Deformed twistors and higher spin conformal (super-)algebras in four dimensions
Abstract
Massless conformal scalar field in d = 4 corresponds to the minimal unitary representation (minrep) of the conformal group SU(2, 2) which admits a one-parameter family of deformations that describe massless fields of arbitrary helicity. The minrep and its deformations were obtained by quantization of the nonlinear realization of SU(2, 2) as a quasiconformal group in arXiv:0908.3624. We show that the generators of SU(2,2) for these unitary irreducible representations can be written as bilinears of deformed twistorial oscillators which transform nonlinearly under the Lorentz group and apply them to define and study higher spin algebras and superalgebras in AdS 5. The higher spin (HS) algebra of Fradkin-Vasiliev type in AdS5 is simply the enveloping algebra of SU(2, 2) quotiented by a two-sided ideal (Joseph ideal) which annihilates the minrep. We show that the Joseph ideal vanishes identically for the quasiconformal realization of the minrep and its enveloping algebra leads directly to the HS algebra in AdS5. Furthermore, the enveloping algebras of the deformations of the minrep define a one parameter family of HS algebras in AdS5 for which certain 4d covariant deformations of the Joseph ideal vanish identically. These results extend to superconformal algebras SU(2, 2|N) and we find amore »
- Authors:
-
- Pennsylvania State Univ., University Park, PA (United States). Inst. for Gravitation and the Cosmos, Dept of Physics
- Pennsylvania State Univ., University Park, PA (United States). Inst. for Gravitation and the Cosmos, Dept of Physics; European Organization for Nuclear Research (CERN), Geneva (Switzerland). Theory Division, Physics Dept.
- Publication Date:
- Research Org.:
- Pennsylvania State Univ., University Park, PA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC); National Science Foundation (NSF)
- OSTI Identifier:
- 1440969
- Grant/Contract Number:
- SC0010534; PHY-1213183; PHY-08-55356
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2015; Journal Issue: 3; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Berlin
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Gauge-gravity correspondence; Extended Supersymmetry; Space-Time Symmetries
Citation Formats
Govil, Karan, and Gunaydin, Murat. Deformed twistors and higher spin conformal (super-)algebras in four dimensions. United States: N. p., 2015.
Web. doi:10.1007/JHEP03(2015)026.
Govil, Karan, & Gunaydin, Murat. Deformed twistors and higher spin conformal (super-)algebras in four dimensions. United States. https://doi.org/10.1007/JHEP03(2015)026
Govil, Karan, and Gunaydin, Murat. Thu .
"Deformed twistors and higher spin conformal (super-)algebras in four dimensions". United States. https://doi.org/10.1007/JHEP03(2015)026. https://www.osti.gov/servlets/purl/1440969.
@article{osti_1440969,
title = {Deformed twistors and higher spin conformal (super-)algebras in four dimensions},
author = {Govil, Karan and Gunaydin, Murat},
abstractNote = {Massless conformal scalar field in d = 4 corresponds to the minimal unitary representation (minrep) of the conformal group SU(2, 2) which admits a one-parameter family of deformations that describe massless fields of arbitrary helicity. The minrep and its deformations were obtained by quantization of the nonlinear realization of SU(2, 2) as a quasiconformal group in arXiv:0908.3624. We show that the generators of SU(2,2) for these unitary irreducible representations can be written as bilinears of deformed twistorial oscillators which transform nonlinearly under the Lorentz group and apply them to define and study higher spin algebras and superalgebras in AdS 5. The higher spin (HS) algebra of Fradkin-Vasiliev type in AdS5 is simply the enveloping algebra of SU(2, 2) quotiented by a two-sided ideal (Joseph ideal) which annihilates the minrep. We show that the Joseph ideal vanishes identically for the quasiconformal realization of the minrep and its enveloping algebra leads directly to the HS algebra in AdS5. Furthermore, the enveloping algebras of the deformations of the minrep define a one parameter family of HS algebras in AdS5 for which certain 4d covariant deformations of the Joseph ideal vanish identically. These results extend to superconformal algebras SU(2, 2|N) and we find a one parameter family of HS superalgebras as enveloping algebras of the minimal unitary supermultiplet and its deformations. Our results suggest the existence of a family of (supersymmetric) HS theories in AdS 5 which are dual to free (super)conformal field theories (CFTs) or to interacting but integrable (supersymmetric) CFTs in 4d. We also discuss the corresponding picture in HS algebras in AdS 4 where the corresponding 3d conformal group Sp(4,R) admits only two massless representations (minreps), namely the scalar and spinor singletons.},
doi = {10.1007/JHEP03(2015)026},
journal = {Journal of High Energy Physics (Online)},
number = 3,
volume = 2015,
place = {United States},
year = {Thu Mar 05 00:00:00 EST 2015},
month = {Thu Mar 05 00:00:00 EST 2015}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 18 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
One massless particle equals two Dirac singletons: VI: Elementary particles in a curved space
journal, September 1978
- Flato, M.; Fronsdal, C.
