On Correlation Functions as Higher-Spin Invariants
Abstract
:1. Introduction
2. Structure of Correlation Functions in Three Dimensions
3. Correlation Functions as Higher-Spin Invariants
3.1. Higher-Spin Algebra
3.1.1. Star-Product
3.1.2. Conformally Adapted Basis
3.2. Wave-Functions
Wave-Functions’ Properties
3.3. Correlation Functions
3.3.1. Two-Point Correlators
3.3.2. Higher-Point Procedure
3.3.3. Star-Product of Gaussians
3.3.4. Higher-Point Correlators
3.3.5. -pt Functions
4. Conclusions and Discussion
Funding
Institutional Review Board Statement
Informed Consent Statement
Acknowledgments
Conflicts of Interest
Appendix A. Vector-Spinor Dictionary
Appendix B. Conformal Structures
References
- Sezgin, E.; Sundell, P. Massless higher spins and holography. Nucl. Phys. 2002, B644, 303–370. [Google Scholar] [CrossRef]
- Klebanov, I.R.; Polyakov, A.M. AdS dual of the critical O(N) vector model. Phys. Lett. 2002, B550, 213–219. [Google Scholar] [CrossRef]
- Sezgin, E.; Sundell, P. Holography in 4D (super) higher spin theories and a test via cubic scalar couplings. J. High Energy Phys. 2005, 0507, 044. [Google Scholar] [CrossRef]
- Leigh, R.G.; Petkou, A.C. Holography of the N=1 higher spin theory on AdS(4). J. High Energy Phys. 2003, 0306, 011. [Google Scholar] [CrossRef]
- Das, S.R.; Jevicki, A. Large N collective fields and holography. Phys. Rev. D 2003, 68, 044011. [Google Scholar] [CrossRef]
- Bekaert, X.; Erdmenger, J.; Ponomarev, D.; Sleight, C. Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory. J. High Energy Phys. 2015, 11, 149. [Google Scholar] [CrossRef]
- de Mello Koch, R.; Jevicki, A.; Suzuki, K.; Yoon, J. AdS Maps and Diagrams of Bi-local Holography. J. High Energy Phys. 2019, 03, 133. [Google Scholar] [CrossRef]
- Aharony, O.; Chester, S.M.; Urbach, E.Y. A Derivation of AdS/CFT for Vector Models. J. High Energy Phys. 2020, 1–72. [Google Scholar] [CrossRef]
- Giombi, S.; Minwalla, S.; Prakash, S.; Trivedi, S.P.; Wadia, S.R.; Yin, X. Chern-Simons Theory with Vector Fermion Matter. Eur. Phys. J. 2012, C72, 2112. [Google Scholar] [CrossRef]
- Maldacena, J.; Zhiboedov, A. Constraining conformal field theories with a slightly broken higher spin symmetry. Class. Quantum Gravity 2012, 30, 104003. [Google Scholar] [CrossRef]
- Aharony, O.; Gur-Ari, G.; Yacoby, R. Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions. J. High Energy Phys. 2012, 12, 028. [Google Scholar] [CrossRef]
- Aharony, O. Baryons, monopoles and dualities in Chern-Simons-matter theories. J. High Energy Phys. 2016, 02, 093. [Google Scholar] [CrossRef]
- Karch, A.; Tong, D. Particle-Vortex Duality from 3d Bosonization. Phys. Rev. 2016, X6, 031043. [Google Scholar] [CrossRef]
- Seiberg, N.; Senthil, T.; Wang, C.; Witten, E. A Duality Web in 2+1 Dimensions and Condensed Matter Physics. Annals Phys. 2016, 374, 395–433. [Google Scholar] [CrossRef]
- Dirac, P.A.M. A Remarkable representation of the 3 + 2 de Sitter group. J. Math. Phys. 1963, 4, 901–909. [Google Scholar] [CrossRef]
