Related papers: Large N flavor beta-functions: a recap
Motivated mainly by certain interesting recent extensions of the Gamma, Beta and hypergeometric functions, we introduce here new extensions of the Beta function, hypergeometric and confluent hypergeometric functions. We systematically…
Several expansions of the solutions to the confluent Heun equation in terms of incomplete Beta functions are constructed. A new type of expansion involving certain combinations of the incomplete Beta functions as expansion functions is…
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…
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…
For every natural number k we introduce the notion of k-th order convolution of functions on abelian groups. We study the group of convolution preserving automorphisms of function algebras in the limit. It turns out that such groups have…
We present calculations of certain limits of scheme-independent series expansions for the anomalous dimensions of gauge-invariant fermion bilinear operators and for the derivative of the beta function at an infrared fixed point in SU($N_c$)…
We consider SU(2) gauge potentials over a space with a compactified dimension. A non-Abelian Fourier transform of the gauge potential in the compactified dimension is defined in such a way that the Fourier coefficients are (almost) gauge…
We report new results on the conformal properties of an important strongly coupled gauge theory, a building block of composite Higgs models beyond the Standard Model. With twelve massless fermions in the fundamental representation of the…
We present general four-loop template $\beta$-functions and anomalous field dimensions for renormalisable scalar-fermion theories in three dimensions. By imposing $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetry, we obtain relations…
We study the addition of flavor degrees of freedom to the supergravity dual of the non-commutative deformation of the maximally supersymmetric gauge theories. By considering D7 flavor branes in the probe approximation and studying their…
We study new supergravity solutions related to large-$N_c$ ${\cal N}=1$ supersymmetric gauge field theories with a large number $N_f$ of massive flavors. We use a recently proposed framework based on configurations with $N_c$ color D5…
In this paper we discuss some aspects of the behavior of superconformal N=1 models under Seiberg's duality. Our claim is that if an electric gauge theory is superconformal on some marginal subspace of all coupling constants then its…
The abelian projection in SU(N) gauge theories is discussed in detail, as well as the construction of a disorder parameter to study dual superconductivity as a mechanism for color confinement. If the ideas of the large N limit are correct,…
We consider a large class of models where an SU(5) gauge symmetry and a Froggatt-Nielsen (FN) Abelian flavor symmetry arise from a quiver gauge theory. Such quiver models are very restrictive and therefore have strong predictive power. In…
In this paper we study the effects of a nonzero chemical potential in the effective action for massless fermions in (1+1) dimensions in an abelian gauge field background at finite temperature. We calculate the n-point function and show that…
We compute at the one-loop order the beta-functions for a renormalisable non-commutative analog of the Gross Neveu model defined on the Moyal plane. The calculation is performed within the so called x-space formalism. We find that this…
In differential geometry, the notation d^n f along with the corresponding formalism has fallen into disuse since the birth of exterior calculus. However, differentials of higher order are useful objects that can be interpreted in terms of…
Ultrafunctions are a particular class of functions defined on a Non Archimedean field E. They have been introduced and studied in some previous works. In this paper we develop the notion of fine ultrafunctions which improves the older…
We consider the resolvent of a system of first order differential operators with a regular singularity, admitting a family of self-adjoint extensions. We find that the asymptotic expansion for the resolvent in the general case presents…
The dynamics of high temperature gauge fields, on scales relevant for non-perturbative phenomena such as electroweak baryogenesis, may be described by a remarkably simple effective theory. This theory, which takes the form of a local,…