Abstract
In this paper we relate the parity-odd part of two and three point correlation functions in theories with exactly conserved or weakly broken higher spin symmetries to the parity-even part which can be computed from free theories. We also comment on higher point functions.
The well known connection of CFT correlation functions with de-Sitter amplitudes in one higher dimension implies a relation between parity-even and parity-odd amplitudes calculated using non-minimal interactions such as \( {\mathcal{W}}^3 \) and \( {\mathcal{W}}^2\tilde{\mathcal{W}} \). In the flat-space limit this implies a relation between parity-even and parity-odd parts of flat-space scattering amplitudes.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. M. Maldacena and G. L. Pimentel, On graviton non-Gaussianities during inflation, JHEP 09 (2011) 045 [arXiv:1104.2846] [INSPIRE].
I. Mata, S. Raju and S. Trivedi, CMB from CFT, JHEP 07 (2013) 015 [arXiv:1211.5482] [INSPIRE].
M. Geracie, M. Goykhman and D. T. Son, Dense Chern-Simons matter with fermions at large N , JHEP 04 (2016) 103 [arXiv:1511.04772] [INSPIRE].
A. Karch and D. Tong, Particle-vortex duality from 3d bosonization, Phys. Rev. X 6 (2016) 031043 [arXiv:1606.01893] [INSPIRE].
N. Seiberg, T. Senthil, C. Wang and E. Witten, A duality web in 2 + 1 dimensions and condensed matter physics, Annals Phys. 374 (2016) 395 [arXiv:1606.01989] [INSPIRE].
J. Murugan and H. Nastase, Particle-vortex duality in topological insulators and superconductors, JHEP 05 (2017) 159 [arXiv:1606.01912] [INSPIRE].
S. Minwalla, A. Mishra and N. Prabhakar, Fermi seas from Bose condensates in Chern-Simons matter theories and a bosonic exclusion principle, JHEP 11 (2020) 171 [arXiv:2008.00024] [INSPIRE].
O. Aharony, O. Bergman and D. L. Jafferis, Fractional M2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [INSPIRE].
O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
M. A. Vasiliev, More on equations of motion for interacting massless fields of all spins in (3 + 1)-dimensions, Phys. Lett. B 285 (1992) 225 [INSPIRE].
M. A. Vasiliev, Higher spin gauge theories in four-dimensions, three-dimensions, and two-dimensions, Int. J. Mod. Phys. D 5 (1996) 763 [hep-th/9611024] [INSPIRE].
M. A. Vasiliev, Higher spin gauge theories: star product and AdS space, hep-th/9910096 [INSPIRE].
M. A. Vasiliev, Nonlinear equations for symmetric massless higher spin fields in (A)dSd, Phys. Lett. B 567 (2003) 139 [hep-th/0304049] [INSPIRE].
I. R. Klebanov and A. M. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [INSPIRE].
E. Sezgin and P. Sundell, Massless higher spins and holography, Nucl. Phys. B 644 (2002) 303 [Erratum ibid. 660 (2003) 403] [hep-th/0205131] [INSPIRE].
S. Giombi and X. Yin, Higher spin gauge theory and holography: the three-point functions, JHEP 09 (2010) 115 [arXiv:0912.3462] [INSPIRE].
S. Giombi, S. Minwalla, S. Prakash, S. P. Trivedi, S. R. Wadia and X. Yin, Chern-Simons theory with vector fermion matter, Eur. Phys. J. C 72 (2012) 2112 [arXiv:1110.4386] [INSPIRE].
O. Aharony, G. Gur-Ari and R. Yacoby, d = 3 bosonic vector models coupled to Chern-Simons gauge theories, JHEP 03 (2012) 037 [arXiv:1110.4382] [INSPIRE].
S. Jain, S. P. Trivedi, S. R. Wadia and S. Yokoyama, Supersymmetric Chern-Simons theories with vector matter, JHEP 10 (2012) 194 [arXiv:1207.4750] [INSPIRE].
G. Gur-Ari and R. Yacoby, Three dimensional bosonization from supersymmetry, JHEP 11 (2015) 013 [arXiv:1507.04378] [INSPIRE].
S. Giombi, S. Prakash and X. Yin, A note on CFT correlators in three dimensions, JHEP 07 (2013) 105 [arXiv:1104.4317] [INSPIRE].
M. S. Costa, J. Penedones, D. Poland and S. Rychkov, Spinning conformal correlators, JHEP 11 (2011) 071 [arXiv:1107.3554] [INSPIRE].
M. S. Costa, J. Penedones, D. Poland and S. Rychkov, Spinning conformal blocks, JHEP 11 (2011) 154 [arXiv:1109.6321] [INSPIRE].