- Günaydin, M.; Saclioglu, C. Oscillator Like Unitary Representations of Noncompact Groups With a Jordan Structure and the Noncompact Groups of Supergravity. Commun. Math. Phys. 1982, 87, 159. [Google Scholar] [CrossRef]
- Günaydin, M. Oscillator like unitary representations of noncompact groups and supergroups and extended supergravity theories. In Proceedings of the Group Theoretical Methods in Physics, 11th International Colloquium, Istanbul, Turkey, 23–28 August 1982; pp. 192–213. [Google Scholar]
- Vasiliev, M.A. Extended higher spin superalgebras and their realizations in terms of quantum operators. Fortsch. Phys. 1988, 36, 33–62. [Google Scholar] [CrossRef]
- Eastwood, M.G. Higher symmetries of the Laplacian. Ann. Math. 2005, 161, 1645–1665. [Google Scholar] [CrossRef]
- Joung, E.; Mkrtchyan, K. Notes on higher-spin algebras: Minimal representations and structure constants. J. High Energy Phys. 2014, 05, 103. [Google Scholar] [CrossRef]
- Flato, M.; Fronsdal, C. One Massless Particle Equals Two Dirac Singletons: Elementary Particles in a Curved Space. Lett. Math. Phys. 1978, 2, 421–426. [Google Scholar] [CrossRef]
- Craigie, N.S.; Dobrev, V.K.; Todorov, I.T. Conformally Covariant Composite Operators in Quantum Chromodynamics. Annals Phys. 1985, 159, 411–444. [Google Scholar] [CrossRef]
- Colombo, N.; Sundell, P. Higher Spin Gravity Amplitudes From Zero-form Charges. arXiv 2012, arXiv:1208.3880. [Google Scholar]
- Didenko, V.; Skvortsov, E. Exact higher-spin symmetry in CFT: All correlators in unbroken Vasiliev theory. J. High Energy Phys. 2013, 1304, 158. [Google Scholar] [CrossRef]
- Didenko, V.E.; Mei, J.; Skvortsov, E.D. Exact higher-spin symmetry in CFT: Free fermion correlators from Vasiliev Theory. Phys. Rev. 2013, D88, 046011. [Google Scholar] [CrossRef]
- Bonezzi, R.; Boulanger, N.; De Filippi, D.; Sundell, P. Noncommutative Wilson lines in higher-spin theory and correlation functions of conserved currents for free conformal fields. J. Phys. 2017, A50, 475401. [Google Scholar] [CrossRef]
- Maldacena, J.; Zhiboedov, A. Constraining Conformal Field Theories with A Higher Spin Symmetry. J. Phys. Math. Theor. 2011, 46, 214011. [Google Scholar] [CrossRef]
- Boulanger, N.; Ponomarev, D.; Skvortsov, E.D.; Taronna, M. On the uniqueness of higher-spin symmetries in AdS and CFT. Int. J. Mod. Phys. 2013, A28, 1350162. [Google Scholar] [CrossRef]
- Alba, V.; Diab, K. Constraining conformal field theories with a higher spin symmetry in d = 4. arXiv 2013, arXiv:1307.8092. [Google Scholar]
- Alba, V.; Diab, K. Constraining conformal field theories with a higher spin symmetry in d > 3 dimensions. J. High Energy Phys. 2015, 44. [Google Scholar] [CrossRef]
- Sharapov, A.; Skvortsov, E. Characteristic Cohomology and Observables in Higher Spin Gravity. J. High Energy Phys. 2020, 12, 190. [Google Scholar] [CrossRef]
- Sharapov, A.; Skvortsov, E. A∞ algebras from slightly broken higher spin symmetries. J. High Energy Phys. 2019, 09, 024. [Google Scholar] [CrossRef]
