SU(2) deformations of the minimal unitary representation of OSp(8*|2N) as massless 6D conformal supermultiplets

Abstract

Minimal unitary representation of SO*(8) = SO(6,2) realized over the Hilbert space of functions of five variables and its deformations labeled by the spin t of an SU(2) subgroup correspond to massless conformal fields in six dimensions as was shown in arXiv:1005.3580. In this paper we study the minimal unitary supermultiplet of OSp(8*|2N) with the even subgroup SO*(8) x USp(2N) and its deformations using quasiconformal methods. We show that the minimal unitary supermultiplet of OSp(8*|2N) admits deformations labeled uniquely by the spin t of an SU(2) subgroup of the little group SO(4) of lightlike vectors in six dimensions. We construct the deformed minimal unitary representations and show that they correspond to massless 6D conformal supermultiplets. The minimal unitary supermultiplet of OSp(8*|4) is the massless supermultiplet of (2,0) conformal field theory that is believed to be dual to M-theory on AdS_7 x S^4. We study its deformations in further detail and show that they are isomorphic to the doubleton supermultiplets constructed by using twistorial oscillators.

arXiv comment40 pages; Latex file

References in corpus (25)

• Gauge Theory Correlators from Non-Critical String Theory
• Orbits of Exceptional Groups, Duality and BPS States in String Theory
• Conformal and Quasiconformal Realizations of Exceptional Lie Groups
• 4D Doubleton Conformal Theories, CPT and IIB String on AdS_5 X S^5
• Analysis on the minimal representation of O(p,q) -- III. ultrahyperbolic equations on R^{p-1,q-1}
• A quantum exactly solvable non-linear oscillator related with the isotonic oscillator
• BPS black holes, quantum attractor flows and automorphic forms
• Novel supermultiplets of SU(2,2|4) and the AdS_5/CFT_4 duality
• Minimal representations, spherical vectors, and exceptional theta series I
• Quantum Attractor Flows
• Analysis on the minimal representation of O(p,q) -- II. Branching laws
• Analysis on the minimal representation of O(p,q) -- I. Realization via conformal geometry
• Generalized spacetimes defined by cubic forms and the minimal unitary realizations of their quasiconformal groups
• Unitary Realizations of U-duality Groups as Conformal and Quasiconformal Groups and Extremal Black Holes of Supergravity Theories
• Minimal unitary representation of SU(2,2) and its deformations as massless conformal fields and their supersymmetric extensions
• Quasi-conformal actions, quaternionic discrete series and twistors: SU(2,1) and G_2(2)
• A Unified Approach to the Minimal Unitary Realizations of Noncompact Groups and Supergroups
• Positive energy unitary irreducible representations of D=6 conformal supersymmetry
• Minimal Unitary Realizations of Exceptional U-duality Groups and Their Subgroups as Quasiconformal Groups
• Unitary Supermultiplets of OSp(8^*|4) and the AdS_7/CFT_6 Duality
• Representations of superconformal algebras in the AdS_7/4/CFT_6/3 correspondence
• Supercoherent States of OSp(8*|2N), Conformal Superfields and the AdS_7/CFT_6 Duality
• Minimal unitary representation of SO*(8) = SO(6,2) and its SU(2) deformations as massless 6D conformal fields and their supersymmetric extensions
• The so(d+2,2) Minimal Representation and Ambient Tractors: the Conformal Geometry of Momentum Space
• Realizations of exceptional U-duality groups as conformal and quasiconformal groups and their minimal unitary representations

Cited by in corpus (7)

• Superconformal symmetry and maximal supergravity in various dimensions
• Deformed Twistors and Higher Spin Conformal (Super-)Algebras in Six Dimensions
• Massless conformal fields, AdS_{d+1}/CFT_d higher spin algebras and their deformations
• Minimal unitary representation of D(2,1;λ) and its SU(2) deformations and d=1, N=4 superconformal models
• Minimal unitary representation of 5d superconformal algebra F(4) and AdS_6/CFT_5 higher spin (super)-algebras
• Quasiconformal Group Approach to Higher Spin Algebras, their Deformations and Supersymmetric Extensions
• Massless chiral fields in six dimensions