J. Maldacena and A. Zhiboedov, Constraining conformal field theories with a higher spin symmetry, J. Phys. A 46 (2013) 214011 [arXiv:1112.1016] [INSPIRE].
J. Maldacena and A. Zhiboedov, Constraining conformal field theories with a slightly broken higher spin symmetry, Class. Quant. Grav. 30 (2013) 104003 [arXiv:1204.3882] [INSPIRE].
S. Giombi, V. Gurucharan, V. Kirilin, S. Prakash and E. Skvortsov, On the higher-spin spectrum in large N Chern-Simons vector models, JHEP 01 (2017) 058 [arXiv:1610.08472] [INSPIRE].
H. Osborn and A. C. Petkou, Implications of conformal invariance in field theories for general dimensions, Annals Phys. 231 (1994) 311 [hep-th/9307010] [INSPIRE].
J. Erdmenger and H. Osborn, Conserved currents and the energy momentum tensor in conformally invariant theories for general dimensions, Nucl. Phys. B 483 (1997) 431 [hep-th/9605009] [INSPIRE].
C. Corianò, L. Delle Rose, E. Mottola and M. Serino, Solving the conformal constraints for scalar operators in momentum space and the evaluation of Feynman’s master integrals, JHEP 07 (2013) 011 [arXiv:1304.6944] [INSPIRE].
A. Bzowski, P. McFadden and K. Skenderis, Implications of conformal invariance in momentum space, JHEP 03 (2014) 111 [arXiv:1304.7760] [INSPIRE].
A. Bzowski, P. McFadden and K. Skenderis, Renormalised 3-point functions of stress tensors and conserved currents in CFT, JHEP 11 (2018) 153 [arXiv:1711.09105] [INSPIRE].
H. Isono, T. Noumi and G. Shiu, Momentum space approach to crossing symmetric CFT correlators, JHEP 07 (2018) 136 [arXiv:1805.11107] [INSPIRE].
A. Bzowski, P. McFadden and K. Skenderis, Renormalised CFT 3-point functions of scalars, currents and stress tensors, JHEP 11 (2018) 159 [arXiv:1805.12100] [INSPIRE].
H. Isono, T. Noumi and T. Takeuchi, Momentum space conformal three-point functions of conserved currents and a general spinning operator, JHEP 05 (2019) 057 [arXiv:1903.01110] [INSPIRE].
H. Isono, T. Noumi and G. Shiu, Momentum space approach to crossing symmetric CFT correlators. Part II. General spacetime dimension, JHEP 10 (2019) 183 [arXiv:1908.04572] [INSPIRE].
C. Corianò, M. M. Maglio and D. Theofilopoulos, Four-point functions in momentum space: conformal Ward identities in the scalar/tensor case, Eur. Phys. J. C 80 (2020) 540 [arXiv:1912.01907] [INSPIRE].
C. Corianò and M. M. Maglio, Conformal field theory in momentum space and anomaly actions in gravity: the analysis of three- and four-point functions, arXiv:2005.06873 [INSPIRE].
S. Jain, R. R. John and V. Malvimat, Momentum space spinning correlators and higher spin equations in three dimensions, JHEP 11 (2020) 049 [arXiv:2005.07212] [INSPIRE].
S. Jain, R. R. John, A. Mehta, A. A. Nizami and A. Suresh, Momentum space parity-odd CFT 3-point functions, arXiv:2101.11635 [INSPIRE].
S. Caron-Huot and Y.-Z. Li, Helicity basis for three-dimensional conformal field theory, arXiv:2102.08160 [INSPIRE].
S. Jain, R. R. John, A. Mehta, A. A. Nizami and A. Suresh, Higher spin 3-point functions in 3d CFT using spinor-helicity variables, JHEP 09 (2021) 041 [arXiv:2106.00016] [INSPIRE].
B. Nagaraj and D. Ponomarev, Spinor-helicity formalism for massless fields in AdS4, Phys. Rev. Lett. 122 (2019) 101602 [arXiv:1811.08438] [INSPIRE].
R. R. Metsaev, Light-cone gauge cubic interaction vertices for massless fields in AdS4, Nucl. Phys. B 936 (2018) 320 [arXiv:1807.07542] [INSPIRE].
E. Skvortsov, Light-front bootstrap for Chern-Simons matter theories, JHEP 06 (2019) 058 [arXiv:1811.12333] [INSPIRE].
O. Aharony, G. Gur-Ari and R. Yacoby, Correlation functions of large N Chern-Simons-matter theories and bosonization in three dimensions, JHEP 12 (2012) 028 [arXiv:1207.4593] [INSPIRE].
G. Gur-Ari and R. Yacoby, Correlators of large N fermionic Chern-Simons vector models, JHEP 02 (2013) 150 [arXiv:1211.1866] [INSPIRE].
