Related papers: Supersymmetry and Superfields in Three Euclidean D…
Supersymmetry is deeply related to division algebras. Nonabelian Yang-Mills fields minimally coupled to massless spinors are supersymmetric if and only if the dimension of spacetime is 3, 4, 6 or 10. The same is true for the Green-Schwarz…
We consider the map of three-dimensional N=4 superfields to N=3 harmonic superspace. The left and right representations of the N=4 superconformal group are constructed on N=3 analytic superfields. These representations are convenient for…
Assuming the existence of a field theory in D dimensions dual to (D+1)-dimensional flat space, governed by the asymptotic symmetries of flat space, we make some preliminary remarks about the properties of this field theory. We review…
We explain how the representation theory associated with supersymmetry in diverse dimensions is encoded within the representation theory of supersymmetry in one time-like dimension. This is enabled by algebraic criteria, derived, exhibited,…
In harmonic superspace, the classical equations of motion of $D=4, N=2$ supersymmetric Yang-Mills theory for Minkowski and Euclidean spaces are analyzed. We study dual superfield representations of equations and subsidiary conditions…
We consider supersymmetry in five dimensions, where the fermionic parameters are a 2-form under SL(5). Supermultiplets are investigated using the pure spinor superfield formalism, and are found to be closely related to infinite-dimensional…
Representations of four-dimensional superconformal groups on harmonic superfields are discussed. It is shown how various short representations can be obtained by parabolic induction. It is also shown that such short multiplets may admit…
In this paper we define infinite-dimensional algebra and its representation, whose basis is naturally identified with semi-infinite configurations of the square ladder model. We also extrapolate the ideas for the cyclic 3-leg triangular…
This brief set of notes presents a modest introduction to the basic features entering the construction of supersymmetric quantum field theories in four-dimensional Minkowski spacetime, building a bridge from similar lectures presented at a…
We present an explicit formulation of supersymmetric Yang-Mills theories from $\D=$ 5 to 10 dimensions in the familiar $\N=1,\D=4$ superspace. This provides the rules for globally supersymmetric model building with extra dimensions and in…
We interpret superfields in a functorial formalism that explains the properties that are assumed for them in the physical applications. The starting point of this research was the need to understand in a sound mathematical framework some…
We study supersymmetric field theories in three space-time dimensions doped by various configurations of electric charges or magnetic fluxes. These are supersymmetric avatars of impurity models. In the presence of additional sources such…
As an example of a noncommutative space we discuss the quantum 3-dimensional Euclidean space $R^3_q$ together with its symmetry structure in great detail. The algebraic structure and the representation theory are clarified and discrete…
We give an expanded discussion of the proposal that spacetime supersymmetry representations may be viewed as having their origins in 1D theories that involve a special class of real Clifford algebras. These 1D theories reproduce the…
We generalise the notions of supersymmetry and superspace by allowing generators and coordinates transforming according to more general Lorentz representations than the spinorial and vectorial ones of standard lore. This yields novel…
The N=2 supersymmetric extension of the 2+1 dimensional Abelian Higgs model is discussed. By analysing the resulting supercharge algebra, the connection between supersymmetry and Bogomol'nyi equations is clarified. Analogous results are…
Within the superfield approach, we formulate the superfield supersymmetric aether-like Lorentz-breaking models, both in three- and in four-dimensional cases.
In this text we combine the notions of supergeometry and supersymmetry. We construct a special class of supermanifolds whose reduced manifolds are (pseudo) Riemannian manifolds. These supermanifolds allow us to treat vector fields on the…
Beginning from a discussion of the known most fundamental dynamical structures of the Standard Model of physics, extended into the realms of mathematics and theory by the concept of "supersymmetry" or "SUSY," an introduction to efforts to…
Based on an argument for the noncommutativity of momenta in noncommutative directions, we arrive at a generalization of the ${\cal N}=1$ super $E^2$ algebra associated to the deformation of translations in a noncommutative Euclidean plane.…