Related papers: A tale of two SUSYs
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
Below, we summarize the appearances and possible uses of the two-sided approach and the two-sided counting in the most diverse areas of (secondary) school mathematics.
In [arXiv:0808.1677] 3 dimensional field theories are proposed to on-shell represent N=8 SUSY algebra and SO(7) or SO(4)xSO(4) subgroups of full SO(8) automorphism. They are theories of 8 scalar and 8 spinor matrix fields with Yukawa,…
We propose a renormalization group flow with emergent supersymmetry in two dimensions from a non-Lagrangian theory. The ultraviolet theory does not have supersymmetry while the infrared theory does. We constrain the flow both analytically…
These notes are intended to provide an introduction to supersymmetry. The notes begin with supersymmetric quantum mechanics and the basic properties of spinor fields. The supersymmetry of simple theories of spin-zero and spin-one-half…
This preprint deals with the symmetry of parametrized families of systems and the changes therein as the parameter changes. There are (at least ?) two kinds of symmetry: generic and specific which behave in almost totally opposite ways as…
Supersymmetry and Compositeness are two prevalent paradigms providing both a solution to the hierarchy problem and a motivation for a light Higgs boson state. As the latter has now been found, its dynamics can hold the key to disentangle…
We investigate (pseudo)differential forms in the framework of supergeometry. Definitions, basic properties and Cartan calculus (DeRham differential, Lie derivative, inner product, Hodge operator) are presented; the symplectic supermechanics…
These lectures contain an introduction to supersymmetric theories and the minimal supersymmetric standard model. Phenomenological and cosmological consequences of supersymmetry are also discussed.
We formulate a geometric measurement theory of dynamical classical systems possessing both continuous and discrete degrees of freedom. The approach is covariant with respect to choices of clocks and canonically incorporates laboratories.…
A variant of the classical optimal transportation problem is: among all joint measures with fixed marginals and which are dominated by a given density, find the optimal one. Existence and uniqueness of solutions to this variant were…
Elements of supergeometry are an ingredient in many contemporary classical and quantum field models involving odd fields. For instance, this is the case of SUSY field theory, BRST theory, supergravity. Addressing to theoreticians, these…
In these lecture proceedings, we describe some of the fundamental mathematical concepts that underlie supersymmetric string theory and field theory, and their role in describing and testing dualities. In particular, we provide a pedagogical…
Different viewpoints on the asymptotic expansion of Feynman diagrams are reviewed. The relations between the field theoretic and diagrammatic approaches are sketched. The focus is on problems with large masses or large external momenta.…
We relate two formulations of the recently constructed double field theory to a frame-like geometrical formalism developed by Siegel. A self-contained presentation of this formalism is given, including a discussion of the constraints and…
Traditional statistical inference considers relatively small data sets and the corresponding theoretical analysis focuses on the asymptotic behavior of a statistical estimator when the number of samples approaches infinity. However, many…
The problem of building supersymmetry in the quantum mechanics of two Coulombian centers of force is analyzed. It is shown that there are essentially two ways of proceeding. The spectral problems of the SUSY (scalar) Hamiltonians are quite…
Using the superfield formalism and the master action approach, we prove, both at the classical and quantum levels, the dual equivalence between four-dimensional supersymmetric self-dual and topologically massive models coupled to dynamical…
We present the first example of an interacting Carroll supersymmetric field theory with both temporal and spatial derivatives, belonging to the Galileon class, where the non-linear field equation remains second-order in derivative. To…
The random walk to be considered takes place in the d- spherical dual of the group U(n + 1), for a fixed finite dimensional irreducible representation d of U(n). The transition matrix comes from the three term recursion relation satisfied…