Related papers: Regularization of supersymmetric theories - recent…
A new Dimensional Regularization of $\gamma_5$ is proposed. Cyclicity and Lorentz covariance are enforced. The extension to generic dimension is based on the integral representation of the trace of gamma's, presented in a previous paper.
Boson, fermion, and super oscillators and (statistical) mechanism of cosmological constant; finite approximation of the zeta-function and fermion factorization of the bosonic statistical sum considered.
Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…
Recently \cite{Horowitz:2022rpp,Horowitz:2022uak}, denominator regularisation (Den. Reg.) scheme has been proposed to handle divergences in quantum field theory. It is shown to yield results as simple as in dimensional regularisation scheme…
We study gauge hierarchy problem of the Standard Model (SM) not by introducing new physics at the electroweak scale but by utilizing gravitational frames, frames generated by conformal transformations, as a renormalization medium. The…
I quickly review the successes of quantum chromodynamics. Then I assess the current state of the electroweak theory, making brief comments about the search for the Higgs boson and some of the open issues for the theory. I sketch the…
The renormalization of the Minimal Supersymmetric Standard Model is discussed. In particular we focus on the soft-supersymmetry breaking sector of the MSSM and comment on non-renormalization theorems.
I outline some of the challenging issues that could arise in attempting to fully delineate various possible Higgs sectors, with focus on the minimal supersymmetric model, a general two-Higgs-doublet model, and extensions thereof.
Renormalisation group (RG) equations in two-dimensional N=1 supersymmetric field theories with boundary are studied. It is explained how a manifestly N=1 supersymmetric scheme can be chosen, and within this scheme the RG equations are…
The renormalization algorithm based on regularization methods with two regulators is analyzed by means of explicit computations. We show in particular that regularization by higher covariant derivative terms can be complemented with…
The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds…
We analyze the performance of a variant of Newton method with quadratic regularization for solving composite convex minimization problems. At each step of our method, we choose regularization parameter proportional to a certain power of the…
A lattice-type regularization of the supersymmetric field theories on a supersphere is constructed by approximating the ring of scalar superfields by an integer-valued sequence of finite dimensional rings of supermatrices and by using the…
The discovery of a Higgs boson at the electroweak scale appears to point toward supersymmetry, as the most likely mechanism for protecting a scalar boson mass from enormous radiative corrections. The earlier discovery of neutrino masses…
A fairly elementary introduction to supersymmetric field theories in general and the minimal supersymmetric Standard Model (MSSM) in particular is given. Topics covered include the cancellation of quadratic divergencies, the construction of…
This is the first in a series of papers addressing the phenomenon of dimensional transmutation in nonrelativistic quantum mechanics within the framework of dimensional regularization. Scale-invariant potentials are identified and their…
Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.
Regularization is a well studied problem in the context of neural networks. It is usually used to improve the generalization performance when the number of input samples is relatively small or heavily contaminated with noise. The…
We discuss all possible compactifications on flat three-dimensional smooth spaces. In particular, various fields are studied on a box with opposite sides identified, after two of them are rotated by $\pi$, and their spectra are obtained.…
The one-loop radiative corrections to the Higgs boson potential in the MSSM, originating from the top quark and squark loops, are summed in the leading log approximation using the renormalization group. The RG improved effective potential…