Related papers: Anomaly cancellation for a $U(1)$ factor
In the framework of supersymmetric Grand Unified Theories, the minimal Higgs sector is often extended by introducing multi-dimensional Higgs representations in order to obtain realistic models. However these constructions should remain…
The universal enveloping algebra $\mathscr{U}$ of a two-dimensional nonabelian Lie algebra $L$ is a Lie algebra itself with the commutator as Lie bracket. There exists a presentation of $\mathscr{U}$ with generators $x,y$ and relation…
The weak currents with respect to the diagonal neutral bosons $Z$,$Z^{\prime}$, and $Z^{\prime\prime}$ of a specific \textbf{$SU(4)_{L}\otimes U(1)_{Y}$} gauge model are computed in detail for all the fermion families involved therein. Our…
${{\cal N}=4}$ supergravity is understood to contain a $U(1)$ anomaly which manifests itself via the nonvanishing of loop-level scattering amplitudes that violate a tree-level charge conservation rule. In this letter we provide detailed…
We apply the path-integral formalism to compute the anomalies in general orbifold gauge theories (including possible non-trivial Scherk-Schwarz boundary conditions) where a gauge group G is broken down to subgroups H_f at the fixed points…
We reinterpret anomaly-mediated supersymmetry breaking from a field-theoretic perspective in which superconformal anomalies couple to either the chiral compensator or the $U(1)_R$ vector superfield. As supersymmetry in the hidden sector is…
All results concern characteristic 2. Two procedures that to every simple Lie algebra assign simple Lie superalgebras, most of the latter new, are offered. We prove that every simple finite-dimensional Lie superalgebra is obtained as the…
We extend our recently-proposed formalism for calculating anomalies of global and gauge symmetries using the Covariant Derivative Expansion to include a general class of operators that can appear in relativistic Effective Field Theories…
We obtain a characterization of the real Lie algebras admitting abelian complex structures in terms of certain affine Lie algebras $\frak a \frak f \frak f (A)$, where $A$ is a commutative algebra. These affine Lie algebras are natural…
In this paper, we investigate finite-dimensional irreducible representations of the quantum affine general linear superalgebra $\mathrm{U}_q\big(\widehat{\mathfrak{gl}}_{m|n,\mathbf{s}}\big)$ for arbitrary 01-sequences $\mathbf{s}$, using…
We discuss the generalization to global gauge anomalies of the familiar procedure for the cancellation of local gauge anomalies in effective theories of spontaneously broken symmetries. We illustrate this mechanism in a recently proposed…
The Zariski cancellation problem plays a central role in affine algebraic geometry and noncommutative algebra, with locally nilpotent derivations providing a fundamental invariant-theoretic approach. This article presents a unified survey…
We discuss supersymmetric $SU(2)$ gauge theory with a single matter field in the $I=3/2$ representation. This theory has a moduli space of exactly degenerate vacua. Classically it is the complex plane with an orbifold singularity at the…
We present a supersymmetric standard model with three gauged Abelian symmetries, of a type commonly found in superstrings. One is anomalous, the other two are $E_6$ family symmetries. It has a vacuum in which only these symmetries are…
We prove that global anomaly cancellation requires more than one generation of quarks and leptons, provided that the standard model fields propagate in two universal extra dimensions. Furthermore, if the fermions of different generations…
In a minimal extension of the Standard Model, in which new neutral fermions have been introduced, we show that the requirement of vanishing anomalies fixes the hypercharges of all fermions uniquely. This naturally leads to electric charge…
On-shell Pauli-Villars regularization of the one-loop divergences of supergravity theories is used to study the anomaly structure of supergravity and the cancellation of field theory anomalies under a $U(1)$ gauge transformation and under…
For supersymmetric gauge theories with eight supercharges in four, five and six dimensions, a conserved current belongs to the linear multiplet. In the case of six-dimensional $\cal N=(1,0)$ Poincar\'e supersymmetry, we present a consistent…
We show that there exist supersymmetric solutions of five-dimensional, pure, $\mathcal{N}=1$ Supergravity such that the norm of the supersymmetric Killing vector, built out of the Killing spinor, is a real not-everywhere analytic function…
We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation…