TY - JOUR

T1 - Minimal unitary representation of SO*(8)=SO(6,2) and its SU(2) deformations as massless 6D conformal fields and their supersymmetric extensions

AU - Fernando, Sudarshan

AU - Günaydin, Murat

N1 - Funding Information:
This work was supported in part by the National Science Foundation under grants numbered PHY-0555605 and PHY-0855356 . Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation .

PY - 2010/12

Y1 - 2010/12

N2 - We study the minimal unitary representation (minrep) of SO(6,2) over an Hilbert space of functions of five variables, obtained by quantizing its quasiconformal realization. The minrep of SO(6,2), which coincides with the minrep of SO*(8) similarly constructed, corresponds to a massless conformal scalar field in six spacetime dimensions. There exists a family of "deformations" of the minrep of SO*(8) labeled by the spin t of an SU(2)T subgroup of the little group SO(4) of lightlike vectors. These deformations labeled by t are positive energy unitary irreducible representations of SO*(8) that describe massless conformal fields in six dimensions. The SU(2)T spin t is the six-dimensional counterpart of U(1) deformations of the minrep of 4D conformal group SU(2,2) labeled by helicity. We also construct the supersymmetric extensions of the minimal unitary representation of SO*(8) to minimal unitary representations of OSp(8*|2N) that describe massless six-dimensional 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 AdS7×S4.

AB - We study the minimal unitary representation (minrep) of SO(6,2) over an Hilbert space of functions of five variables, obtained by quantizing its quasiconformal realization. The minrep of SO(6,2), which coincides with the minrep of SO*(8) similarly constructed, corresponds to a massless conformal scalar field in six spacetime dimensions. There exists a family of "deformations" of the minrep of SO*(8) labeled by the spin t of an SU(2)T subgroup of the little group SO(4) of lightlike vectors. These deformations labeled by t are positive energy unitary irreducible representations of SO*(8) that describe massless conformal fields in six dimensions. The SU(2)T spin t is the six-dimensional counterpart of U(1) deformations of the minrep of 4D conformal group SU(2,2) labeled by helicity. We also construct the supersymmetric extensions of the minimal unitary representation of SO*(8) to minimal unitary representations of OSp(8*|2N) that describe massless six-dimensional 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 AdS7×S4.

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U2 - 10.1016/j.nuclphysb.2010.07.001

DO - 10.1016/j.nuclphysb.2010.07.001

M3 - Article

AN - SCOPUS:77956649899

VL - 841

SP - 339

EP - 387

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -