Related papers: Unidexterously Constrained Worldsheet Superfields
A rigidity theory is developed for frameworks in a metric space with two types of distance constraints. Mixed sparsity graph characterisations are obtained for the infinitesimal and continuous rigidity of completely regular bar-joint…
We obtain by superfield methods the exceptional representations of the OSp(2N/4,R) and SU(2,2/1) superalgebras which extend to supersingletons of SU(2,2/2N) and F(4), respectively. These representations describe superconformally coupled…
The notion of hidden symmetry algebra used in the context of exactly solvable systems is re-examined from the purely algebraic way, analyzing subspaces of commuting polynomials that generate finite-dimensional quadratic algebras. By…
The chiral algebra of a 4D $N\geq2$ superconformal field theory is a vertex operator algebra generated by the Schur subsector of the 4D theory and its rigid (yet rich) structure has been useful in constraining and classifying 4D N=2 SCFTs.…
The mirror map in the D=3, N=4 supersymmetry connects the left and right SU(2) automorphism groups and also the superfield representations of the corresponding N=4 supermultiplets. The mirror N=4 harmonic superspaces use the harmonics of…
In recent years it has been recognized that the hyperbolic numbers (an extension of complex numbers, defined as z=x+h*y with h*h=1 and x,y real numbers) can be associated to space-time geometry as stated by the Lorentz transformations of…
These notes consist of a study of special Lagrangian submanifolds of Calabi-Yau manifolds and their moduli spaces. The particular case of three dimensions, important in string theory, allows us to introduce the notion of gerbes. These offer…
This is the first of two papers devoted to the local "metric-like" unconstrained Lagrangians and field equations for higher-spin gauge fields of mixed symmetry in flat space. Here we complete the previous constrained formulation of…
The article is devoted to some ``strange'' phenomena of representation theory and their interrelations. Cross-projective representations of pairs of anticommutative algebras, alloys, their universal envelopping Lie algebras and their…
This thesis is dedicated to the study of the geometry of six-dimensional superspace, endowed with the minimal amount of supersymmetry. In the first part of it, we unfold the main geometrical features of such superspace by solving completely…
Compactifications of the heterotic string are a viable route to phenomenologically realistic vacua and interesting new mathematics. While supergravity aspects of heterotic compactifications are largely well-understood their worldsheet…
It is shown that for N=2 supersymmetry a hidden symmetry arises from the hybrid structure of a quartic algebra. The implications for invariant Lagrangians and multiplets are explored.
Derived geometry provides powerful tools to handle non-transverse intersections and singular moduli problems arising in geometry and theoretical physics. While derived algebraic geometry has been extensively developed, classical field…
We consider ways in which conventional supersymmetry can be embedded in the set of more general fermionic transformations proposed recently [\Ref{B}] as a framework in which to study $d=10$ super Yang-Mills. Solutions are exhibited which…
We introduce a new combinatorial abstraction for the graphs of polyhedra. The new abstraction is a flexible framework defined by combinatorial properties, with each collection of properties taken providing a variant for studying the…
Superstring compactifications have been vigorously studied for over four decades, and have flourished involving an active iterative feedback between physics and (complex) algebraic geometry. This led to an unprecedented wealth of…
We examine super symmetric representations of the B-type Hecke algebra. We exploit such representations to obtain new non-diagonal solutions of the reflection equation associated to the super algebra U_q(gl(m|n)). The boundary super algebra…
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…
Studying a quantum field theory involves a choice of space-time manifold and a choice of background for any global symmetries of the theory. We argue that many more choices are possible when specifying the background. In the context of…
A four dimensional non-trivial extension of the Poincar\'e algebra different from supersymmetry is explicitly studied. Representation theory is investigated and an invariant Lagrangian is exhibited. Some discussion on the Noether theorem is…