- Letters in Mathematical Physics, Vol. 2, Issue 5
Higher-Spin Gauge Theories in Four, Three and two Dimensions
journal, December 1996
- Vasiliev, M. A.
- International Journal of Modern Physics D, Vol. 05, Issue 06
deformations of the minimal unitary representation of as massless 6D conformal supermultiplets
journal, February 2011
- Fernando, Sudarshan; Günaydin, Murat
- Nuclear Physics B, Vol. 843, Issue 3
Special tensors in the deformation theory of quadratic algebras for the classical Lie algebras
journal, December 2007
- Eastwood, Michael; Somberg, Petr; Souček, Vladimír
- Journal of Geometry and Physics, Vol. 57, Issue 12
Massless representations and admissibility condition for higher spin superalgebras
journal, January 1989
- Konstein, S. E.; Vasiliev, M. A.
- Nuclear Physics B, Vol. 312, Issue 2
Massless higher spins and holography
journal, November 2002
- Sezgin, E.; Sundell, P.
- Nuclear Physics B, Vol. 644, Issue 1-2
Exceptional supergravity theories and the magic square
journal, December 1983
- Günaydin, M.; Sierra, G.; Townsend, P. K.
- Physics Letters B, Vol. 133, Issue 1-2
Superconformal symmetry and maximal supergravity in various dimensions
journal, March 2012
- Chiodaroli, Marco; Günaydin, Murat; Roiban, Radu
- Journal of High Energy Physics, Vol. 2012, Issue 3
Tensor products of positive energy representations of S̃O(3,2) and S̃O(4,2)
journal, August 1981
- Heidenreich, W.
- Journal of Mathematical Physics, Vol. 22, Issue 8
Minimal unitary representation of SU(2,2) and its deformations as massless conformal fields and their supersymmetric extensions
journal, August 2010
- Fernando, Sudarshan; Günaydin, Murat
- Journal of Mathematical Physics, Vol. 51, Issue 8
Kac–Dynkin diagrams and supertableaux
journal, September 1983
- Bars, I.; Morel, B.; Ruegg, H.
- Journal of Mathematical Physics, Vol. 24, Issue 9
$ \mathcal{N} = 8 $ superspace constraints for three-dimensional gauge theories
journal, February 2010
- Samtleben, Henning; Wimmer, Robert
- Journal of High Energy Physics, Vol. 2010, Issue 2
Stringy gravity, interacting tensionless strings and massless higher spins
journal, September 2001
- Sundborg, Bo
- Nuclear Physics B - Proceedings Supplements, Vol. 102-103
A Remarkable Representation of the 3 + 2 de Sitter Group
journal, July 1963
- Dirac, P. A. M.
- Journal of Mathematical Physics, Vol. 4, Issue 7
Unitary lowest weight representations of the noncompact supergroup OSp(2 n /2 m , R )
journal, November 1988
- Günaydin, M.; Hyun, S. J.
- Journal of Mathematical Physics, Vol. 29, Issue 11
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
- Günaydin, M.; van Nieuwenhuizen, P.; Warner, N. P.
- Nuclear Physics B, Vol. 255
Conformal higher spin currents in any dimension and AdS/CFT correspondence
journal, December 2000
- Konstein, Semjon E.; Vasiliev, Mikhail A.; Zaikin, Vladimir N.
- Journal of High Energy Physics, Vol. 2000, Issue 12
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
- Gunaydin, M.; Marcus, N.
- Classical and Quantum Gravity, Vol. 2, Issue 2
Supercoherent states of , conformal superfields and the AdS7/CFT6 duality
journal, April 2002
- Fernando, Sudarshan; Günaydin, Murat; Takemae, Seiji
- Nuclear Physics B, Vol. 628, Issue 1-2
A fiber approach to harmonic analysis of unfolded higher-spin field equations
journal, October 2008
- Iazeolla, C.; Sundell, P.
- Journal of High Energy Physics, Vol. 2008, Issue 10
Singleton representations of Osp(N,4)
journal, August 1984
- Nicolai, H.; Sezgin, E.
- Physics Letters B, Vol. 143, Issue 4-6
Minimal unitary representation of and its deformations as massless 6D conformal fields and their supersymmetric extensions
journal, December 2010
- Fernando, Sudarshan; Günaydin, Murat
- Nuclear Physics B, Vol. 841, Issue 3
Novel supermultiplets of SU (2, 2|4) and the AdS5/CFT4 duality
journal, April 1999
- Günaydin, M.; Minis, D.; Zagermann, M.