Y. Gandhi, S. Jain and R. R. John, Anyonic correlation functions in Chern-Simons matter theories, arXiv:2106.09043 [INSPIRE].
S. Jain, R. R. John, A. Mehta, A. A. Nizami and A. Suresh, Double copy structure of parity-violating CFT correlators, JHEP 07 (2021) 033 [arXiv:2104.12803] [INSPIRE].
D. Baumann, C. Duaso Pueyo, A. Joyce, H. Lee and G. L. Pimentel, The cosmological bootstrap: spinning correlators from symmetries and factorization, SciPost Phys. 11 (2021) 071 [arXiv:2005.04234] [INSPIRE].
A. Zhiboedov, A note on three-point functions of conserved currents, arXiv:1206.6370 [INSPIRE].
D. Baumann, W.-M. Chen, C. Duaso Pueyo, A. Joyce, H. Lee and G. L. Pimentel, Linking the singularities of cosmological correlators, arXiv:2106.05294 [INSPIRE].
S. Jain, R. R. John, A. Mehta and D. K. S, Constraining momentum space CFT correlators with consistent position space OPE limit and the collider bound, arXiv:2111.08024 [INSPIRE].
Z. Li, Bootstrapping conformal four-point correlators with slightly broken higher spin symmetry and 3D bosonization, JHEP 10 (2020) 007 [arXiv:1906.05834] [INSPIRE].
R. R. Kalloor, Four-point functions in large N Chern-Simons fermionic theories, JHEP 10 (2020) 028 [arXiv:1910.14617] [INSPIRE].
J. A. Silva, Four point functions in CFT’s with slightly broken higher spin symmetry, JHEP 05 (2021) 097 [arXiv:2103.00275] [INSPIRE].
A. Bedhotiya and S. Prakash, A test of bosonization at the level of four-point functions in Chern-Simons vector models, JHEP 12 (2015) 032 [arXiv:1506.05412] [INSPIRE].
A. Bzowski, P. McFadden and K. Skenderis, Conformal n-point functions in momentum space, Phys. Rev. Lett. 124 (2020) 131602 [arXiv:1910.10162] [INSPIRE].
A. Bzowski, P. McFadden and K. Skenderis, Conformal correlators as simplex integrals in momentum space, JHEP 01 (2021) 192 [arXiv:2008.07543] [INSPIRE].
G. J. Turiaci and A. Zhiboedov, Veneziano amplitude of Vasiliev theory, JHEP 10 (2018) 034 [arXiv:1802.04390] [INSPIRE].
R. Yacoby, Scalar correlators in bosonic Chern-Simons vector models, arXiv:1805.11627 [INSPIRE].
V. K. Dobrev, G. Mack, V. B. Petkova, S. G. Petrova and I. T. Todorov, Harmonic analysis on the n-dimensional Lorentz group and its application to conformal quantum field theory, Lect. Notes Phys. 63 (1977) 1 [INSPIRE].
S. Jain, R. R. John and V. Malvimat, Constraining momentum space correlators using slightly broken higher spin symmetry, JHEP 04 (2021) 231 [arXiv:2008.08610] [INSPIRE].
S. D. Chowdhury, A. Gadde, T. Gopalka, I. Halder, L. Janagal and S. Minwalla, Classifying and constraining local four photon and four graviton S-matrices, JHEP 02 (2020) 114 [arXiv:1910.14392] [INSPIRE].
K. Inbasekar, S. Jain, V. Malvimat, A. Mehta, P. Nayak and T. Sharma, Correlation functions in N = 2 supersymmetric vector matter Chern-Simons theory, JHEP 04 (2020) 207 [arXiv:1907.11722] [INSPIRE].
S. Jain, M. Mandlik, S. Minwalla, T. Takimi, S. R. Wadia and S. Yokoyama, Unitarity, crossing symmetry and duality of the S-matrix in large N Chern-Simons theories with fundamental matter, JHEP 04 (2015) 129 [arXiv:1404.6373] [INSPIRE].
K. Inbasekar, S. Jain, S. Mazumdar, S. Minwalla, V. Umesh and S. Yokoyama, Unitarity, crossing symmetry and duality in the scattering of N = 1 SUSY matter Chern-Simons theories, JHEP 10 (2015) 176 [arXiv:1505.06571] [INSPIRE].
G. Gur-Ari, S. A. Hartnoll and R. Mahajan, Transport in Chern-Simons-matter theories, JHEP 07 (2016) 090 [arXiv:1605.01122] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2107.00695
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Jain, S., John, R.R. Relation between parity-even and parity-odd CFT correlation functions in three dimensions. J. High Energ. Phys. 2021, 67 (2021). https://doi.org/10.1007/JHEP12(2021)067
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2021)067