Related papers: Superconformal symmetry and representations
In this white paper we summarise the construction and applications of lattice theories possessing exact supersymmetry focusing, in particular, on N=4 Yang-Mills theory. Lattice formulations of this theory allow for numerical simulation of…
We discuss two different nonlinear generalizations of the osp(2|2) supersymmetry which arise in superconformal mechanics and fermion-monopole models.
We present a symbolic method for organizing the representation theory of one-dimensional superalgebras. This relies on special objects, which we have called adinkra symbols, which supply tangible geometric forms to the still-emerging…
Conformal field theory of the D1/D5 system and superstrings on $AdS_3\times S^3\times T^4$ is studied with particular attention to the world-sheet fields corresponding to the $T^4$ part. A solution to the spacetime N=4 superconformal…
In this essay we give an introduction to conformal symmetry, based on the example of the Yamabe operator and its use in conformal differential geometry, and in representation theory.
Superconformal blocks and crossing symmetry equations are among central ingredients in any superconformal field theory. We review the approach to these objects rooted in harmonic analysis on the superconformal group that was put forward in…
In these lectures my aim is to review enough of conformal differential geometry in four dimensions to give an account of Penrose's conformal cyclic geometry.
Representations of four-dimensional superconformal groups on harmonic superfields are discussed. It is argued that any representation can be given as a superfield on many superflag manifolds. Representations on analytic superspaces do not…
In this paper we continue the study of representation theory of formal distribution Lie superalgebras initiated in q-alg/9706030. We study finite Verma-type conformal modules over the N=2, N=3 and the two N=4 superconformal algebras and…
We study briefly some properties of real Clifford algebras and identify them as matrix algebras. We then show that the representation space on which Clifford algebras act are spinors and we study in details matrix representations. The…
Semichiral $(2,2)$ sigma models with $4d$ target space are discussed. A novel description in $(1,1)$ superspace allows an analysis of possible extended supersymmetries. It is argued that a manifest semichiral realization of an extra…
N=1, d=4 superconformal group is studied and its representations are discussed. Under superconformal transformations, left invariant derivatives and some class of superfields, including supercurrents, are shown to follow these…
An overview of supersymmetry and its different applications is presented. We motivate supersymmetry in particle physics. We then explain how supersymmetry helps us analyze field theories exactly, and what dynamical lessons these solutions…
The Galilean conformal algebra has recently been realised in the study of the non-relativistic limit of the AdS/CFT conjecture. This was obtained by a systematic parametric group contraction of the parent relativistic conformal field…
We present part of our investigations on two dimensional N=1 and N=2 superconformal field theories. As a direct generalization we consider the SU(2) coset models, in particular their renormalization group properties. A search and possible…
We present the explicit superfield realizations of the hidden $SU(4)$ and $O(5)$ $R$-symmetries in $4D, {\cal N}=4$ and $5D, {\cal N}=2$ supersymmetric Yang-Mills theories in the harmonic superspace approach. The $R$-symmetry…
Superconformal geometries in spacetime dimensions $D=3,4,{5}$ and $6$ are discussed in terms of local supertwistor bundles over standard superspace. These natually admit superconformal connections as matrix-valued one-forms. In order to…
We consider bosonic supersymmetric backgrounds of ten-dimensional conformal supergravity. Up to local conformal isometry, we classify the maximally supersymmetric backgrounds, determine their conformal symmetry superalgebras and show how…
We give explicitly the reduction of supersymmetries of the positive energy unitary irreducible representations of the N-extended D=4 conformal superalgebras su(2,2/N). Further we give the classification of BPS and possibly protected states.
We determine the dimensions of the irreducible representations of the Sklyanin algebras with global dimension 3. This contributes to the study of marginal deformations of the N=4 super Yang-Mills theory in four dimensions in supersymmetric…