Abstract
We use on-shell methods to study the non-supersymmetric and supersymmetric low-energy S-matrix on a probe D3-brane, including both the 1-loop contributions of massless states as well as the effects of higher-derivative operators. Our results include: (1) A derivation of the duality invariance of Born-Infeld electrodynamics as the dimensional oxidation of the group of spatial rotations transverse to a probe M2-brane; this is done using a novel implementation of subtracted on-shell recursion. (2) The first explicit loop-level BCJ double-copy in a non-gravitational model, namely the calculation of the 4-point self-dual amplitude of non-supersymmetric Born-Infeld. (3) From previous results for n-point self-dual 1-loop BI amplitudes and the conjectured dimension-shifting relations in Yang-Mills, we obtain an explicit all-multiplicity, at all orders in E, expression for the 1-loop integrand of the MHV sector of \( \mathcal{N} \) = 4 DBI. (4) For all n > 4, the explicitly integrated duality-violating 1-loop amplitudes (self-dual and next-to-self-dual in pure BI as well as MHV in \( \mathcal{N} \) = 4 DBI) are shown to be removable at \( \mathcal{O}\left({\upepsilon}^0\right) \) by adding finite local counterterms; we propose that this may be true more generally at 1-loop order. (5) We find that in non-supersymmetric Born-Infeld, not all finite local counterterms needed to restore electromagnetic duality can be constructed using the double-copy with higher-derivative corrections, suggesting a fundamental tension between electromagnetic duality and color-kinematics duality at loop-level. Finally we comment on oxidation of duality symmetries in supergravity and the parallels it has to the M2-brane to D3-brane oxidation demonstrated in this paper.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C. Montonen and D. I. Olive, Magnetic monopoles as gauge particles?, Phys. Lett. B 72 (1977) 117 [INSPIRE].
M. K. Gaillard and B. Zumino, Duality rotations for interacting fields, Nucl. Phys. B 193 (1981) 221 [INSPIRE].
J. Novotný, Self-duality, helicity conservation and normal ordering in nonlinear QED, Phys. Rev. D 98 (2018) 085015 [arXiv:1806.02167] [INSPIRE].
A. A. Rosly and K. G. Selivanov, Helicity conservation in Born-Infeld theory, in Workshop on string theory and complex geometry, (2002) [hep-th/0204229] [INSPIRE].
Z. Bern, J. Parra-Martinez and R. Roiban, Canceling the U(1) anomaly in the S matrix of N = 4 supergravity, Phys. Rev. Lett. 121 (2018) 101604 [arXiv:1712.03928] [INSPIRE].
H. Kawai, D. C. Lewellen and S.-H. Henry Tye, A relation between tree amplitudes of closed and open strings, Nucl. Phys. B 269 (1986) 1 [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].
F. Cachazo, S. He and E. Y. Yuan, Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM, JHEP 07 (2015) 149 [arXiv:1412.3479] [INSPIRE].
H. Elvang, M. Hadjiantonis, C. R. T. Jones and S. Paranjape, All-multiplicity one-loop amplitudes in Born-Infeld electrodynamics from generalized unitarity, JHEP 03 (2020) 009 [arXiv:1906.05321] [INSPIRE].
S. Deser and C. Teitelboim, Duality transformations of Abelian and non-Abelian gauge fields, Phys. Rev. D 13 (1976) 1592 [INSPIRE].
J. H. Schwarz and A. Sen, Duality symmetric actions, Nucl. Phys. B 411 (1994) 35 [hep-th/9304154] [INSPIRE].
M. Aganagic, C. Popescu and J. H. Schwarz, D-brane actions with local kappa symmetry, Phys. Lett. B 393 (1997) 311 [hep-th/9610249] [INSPIRE].
E. S. Fradkin and A. A. Tseytlin, Nonlinear electrodynamics from quantized strings, Phys. Lett. B 163 (1985) 123 [INSPIRE].
C. Cheung, K. Kampf, J. Novotny, C.-H. Shen, J. Trnka and C. Wen, Vector effective field theories from soft limits, Phys. Rev. Lett. 120 (2018) 261602 [arXiv:1801.01496] [INSPIRE].
C. Cheung, K. Kampf, J. Novotny and J. Trnka, Effective field theories from soft limits of scattering amplitudes, Phys. Rev. Lett. 114 (2015) 221602 [arXiv:1412.4095] [INSPIRE].
