Related papers: A challenge to the $a$-theorem in six dimensions
The existence of an Almeida-Thouless (AT) instability surface below the upper critical dimension 6 is demonstrated in the generic replica symmetric field theory. Renormalization flows from around the zero-field fixed point are investigated.…
Recently, evidence was provided for the existence of an $a$-function for renormalisable quantum field theories in three dimensions. An explicit expression was given at lowest order for general theories involving scalars and fermions, and…
Recently, a topological field theory of membrane-matter coupled to BF theory in arbitrary spacetime dimensions was proposed [1]. In this paper, we discuss various aspects of the four-dimensional theory. Firstly, we study classical solutions…
We study a three-dimensional abelian lattice model in which the analogue of a theta term can be defined. This term is defined by introducing a neutral scalar field and its effect is to couple magnetic monopoles to the scalar field and…
The existing observational data on possible variations of fundamental physical constants (FPC) confirm more or less confidently only a variability of the fine structure constant $\alpha$ in space and time. A model construction method is…
The general form of the stress-tensor three-point function in four dimensions is obtained by solving the Ward identities for the diffeomorphism and Weyl symmetries. Several properties of this correlator are discussed, such as the…
The presence of a cosmological constant, Lambda, in an action with higher powers of the curvature can produce rapidly oscillating metrics. We develop a perturbative approach for generating periodic solutions to the non-linear field…
The structure of the QFT expansion is studied in the framework of a new "Invariant analytic" version of the perturbative QCD. Here, an invariant (running) coupling $a(Q^2/\Lambda^2)=\beta_1\alpha_s(Q^2)/4\pi$ is transformed into a…
Modified Newtonian dynamics can be considered as an effect derived from a squeezable extra dimension space. The third law of Newtonian dynamics can be managed to remain valid in the 5-space. The critical acceleration parameter $a_0$ appears…
There is a general notion of the magnitude of an enriched category, defined subject to hypotheses. In topological and geometric contexts, magnitude is already known to be closely related to classical invariants such as Euler characteristic…
We consider filtrations of objects in an abelian category $\catA$ induced by a tilting object $T$ of homological dimension at most two. We define three disjoint subcategories with no maps between them in one direction, such that each object…
The possibility of physics in multiple time dimensions is investigated. Drawing on recent work by Walter Craig and myself, I show that, contrary to conventional wisdom, there is a well-posed initial value problem--deterministic, stable…
In an earlier paper Almeida and Frenkel considered the calculation of the pressure in g\phi^3 theory in 6 dimensions via the Schwinger--Dyson equation. They found, under certain approximations, that a finite result ensues in the infrared…
We consider a scalar quantum field $\phi$ with arbitrary polynomial self-interaction in perturbation theory. If the field variable $\phi$ is repaced by a local diffeomorphism $\phi(x) = \rho(x) + a_1 \rho^2(x) +\ldots$, this field $\rho$…
Let f be a C1 bivariate function with Lipschitz derivatives, and F = {x $\in$ R2 : f(x) $\lambda$} an upper level set of f, with $\lambda$ $\in$ R. We present a new identity giving the Euler characteristic of F in terms of its three-points…
We study, using Mean Curvature Flow methods, 2+1 dimensional cosmologies with a positive cosmological constant and matter satisfying the dominant and the strong energy conditions. If the spatial slices are compact with non-positive Euler…
In this paper I shall consider field theories in a space of four-dimensions which have field variables consisting of the components of a metric tensor and scalar field. The field equations of these scalar-tensor field theories will be…
In this paper, we study the evolution of smooth, closed planar curves under a fourth order biharmonic flow with an external forcing term. Such flows arise naturally in the theory of biharmonic maps and geometric variational problems…
We perform an all-order resurgence analysis of a quantum field theory renormalon that contributes to an anomalous dimension in six-dimensional scalar $\phi^3$ theory and is governed by a third-order nonlinear differential equation. We…
The effects of three-dimensional perturbations in two-dimensional turbulence are investigated, through a conformal field theory approach. We compute scaling exponents for the energy spectra of enstrophy and energy cascades, in a strong…