Title: Minimal unitary representation of 5d superconformal algebra $F\left(4\right)$ and ${\mathit{AdS}}_6/{\mathit{CFT}}_5$ higher spin (super)-algebras

Abstract

We study the minimal unitary representation (minrep) of SO(5, 2), obtained by quantization of its geometric quasiconformal action, its deformations and supersymmetric extensions. The minrep of SO(5, 2) describes a massless conformal scalar field in five dimensions and admits a unique “deformation” which describes a massless conformal spinor. Scalar and spinor minreps of SO(5, 2) are the 5d analogs of Dirac’s singletons of SO(3, 2). We then construct the minimal unitary representation of the unique 5d supercon-formal algebra F(4) with the even subalgebra SO(5, 2) ×SU(2). The minrep of F(4) describes a massless conformal supermultiplet consisting of two scalar and one spinor fields. We then extend our results to the construction of higher spin AdS₆/CFT₅ (super)-algebras. The Joseph ideal of the minrep of SO(5, 2) vanishes identically as operators and hence its enveloping algebra yields the AdS₆/CFT₅ bosonic higher spin algebra directly. The enveloping algebra of the spinor minrep defines a “deformed” higher spin algebra for which a deformed Joseph ideal vanishes identically as operators. These results are then extended to the construction of the unique higher spin AdS₆/CFT₅ superalgebra as the enveloping algebra of the minimal unitary realization of F(4) obtained by the quasiconformal methods.

Authors:

Fernando, Sudarshan; Günaydin, Murat

Publication Date:

Thu Jan 01 00:00:00 EST 2015

Research Org.:

Pennsylvania State Univ., University Park, PA (United States)

Sponsoring Org.:

USDOE Office of Science (SC)

OSTI Identifier:

1228325

Alternate Identifier(s):

OSTI ID: 1203557

Grant/Contract Number:  

SC0010534

Resource Type:

Published Article

Journal Name:

Nuclear Physics. B

Additional Journal Information:

Journal Name: Nuclear Physics. B Journal Volume: 890 Journal Issue: C; Journal ID: ISSN 0550-3213

Publisher:

Elsevier

Country of Publication:

Netherlands

Language:

English

Subject:

97 MATHEMATICS AND COMPUTING