- Gerasimenko, P.; Sharapov, A.; Skvortsov, E. Slightly broken higher spin symmetry: General structure of correlators. J. High Energy Phys. 2022, 01, 097. [Google Scholar] [CrossRef]
- Skvortsov, E.; Sharapov, A. Integrable models from non-commutative geometry, with applications to 3d dualities. PoS 2022, CORFU2021, 253. [Google Scholar] [CrossRef]
- Li, Z. Bootstrapping conformal four-point correlators with slightly broken higher spin symmetry and 3D bosonization. J. High Energy Phys. 2020, 10, 007. [Google Scholar] [CrossRef]
- Kalloor, R.R. Four-point functions in large N Chern-Simons fermionic theories. J. High Energy Phys. 2020, 10, 028. [Google Scholar] [CrossRef]
- Turiaci, G.J.; Zhiboedov, A. Veneziano Amplitude of Vasiliev Theory. J. High Energy Phys. 2018, 10, 034. [Google Scholar] [CrossRef]
- Jain, S.; John, R.R.; Malvimat, V. Constraining momentum space correlators using slightly broken higher spin symmetry. J. High Energy Phys. 2021, 04, 231. [Google Scholar] [CrossRef]
- Jain, S.; John, R.R.; Mehta, A.; Nizami, A.A.; Suresh, A. Higher spin 3-point functions in 3d CFT using spinor-helicity variables. J. High Energy Phys. 2021, 09, 041. [Google Scholar] [CrossRef]
- Jain, S.; John, R.R. Relation between parity-even and parity-odd CFT correlation functions in three dimensions. J. High Energy Phys. 2021, 67. [Google Scholar] [CrossRef]
- Jain, S.; John, R.R.; Mehta, A.; S, D.K. Constraining momentum space CFT correlators with consistent position space OPE limit and the collider bound. J. High Energy Phys. 2022, 02, 084. [Google Scholar] [CrossRef]
- Silva, J.A. Four point functions in CFT’s with slightly broken higher spin symmetry. J. High Energy Phys. 2021, 05, 097. [Google Scholar] [CrossRef]
- Giombi, S.; Yin, X. Higher Spins in AdS and Twistorial Holography. J. High Energy Phys. 2011, 1104, 086. [Google Scholar] [CrossRef]
- Boulanger, N.; Kessel, P.; Skvortsov, E.D.; Taronna, M. Higher spin interactions in four-dimensions: Vasiliev versus Fronsdal. J. Phys. 2016, A49, 095402. [Google Scholar] [CrossRef]
- Skvortsov, E.D.; Taronna, M. On Locality, Holography and Unfolding. J. High Energy Phys. 2015, 11, 044. [Google Scholar] [CrossRef]
- Gelfond, O.A.; Vasiliev, M.A. Operator algebra of free conformal currents via twistors. Nucl. Phys. 2013, B876, 871–917. [Google Scholar] [CrossRef]
- Metsaev, R.R. Light-cone gauge cubic interaction vertices for massless fields in AdS(4). Nucl. Phys. 2018, B936, 320–351. [Google Scholar] [CrossRef]
- Skvortsov, E. Light-Front Bootstrap for Chern-Simons Matter Theories. J. High Energy Phys. 2019, 06, 058. [Google Scholar] [CrossRef]
- Sharapov, A.; Skvortsov, E. Chiral Higher Spin Gravity in (A)dS4 and secrets of Chern–Simons Matter Theories. Nucl. Phys. B 2022, 985, 115982. [Google Scholar] [CrossRef]
- Sharapov, A.; Skvortsov, E.; Van Dongen, R. Chiral Higher Spin Gravity and Convex Geometry. arXiv 2022, arXiv:2209.01796. [Google Scholar] [CrossRef]
- Sharapov, A.; Skvortsov, E.; Sukhanov, A.; Van Dongen, R. More on Chiral Higher Spin Gravity and Convex Geometry. Nucl. Phys. B 2022, 990, 116152. [Google Scholar] [CrossRef]