M. Heydeman, J. H. Schwarz and C. Wen, M5-brane and D-brane scattering amplitudes, JHEP 12 (2017) 003 [arXiv:1710.02170] [INSPIRE].
C. Wen and S.-Q. Zhang, D3-brane loop amplitudes from M5-brane tree amplitudes, JHEP 07 (2020) 098 [arXiv:2004.02735] [INSPIRE].
C. Cheung, K. Kampf, J. Novotny, C.-H. Shen and J. Trnka, On-shell recursion relations for effective field theories, Phys. Rev. Lett. 116 (2016) 041601 [arXiv:1509.03309] [INSPIRE].
C. Cheung, K. Kampf, J. Novotny, C.-H. Shen and J. Trnka, A periodic table of effective field theories, JHEP 02 (2017) 020 [arXiv:1611.03137] [INSPIRE].
H. Lüo and C. Wen, Recursion relations from soft theorems, JHEP 03 (2016) 088 [arXiv:1512.06801] [INSPIRE].
H. Elvang, M. Hadjiantonis, C. R. T. Jones and S. Paranjape, Soft bootstrap and supersymmetry, JHEP 01 (2019) 195 [arXiv:1806.06079] [INSPIRE].
C. de Rham and A. J. Tolley, DBI and the Galileon reunited, JCAP 05 (2010) 015 [arXiv:1003.5917] [INSPIRE].
J. Polchinski, String theory. Volume 1: an introduction to the bosonic string, Cambridge University Press, Cambridge, U.K. (2007) [INSPIRE].
C. Schmidhuber, D-brane actions, Nucl. Phys. B 467 (1996) 146 [hep-th/9601003] [INSPIRE].
P. K. Townsend, D-branes from M-branes, Phys. Lett. B 373 (1996) 68 [hep-th/9512062] [INSPIRE].
E. Witten, Conformal field theory in four and six dimensions, in Symposium on topology, geometry and quantum field theory (Segalfest), (2007) [arXiv:0712.0157] [INSPIRE].
O. D. Andreev and A. A. Tseytlin, Partition function representation for the open superstring effective action: cancellation of Mobius infinities and derivative corrections to Born-Infeld Lagrangian, Nucl. Phys. B 311 (1988) 205 [INSPIRE].
F. Cachazo, S. He and E. Y. Yuan, Scattering of massless particles in arbitrary dimensions, Phys. Rev. Lett. 113 (2014) 171601 [arXiv:1307.2199] [INSPIRE].
F. Cachazo, S. He and E. Y. Yuan, Scattering equations and Kawai-Lewellen-Tye orthogonality, Phys. Rev. D 90 (2014) 065001 [arXiv:1306.6575] [INSPIRE].
F. Cachazo, S. He and E. Y. Yuan, Scattering of massless particles: scalars, gluons and gravitons, JHEP 07 (2014) 033 [arXiv:1309.0885] [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].
J. Faller and J. Plefka, Positive helicity Einstein-Yang-Mills amplitudes from the double copy method, Phys. Rev. D 99 (2019) 046008 [arXiv:1812.04053] [INSPIRE].
Z. Bern, A. De Freitas, L. J. Dixon and H. L. Wong, Supersymmetric regularization, two loop QCD amplitudes and coupling shifts, Phys. Rev. D 66 (2002) 085002 [hep-ph/0202271] [INSPIRE].
Z. Bern, L. J. Dixon, D. C. Dunbar and D. A. Kosower, One loop selfdual and N = 4 super Yang-Mills, Phys. Lett. B 394 (1997) 105 [hep-th/9611127] [INSPIRE].
R. Britto, G. R. Jehu and A. Orta, The dimension-shift conjecture for one-loop amplitudes, arXiv:2011.13821 [INSPIRE].
M. Shmakova, One loop corrections to the D3-brane action, Phys. Rev. D 62 (2000) 104009 [hep-th/9906239] [INSPIRE].
Z. Bern, L. J. Dixon and D. A. Kosower, New QCD results from string theory, in International conference on strings ′93, (1993) [hep-th/9311026] [INSPIRE].
G. Ossola, C. G. Papadopoulos and R. Pittau, On the rational terms of the one-loop amplitudes, JHEP 05 (2008) 004 [arXiv:0802.1876] [INSPIRE].
