skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Minimal unitary representation of 5d superconformal algebra F ( 4 ) and AdS 6 / CFT 5 higher spin (super)-algebras

Journal Article · · Nuclear Physics. B
;

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.

Research Organization:
Pennsylvania State Univ., University Park, PA (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
SC0010534
OSTI ID:
1228325
Alternate ID(s):
OSTI ID: 1203557
Journal Information:
Nuclear Physics. B, Journal Name: Nuclear Physics. B Vol. 890 Journal Issue: C; ISSN 0550-3213
Publisher:
ElsevierCopyright Statement
Country of Publication:
Netherlands
Language:
English
Citation Metrics:
Cited by: 6 works
Citation information provided by
Web of Science

References (27)

Masslessness in n-Dimensions journal April 1998
F (4) supergravity and 5D superconformal field theories journal August 2001
deformations of the minimal unitary representation of as massless 6D conformal supermultiplets journal February 2011
Massless representations and admissibility condition for higher spin superalgebras journal January 1989
Unitary supermultiplets of and the AdS7/CFT6 duality journal July 2000
Conformal invariance in quantum mechanics journal August 1976
AdS6 interpretation of 5D superconformal field theories journal July 1998
Minimal unitary representation of SU(2,2) and its deformations as massless conformal fields and their supersymmetric extensions journal August 2010
The minimal orbit in a simple Lie algebra and its associated maximal ideal journal January 1976
A quantum exactly solvable nonlinear oscillator related to the isotonic oscillator journal February 2008
General construction of the unitary representations of anti-de sitter superalgebras and the spectrum of the S4 compactification of 11-dimensional supergravity journal January 1985
The spectrum of the S 5 compactification of the chiral N=2, D=10 supergravity and the unitary supermultiplets of U(2,2/4) journal March 1985
The Cartan Product journal March 2005
Solution of the One‐Dimensional N ‐Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials journal March 1971
The large $N$ limit of superconformal field theories and supergravity journal January 1998
Minimal realizations and spectrum generating algebras journal December 1974
Minimal unitary representation of and its deformations as massless 6D conformal fields and their supersymmetric extensions journal December 2010
The minimal unitary representation of $E_{8(8)}$ journal January 2001
A unified approach to the minimal unitary realizations of noncompact groups and supergroups journal September 2006
Lower Bounds to the Ground‐State Energy of Systems Containing Identical Particles journal April 1969
Matter coupled F(4) supergravity and the AdS 6 / CFT 5 correspondence journal October 2000
Higher symmetries of the Laplacian journal January 2005
AdS6/CFT5 Correpondence for F(4) Supergravity journal May 2001
Generalized spacetimes defined by cubic forms and the minimal unitary realizations of their quasiconformal groups journal August 2005
On a novel supersymmetric connections between harmonic and isotonic oscillators journal August 1995
Deformed twistors and higher spin conformal (super-)algebras in six dimensions journal July 2014
Cubic interaction in extended theories of massless higher-spin fields journal January 1987

Similar Records

Deformed twistors and higher spin conformal (super-)algebras in four dimensions
Journal Article · Thu Mar 05 00:00:00 EST 2015 · Journal of High Energy Physics (Online) · OSTI ID:1228325
Massless conformal fields, AdS(+1)/CFT higher spin algebras and their deformations
Journal Article · Tue Mar 01 00:00:00 EST 2016 · Nuclear Physics. B · OSTI ID:1228325
Finite-Temperature Conformal Field Theory Results for All Couplings: O ( N ) Model in 2 + 1 Dimensions
Journal Article · Fri Jun 14 00:00:00 EDT 2019 · Physical Review Letters · OSTI ID:1228325

Related Subjects

97 MATHEMATICS AND COMPUTING