- Metsaev, R.R. Poincare invariant dynamics of massless higher spins: Fourth order analysis on mass shell. Mod. Phys. Lett. 1991, A6, 359–367. [Google Scholar] [CrossRef]
- Metsaev, R.R. S matrix approach to massless higher spins theory. 2: The Case of internal symmetry. Mod. Phys. Lett. 1991, A6, 2411–2421. [Google Scholar] [CrossRef]
- Ponomarev, D.; Skvortsov, E.D. Light-Front Higher-Spin Theories in Flat Space. J. Phys. 2017, A50, 095401. [Google Scholar] [CrossRef]
- Ponomarev, D. Chiral Higher Spin Theories and Self-Duality. J. High Energy Phys. 2017, 12, 141. [Google Scholar] [CrossRef]
- Skvortsov, E.D.; Tran, T.; Tsulaia, M. Quantum Chiral Higher Spin Gravity. Phys. Rev. Lett. 2018, 121, 031601. [Google Scholar] [CrossRef]
- Skvortsov, E.; Tran, T.; Tsulaia, M. More on Quantum Chiral Higher Spin Gravity. Phys. Rev. 2020, D101, 106001. [Google Scholar] [CrossRef]
- Skvortsov, E.; Van Dongen, R. Minimal models of field theories: Chiral Higher Spin Gravity. Phys. Rev. D 2022, 106, 045006. [Google Scholar] [CrossRef]
- Sharapov, A.; Skvortsov, E.; Sukhanov, A.; Van Dongen, R. Minimal model of Chiral Higher Spin Gravity. J. High Energy Phys. 2022, 134. [Google Scholar] [CrossRef]
- Bekaert, X.; Boulanger, N.; Campoleoni, A.; Chiodaroli, M.; Francia, D.; Grigoriev, M.; Sezgin, E.; Skvortsov, E. Snowmass White Paper: Higher Spin Gravity and Higher Spin Symmetry. arXiv 2022, arXiv:2205.01567. [Google Scholar]
- Giombi, S.; Prakash, S.; Yin, X. A Note on CFT Correlators in Three Dimensions. J. High Energy Phys. 2011, 105. [Google Scholar] [CrossRef]
- Vasiliev, M.A. Holography, Unfolding and Higher-Spin Theory. J. Phys. 2013, A46, 214013. [Google Scholar] [CrossRef]
- Didenko, V.E.; Vasiliev, M.A. Free field dynamics in the generalized AdS (super)space. J. Math. Phys. 2004, 45, 197–215. [Google Scholar] [CrossRef]
- Ponomarev, D. Chiral higher-spin holography in flat space: The Flato-Fronsdal theorem and lower-point functions. J. High Energy Phys. 2023, 01, 048. [Google Scholar] [CrossRef]
- Ponomarev, D. Towards higher-spin holography in flat space. J. High Energy Phys. 2023, 01, 084. [Google Scholar] [CrossRef]
- Ponomarev, D. Invariant traces of the flat space chiral higher-spin algebra as scattering amplitudes. J. High Energy Phys. 2022, 09, 086. [Google Scholar] [CrossRef]
- Didenko, V.E.; Skvortsov, E.D. Towards higher-spin holography in ambient space of any dimension. J. Phys. 2013, A46, 214010. [Google Scholar] [CrossRef]
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Scalea, A. On Correlation Functions as Higher-Spin Invariants. Symmetry 2023, 15, 950. https://doi.org/10.3390/sym15040950
Scalea A. On Correlation Functions as Higher-Spin Invariants. Symmetry. 2023; 15(4):950. https://doi.org/10.3390/sym15040950
Chicago/Turabian StyleScalea, Adrien. 2023. "On Correlation Functions as Higher-Spin Invariants" Symmetry 15, no. 4: 950. https://doi.org/10.3390/sym15040950
APA StyleScalea, A. (2023). On Correlation Functions as Higher-Spin Invariants. Symmetry, 15(4), 950. https://doi.org/10.3390/sym15040950