalization group method, we argue that ${\cal N}=2$ supersymmetric nonlinear…
We argue that all consistent 4D quantum field theories obey a spacetime-averaged weak energy inequality $\langle T^{00} \rangle \ge -C/L^4$, where $L$ is the size of the smearing region, and $C$ is a positive constant that depends on the…
Smeared null energy has been shown to be bounded from below for free minimally coupled quantum field theories. This is not the case for conformally coupled free bosonic theories where states of unbounded null energy can be constructed by…
We study large N conformal field theories perturbed by relevant double-trace deformations. Using the auxiliary field trick, or Hubbard-Stratonovich transformation, we show that in the infrared the theory flows to another CFT. The generating…
We focus our attention on the one dimensional scalar theories that result from dimensionally reducing the free scalar field theory in arbitrary d dimensions. As is well known, after integrating out the angular coordinates, the free scalar…
We present a proof of the irreversibility of renormalization group flows, i.e. the c-theorem for unitary, renormalizable theories in four (or generally even) dimensions. Using Ward identities for scale transformations and spectral…
We study the functional renormalization group of a three-dimensional tensorial Group Field Theory (GFT) with gauge group SU(2). This model generates (generalized) lattice gauge theory amplitudes, and is known to be perturbatively…
We study the dimensional continuation of the sphere free energy in conformal field theories. In continuous dimension $d$ we define the quantity $\tilde F=\sin (\pi d/2)\log Z$, where $Z$ is the path integral of the Euclidean CFT on the…
We consider free higher derivative theories of scalars and Dirac fermions in the presence of a boundary in general dimension. We establish a method for finding consistent conformal boundary conditions in these theories by removing certain…
The existence of an exactly marginal deformation in a conformal field theory is very special, but it is not well understood how this is reflected in the allowed dimensions and OPE coefficients of local operators. To shed light on this…
The properties of strongly gravitating systems suggest that field theory overcounts the states of a system. Reducing the number of degrees of freedom, without abandoning the notion of effective field theory, may be achieved through a…
We investigate possible renormalization-group fixed points at nonzero coupling in $\phi^3$ theories in six spacetime dimensions, using beta functions calculated to the four-loop level. We analyze three theories of this type, with (a) a…
In the limit where $N\to\infty$ and the coupling constant $g \to g_{c}$ in a correlated manner, O(N) symmetric vector models represent filamentary surfaces. The purpose of these studies is to gain intuition for the long lasting search for a…
We show irreversibility of the renormalization group flow in non-unitary but ${\cal PT}$-invariant quantum field theory in two space-time dimensions. In addition to unbroken $\mathcal{PT}$-symmetry and a positive energy spectrum, we assume…
When studying the collective motion of biological groups a useful theoretical framework is that of ferromagnetic systems, in which the alignment interactions are a surrogate of the effective imitation among the individuals. In this context,…
We show that renormalized non-commutative scalar field theories do not reduce to their planar sector in the limit of large non-commutativity. This follows from the fact that the RG equation of the Wilson-Polchinski type which describes the…