- Nuclear Physics B, Vol. 544, Issue 3
Anti de Sitter space and holography
journal, January 1998
- Witten, Edward
- Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 2
Singular unitary representations
book, January 1981
- Vogan, Jr., David A.
- Non Commutative Harmonic Analysis and Lie Groups
Minimal representations, geometric quantization, and unitarity.
journal, June 1994
- Brylinski, R.; Kostant, B.
- Proceedings of the National Academy of Sciences, Vol. 91, Issue 13
Cubic interactions of bosonic higher spin gauge fields in AdS5
journal, November 2001
- Vasiliev, M. A.
- Nuclear Physics B, Vol. 616, Issue 1-2
4D doubleton conformal theories, CPT and IIB strings on AdS5 × S5
journal, November 1998
- Günaydin, M.; Minic, D.; Zagermann, M.
- Nuclear Physics B, Vol. 534, Issue 1-2
Unitarization of a singular representation ofSO(p, q)
journal, May 1991
- Binegar, B.; Zierau, R.
- Communications in Mathematical Physics, Vol. 138, Issue 2
Unitary highest weight representations of noncompact supergroups
journal, June 1988
- Günaydin, Murat
- Journal of Mathematical Physics, Vol. 29, Issue 6
Analysis on the minimal representation of O(p,q) II. Branching laws
journal, December 2003
- Kobayashi, Toshiyuki; Ørsted, Bent
- Advances in Mathematics, Vol. 180, Issue 2
Conformal and Quasiconformal Realizations¶of Exceptional Lie Groups
journal, July 2001
- Günaydin, M.; Koepsell, K.; Nicolai, H.
- Communications in Mathematical Physics, Vol. 221, Issue 1
Minimal Unitary Realizations of Exceptional U-duality Groups and Their Subgroups as Quasiconformal Groups
journal, January 2005
- Gunaydin, M.; Pavlyk, O.
- Journal of High Energy Physics, Vol. 2005, Issue 01
Generalized spacetimes defined by cubic forms and the minimal unitary realizations of their quasiconformal groups
journal, August 2005
- Günaydin, Murat; Pavlyk, Oleksandr
- Journal of High Energy Physics, Vol. 2005, Issue 08
Higher Spin Superalgebras in any Dimension and their Representations
journal, December 2004
- A. Vasiliev, M.
- Journal of High Energy Physics, Vol. 2004, Issue 12
Oscillator-like unitary representations of non-compact groups with a jordan structure and the non-compact groups of supergravity
journal, June 1982
- Günaydin, M.; Saçlioglu, C.
- Communications in Mathematical Physics, Vol. 87, Issue 2
Unitary supermultiplets of and the spectrum of the S7 compactification of 11-dimensional supergravity
journal, July 1986
- Günaydin, M.; Warner, N. P.
- Nuclear Physics B, Vol. 272, Issue 1
Cubic interaction in extended theories of massless higher-spin fields
journal, January 1987
- Fradkin, E. S.; Vasiliev, M. A.
- Nuclear Physics B, Vol. 291
7D bosonic higher spin gauge theory: symmetry algebra and linearized constraints
journal, July 2002
- Sezgin, E.; Sundell, P.
- Nuclear Physics B, Vol. 634, Issue 1-2
Higher-spin algebras and cubic interactions for simple mixed-symmetry fields in AdS spacetime
journal, September 2011
- Boulanger, Nicolas; Skvortsov, E. D.
- Journal of High Energy Physics, Vol. 2011, Issue 9
AdS dual of the critical O(N) vector model
journal, December 2002
- Klebanov, I. R.; Polyakov, A. M.
- Physics Letters B, Vol. 550, Issue 3-4
Minimal unitary representation of and its deformations and , superconformal models
journal, April 2013
- Govil, Karan; Gunaydin, Murat
- Nuclear Physics B, Vol. 869, Issue 1
Higher spin N = 8 supergravity
journal, November 1998
- Sezgin, Ergin; Sundell, Per
- Journal of High Energy Physics, Vol. 1998, Issue 11
Oscillator-like unitary representations of non-compact groups and supergroups and extended supergravity theories
book, January 1983
- Günaydin, M.
- Group Theoretical Methods in Physics: Proceedings of the XIth International Colloquium Held at Boğaziçi University, Istanbul, Turkey, August 23–28, 1982
Harmonic Matrices for Scattering Amplitudes and Spectral Regularization
journal, March 2013
- Ferro, Livia; Łukowski, Tomasz; Meneghelli, Carlo
- Physical Review Letters, Vol. 110, Issue 12
Conformal Superalgebras of Higher Spins
journal, November 1989
- Fradkin, E. S.; Linetsky, V. Ya.
