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The one-loop beta functions for systems of $N_s$ scalars and $N_f$ fermions interacting via a general potential are analysed as tensorial equations in $4-\varepsilon$ dimensions. Two distinct bounds on combinations of invariants constructed…
We study the beta functions for the dimensionless couplings in quadratic curvature gravity, and find that there is a simple argument to restrict the possible form of the beta functions as derived from the counterterms at an arbitrary loop.…
We present the supersymmetric standard model three-loop $\beta$-functions for gauge and Yukawa couplings and consider the effect of three-loop corrections on the standard running coupling analyses.
The reduction of couplings idea consists in the search for renormalization group invariant relations between seemingly independent parameters of a theory that hold to all orders of perturbation theory. This concept can be applied to $N=1$…
We show that the renormalization group beta functions in the Nambu-Jona-Lasinio model identically vanish in all order due to the compositeness condition. Accordingly the effective coupling constants are entirely fixed and do not run with…
We compute the one-loop gauge couplings in six-dimensional non-Abelian gauge theories on the T^2/Z_2 orbifold with general GUT breaking boundary conditions. For concreteness, we apply the obtained general formulae to the gauge coupling…
Field theories with weakly coupled holographic duals, such as large N gauge theories, have a natural separation of their operators into `single-trace operators' (dual to single-particle states) and `multi-trace operators' (dual to…
In grand unified theories (GUT) based on SO(10) all fermions of one generation are embedded in a single representation. As a result, the top quark, the bottom quark, and the $\tau$ lepton have a universal Yukawa coupling at the GUT scale.…
We study the U(N) non-commutative Yang-Mills theory at the one-loop approximation. We check renormalizability and gauge invariance of the model and calculate the one-loop beta function. The interaction of the SU(N) gauge bosons with the…
In a supersymmetric model where R-Parity and lepton number are violated bilinearly in the superpotential, which can explain the solar and atmospheric neutrino problems, we study the unification of gauge and Yukawa couplings at the GUT…
One of the main advantages of super-renormalizable higher derivative quantum gravity models is the possibility to derive exact beta functions, by making perturbative one-loop calculations. We perform such a calculation for the Newton…
We calculate the two-loop matching corrections for the gauge couplings at the Grand Unification scale in a general framework that aims at making as few assumptions on the underlying Grand Unified Theory (GUT) as possible. In this paper we…
Starting from a consistency requirement between T-duality symmetry and renormalization group flows, the two-loop metric beta function is found for a d=2 bosonic sigma model on a generic, torsionless background. The result is obtained…
We study the quantum properties of two theories with a non-anticommutative (or nilpotent) chiral singlet deformation of N=(1,1) supersymmetry: the abelian model of a vector gauge multiplet and the model of a gauge multiplet interacting with…
A possible generalization of the technique of the standard model to $SU(n)\otimes U(1)$ gauge models is proposed. A special Higgs mechanism and a new kind of Yukawa couplings in unitary gauge are introduced. These allow us to obtain a…
We prove that the beta function of the Grosse-Wulkenhaar model including a magnetic field vanishes at all order of perturbations. We compute the renormalization group flow of the relevant dynamic parameters and find a non-Gaussian infrared…
In four-dimensional theories with massless particles, the one-loop amplitudes can be expressed in terms of a basis of scalar integrals and rational terms. Since the scalar bubble integrals are the only UV divergent integrals, the sum of the…
Gauge-Yukawa Unification (GYU) is a renormalization group invariant functional relation among gauge and Yukawa couplings which holds beyond the unification point in Grand Unified Theories (GUTs). Here, GYU is obtained by requiring…
We give a review of the one-loop divergences in higher derivative gravity theories. We first make the bilinear expansion in the quantum fluctuation on arbitrary backgrounds, introduce a higher-derivative gauge fixing and show that…
We investigate defects in scalar field theories in four and six dimensions in a double-scaling (semiclassical) limit, where bulk loops are suppressed and quantum effects come from the defect coupling. We compute $\beta $-functions up to…