Abstract
We list all potential candidates for U(1) anomalous non-local 1-loop 4-point amplitudes and higher loop UV divergences in \( \mathcal{N} \) ≥ 5 supergravities. The relevant chiral superinvariants are constructed from linearized chiral superfields and define the corresponding superamplitudes. The anomalous amplitudes, of the kind present in \( \mathcal{N} \) = 4, are shown to be absent in \( \mathcal{N} \) ≥ 5. In \( \mathcal{N} \) = 6 supergravity the result is deduced from the double-copy (\( \mathcal{N} \) = 4) Y M × (\( \mathcal{N} \) = 2) Y M model, whereas in \( \mathcal{N} \) = 5, 8 the result on absence of anomalous amplitudes is derived in supergravities as well as in the (\( \mathcal{N} \) = 4) Y M × (\( \mathcal{N} \) − 4) Y M double-copy models.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.M. Christensen and M.J. Duff, Axial and conformal anomalies for arbitrary spin in gravity and supergravity, Phys. Lett. B 76 (1978) 571 [INSPIRE].
S.M. Christensen and M.J. Duff, New gravitational index theorems and supertheorems, Nucl. Phys. B 154 (1979) 301 [INSPIRE].
R.E. Kallosh, Superselfduality (in Russian), JETP Lett. 29 (1979) 172 [Pisma Zh. Eksp. Teor. Fiz. 29 (1979) 192] [INSPIRE].
S.M. Christensen, S. Deser, M.J. Duff and M.T. Grisaru, Chirality, selfduality and supergravity counterterms, Phys. Lett. B 84 (1979) 411 [INSPIRE].
R.E. Kallosh, Selfduality in superspace, Nucl. Phys. B 165 (1980) 119 [INSPIRE].
N. Marcus, Composite anomalies in supergravity, Phys. Lett. B 157 (1985) 383 [INSPIRE].
H. Nicolai and P.K. Townsend, N = 3 supersymmetry multiplets with vanishing trace anomaly: building blocks of the N > 3 supergravities, Phys. Lett. B 98 (1981) 257 [INSPIRE].
M.J. Duff, Ultraviolet divergences in extended supergravity, in First School on Supergravity, Trieste Italy, 22 April-6 May 1981 [arXiv:1201.0386] [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, Off-shell one loop divergences in gauged O(N ) supergravities, Phys. Lett. B 117 (1982) 303 [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, One loop β-function in conformal supergravities, Nucl. Phys. B 203 (1982) 157 [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, Conformal supergravity, Phys. Rept. 119 (1985) 233 [INSPIRE].
M.J. Duff, Twenty years of the Weyl anomaly, Class. Quant. Grav. 11 (1994) 1387 [hep-th/9308075] [INSPIRE].
K.A. Meissner and H. Nicolai, Conformal anomalies and gravitational waves, arXiv:1607.07312 [INSPIRE].
R. Kallosh, Cancellation of conformal and chiral anomalies in N ≥ 5 supergravities, Phys. Rev. D 95 (2017) 041701 [arXiv:1612.08978] [INSPIRE].
J.J.M. Carrasco, R. Kallosh, R. Roiban and A.A. Tseytlin, On the U(1) duality anomaly and the S-matrix of N = 4 supergravity, JHEP 07 (2013) 029 [arXiv:1303.6219] [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, New relations for gauge-theory amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:0805.3993] [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, Perturbative quantum gravity as a double copy of gauge theory, Phys. Rev. Lett. 105 (2010) 061602 [arXiv:1004.0476] [INSPIRE].
H. Elvang and Y.-T. Huang, Scattering amplitudes in gauge theory and gravity, Cambridge University Press, Cambridge U.K., (2015) [INSPIRE].
Z. Bern, S. Davies, T. Dennen and Y.-T. Huang, Absence of three-loop four-point divergences in N = 4 supergravity, Phys. Rev. Lett. 108 (2012) 201301 [arXiv:1202.3423] [INSPIRE].
Z. Bern, S. Davies, T. Dennen, A.V. Smirnov and V.A. Smirnov, Ultraviolet properties of N = 4 supergravity at four loops, Phys. Rev. Lett. 111 (2013) 231302 [arXiv:1309.2498] [INSPIRE].
R.E. Kallosh, Counterterms in extended supergravities, Phys. Lett. B 99 (1981) 122 [INSPIRE].
Z. Bern, S. Davies and T. Dennen, Enhanced ultraviolet cancellations in N = 5 supergravity at four loops, Phys. Rev. D 90 (2014) 105011 [arXiv:1409.3089] [INSPIRE].
P.S. Howe and U. Lindström, Higher order invariants in extended supergravity, Nucl. Phys. B 181 (1981) 487 [INSPIRE].
M.K. Gaillard and B. Zumino, Duality rotations for interacting fields, Nucl. Phys. B 193 (1981) 221 [INSPIRE].
R. Kallosh, On a possibility of a UV finite N = 8 supergravity, arXiv:0808.2310 [INSPIRE].
J.M. Drummond, P.J. Heslop and P.S. Howe, A note on N = 8 counterterms, arXiv:1008.4939 [INSPIRE].
D.Z. Freedman and E. Tonni, The D 2k R 4 invariants of N = 8 supergravity, JHEP 04 (2011) 006 [arXiv:1101.1672] [INSPIRE].
D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press, Cambridge U.K., (2012) [INSPIRE].
G. ’t Hooft and M.J.G. Veltman, Regularization and renormalization of gauge fields, Nucl. Phys. B 44 (1972) 189 [INSPIRE].
M.E. Peskin and D.V. Schroeder, An introduction to quantum field theory, Addison-Wesley, Reading U.S.A., (1995) [INSPIRE].
J.J.M. Carrasco, M. Chiodaroli, M. Günaydin and R. Roiban, One-loop four-point amplitudes in pure and matter-coupled N ≤ 4 supergravity, JHEP 03 (2013) 056 [arXiv:1212.1146] [INSPIRE].
M. Bianchi, H. Elvang and D.Z. Freedman, Generating tree amplitudes in N = 4 SYM and N = 8 SG, JHEP 09 (2008) 063 [arXiv:0805.0757] [INSPIRE].
P.S. Howe, Supergravity in superspace, Nucl. Phys. B 199 (1982) 309 [INSPIRE].
P.H. Damgaard, R. Huang, T. Sondergaard and Y. Zhang, The complete KLT-map between gravity and gauge theories, JHEP 08 (2012) 101 [arXiv:1206.1577] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1703.03879
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Freedman, D.Z., Kallosh, R., Murli, D. et al. Absence of U(1) anomalous superamplitudes in \( \mathcal{N} \) ≥ 5 supergravities. J. High Energ. Phys. 2017, 67 (2017). https://doi.org/10.1007/JHEP05(2017)067
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2017)067