- Modern Physics Letters A, Vol. 04, Issue 24
The Large-N Limit of Superconformal Field Theories and Supergravity
journal, January 1999
- Maldacena, Juan
- International Journal of Theoretical Physics, Vol. 38, Issue 4, p. 1113-1133
Higher spins in AdS and twistorial holography
journal, April 2011
- Giombi, Simone; Yin, Xi
- Journal of High Energy Physics, Vol. 2011, Issue 4
Towards massless higher spin extension of D = 5, N = 8 gauged supergravity
journal, September 2001
- Sezgin, Ergin; Sundell, Per
- Journal of High Energy Physics, Vol. 2001, Issue 09
Minimal Representations, Spherical Vectors¶and Exceptional Theta Series
journal, March 2002
- Kazhdan, David; Pioline, Boris; Waldron, Andrew
- Communications in Mathematical Physics, Vol. 226, Issue 1
Harmonic superspace, minimal unitary representations and quasiconformal groups
journal, May 2007
- Günaydin, Murat
- Journal of High Energy Physics, Vol. 2007, Issue 05
A semi-classical limit of the gauge/string correspondence
journal, August 2002
- Gubser, S. S.; Klebanov, I. R.; Polyakov, A. M.
- Nuclear Physics B, Vol. 636, Issue 1-2
Minimal realizations and spectrum generating algebras
journal, December 1974
- Joseph, A.
- Communications in Mathematical Physics, Vol. 36, Issue 4
Holography in 4D (super) higher spin theories and a test via cubic scalar couplings
journal, July 2005
- Sezgin, Ergin; Sundell, Pear
- Journal of High Energy Physics, Vol. 2005, Issue 07
Unitary representations of non-compact supergroups
journal, March 1983
- Bars, I.; G�naydin, M.
- Communications in Mathematical Physics, Vol. 91, Issue 1
Analysis on the minimal representation of O(p,q) I. Realization via conformal geometry
journal, December 2003
- Kobayashi, Toshiyuki; Ørsted, Bent
- Advances in Mathematics, Vol. 180, Issue 2
On the Uniqueness of Higher-Spin Symmetries in ads and cft
journal, December 2013
- Boulanger, N.; Ponomarev, D.; Skvortsov, E.
- International Journal of Modern Physics A, Vol. 28, Issue 31
Analysis on the minimal representation of O(p,q)
journal, December 2003
- Kobayashi, Toshiyuki; Ørsted, Bent
- Advances in Mathematics, Vol. 180, Issue 2
The minimal unitary representation of $E_{8(8)}$
journal, January 2001
- Günaydin, M.; Koepsell, K.; Nicolai, H.
- Advances in Theoretical and Mathematical Physics, Vol. 5, Issue 5
Quantum field theory of singletons. The Rac
journal, May 1981
- Flato, M.; Fronsdal, C.
- Journal of Mathematical Physics, Vol. 22, Issue 5
A unified approach to the minimal unitary realizations of noncompact groups and supergroups
journal, September 2006
- Günaydin, Murat; Pavlyk, Oleksandr
- Journal of High Energy Physics, Vol. 2006, Issue 09
Higher symmetries of the Laplacian
journal, January 2005
- Eastwood, Michael
- Annals of Mathematics, Vol. 161, Issue 3
Doubletons and 5D higher spin gauge theory
journal, September 2001
- Sezgin, Ergin; Sundell, Per
- Journal of High Energy Physics, Vol. 2001, Issue 09
Higher spin gauge theory and holography: the three-point functions
journal, September 2010
- Giombi, Simone; Yin, Xi
- Journal of High Energy Physics, Vol. 2010, Issue 9
Deformed twistors and higher spin conformal (super-)algebras in six dimensions
journal, July 2014
- Govil, Karan; Günaydin, Murat
- Journal of High Energy Physics, Vol. 2014, Issue 7
The $so(d + 2, 2)$ minimal representation and ambient tractors: the conformal geometry of momentum space
journal, January 2009
- Gover, Ashwin Rod; Waldron, Andrew
- Advances in Theoretical and Mathematical Physics, Vol. 13, Issue 6
The Cartan Product
journal, March 2005
- Eastwood, Michael
- Bulletin of the Belgian Mathematical Society - Simon Stevin, Vol. 11, Issue 5
Works referencing / citing this record:
Notes on super Killing tensors
journal, March 2016
- Howe, P. S.; Lindström, U.
- Journal of High Energy Physics, Vol. 2016, Issue 3
Super-Laplacians and their symmetries
journal, May 2017
- Howe, P. S.; Lindström, U.
- Journal of High Energy Physics, Vol. 2017, Issue 5
The Complete Unitary Dual of Non-compact Lie Superalgebra $${\mathfrak{su}({\rm p}, {\rm q}|{\rm m})}$$ via the Generalised Oscillator Formalism, and Non-compact Young Diagrams
journal, March 2019
- Günaydin, Murat; Volin, Dmytro
- Communications in Mathematical Physics, Vol. 367, Issue 3