G. Passarino and M. J. G. Veltman, One loop corrections for e+ e− annihilation into μ+ μ− in the Weinberg model, Nucl. Phys. B 160 (1979) 151 [INSPIRE].
Z. Bern, L. J. Dixon, M. Perelstein and J. S. Rozowsky, One loop n point helicity amplitudes in (selfdual) gravity, Phys. Lett. B 444 (1998) 273 [hep-th/9809160] [INSPIRE].
Z. Bern and G. Chalmers, Factorization in one loop gauge theory, Nucl. Phys. B 447 (1995) 465 [hep-ph/9503236] [INSPIRE].
R. Kleiss and H. Kuijf, Multi-gluon cross-sections and five jet production at hadron colliders, Nucl. Phys. B 312 (1989) 616 [INSPIRE].
L. J. Dixon and Y. Shadmi, Testing gluon selfinteractions in three jet events at hadron colliders, Nucl. Phys. B 423 (1994) 3 [Erratum ibid. 452 (1995) 724] [hep-ph/9312363] [INSPIRE].
T. Azevedo, M. Chiodaroli, H. Johansson and O. Schlotterer, Heterotic and bosonic string amplitudes via field theory, JHEP 10 (2018) 012 [arXiv:1803.05452] [INSPIRE].
J. J. M. Carrasco, C. R. Mafra and O. Schlotterer, Abelian Z -theory: NLSM amplitudes and α′-corrections from the open string, JHEP 06 (2017) 093 [arXiv:1608.02569] [INSPIRE].
J. Broedel, O. Schlotterer and S. Stieberger, Polylogarithms, multiple zeta values and superstring amplitudes, Fortsch. Phys. 61 (2013) 812 [arXiv:1304.7267] [INSPIRE].
Z. Bern, S. Davies, T. Dennen, Y.-T. Huang and J. Nohle, Color-kinematics duality for pure Yang-Mills and gravity at one and two loops, Phys. Rev. D 92 (2015) 045041 [arXiv:1303.6605] [INSPIRE].
H. Elvang and M. Kiermaier, Stringy KLT relations, global symmetries, and E7(7) violation, JHEP 10 (2010) 108 [arXiv:1007.4813] [INSPIRE].
N. Marcus, Composite anomalies in supergravity, Phys. Lett. B 157 (1985) 383 [INSPIRE].
Y.-T. Huang, U. Kol and D. O’Connell, Double copy of electric-magnetic duality, Phys. Rev. D 102 (2020) 046005 [arXiv:1911.06318] [INSPIRE].
R. Alawadhi, D. S. Berman, B. Spence and D. Peinador Veiga, S-duality and the double copy, JHEP 03 (2020) 059 [arXiv:1911.06797] [INSPIRE].
N. Marcus and J. H. Schwarz, Three-dimensional supergravity theories, Nucl. Phys. B 228 (1983) 145 [INSPIRE].
E. Cremmer, B. Julia, H. Lü and C. N. Pope, Higher dimensional origin of D = 3 coset symmetries, hep-th/9909099 [INSPIRE].
A. Keurentjes, The group theory of oxidation, Nucl. Phys. B 658 (2003) 303 [hep-th/0210178] [INSPIRE].
S. Ananth, L. Brink and S. Majumdar, E8 in N = 8 supergravity in four dimensions, JHEP 01 (2018) 024 [arXiv:1711.09110] [INSPIRE].
F. Cachazo, S. He and E. Y. Yuan, Scattering in three dimensions from rational maps, JHEP 10 (2013) 141 [arXiv:1306.2962] [INSPIRE].
H. Elvang and Y.-T. Huang, Scattering amplitudes in gauge theory and gravity, Cambridge University Press, Cambridge, U.K. (2015).
Z. Bern and A. G. Morgan, Massive loop amplitudes from unitarity, Nucl. Phys. B 467 (1996) 479 [hep-ph/9511336] [INSPIRE].
N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the simplest quantum field theory?, JHEP 09 (2010) 016 [arXiv:0808.1446] [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: 2006.08928
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
Elvang, H., Hadjiantonis, M., Jones, C.R.T. et al. Electromagnetic duality and D3-brane scattering amplitudes beyond leading order. J. High Energ. Phys. 2021, 173 (2021). https://doi.org/10.1007/JHEP04(2021)173
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2021)173