Abstract
We use the amplitude soft bootstrap method to explore the space of effective field theories (EFT) of massless vectors and scalars. It is known that demanding vanishing soft limits fixes uniquely a special class of EFTs: non-linear sigma model, scalar Galileon and Born-Infeld theories. Based on the amplitudes analysis, we conjecture no-go theorems for higher-derivative vector theories and theories with coupled vectors and scalars. We then allow for more general soft theorems where the non-trivial part of the soft limit of the (n+1)-pt amplitude is equal to a linear combination of n-pt amplitudes. We derive the form of these soft theorems for general power-counting and spins of particles and use it as an input into the soft bootstrap method in the case of Galileon power-counting and coupled scalar-vector theories. We show that this unifies the description of existing Galileon theories and leads us to the discovery of a new exceptional theory: Special scalar-vector Galileon.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes, Nucl. Phys. B 435 (1995) 59 [hep-ph/9409265] [INSPIRE].
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys. B 425 (1994) 217 [hep-ph/9403226] [INSPIRE].
R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys. B 715 (2005) 499 [hep-th/0412308] [INSPIRE].
R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94 (2005) 181602 [hep-th/0501052] [INSPIRE].
T. Cohen, H. Elvang and M. Kiermaier, On-shell constructibility of tree amplitudes in general field theories, JHEP 04 (2011) 053 [arXiv:1010.0257] [INSPIRE].
C. Cheung, C.-H. Shen and J. Trnka, Simple recursion relations for general field theories, JHEP 06 (2015) 118 [arXiv:1502.05057] [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].
N. Arkani-Hamed, J.L. Bourjaily, F. Cachazo, S. Caron-Huot and J. Trnka, The all-loop integrand for scattering amplitudes in planar N = 4 SYM, JHEP 01 (2011) 041 [arXiv:1008.2958] [INSPIRE].
C. Baadsgaard et al., New representations of the perturbative S-matrix, Phys. Rev. Lett. 116 (2016) 061601 [arXiv:1509.02169] [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 of massless particles: scalars, gluons and gravitons, JHEP 07 (2014) 033 [arXiv:1309.0885] [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].
Z. Bern, J.J. Carrasco, M. Chiodaroli, H. Johansson and R. Roiban, The duality between color and kinematics and its applications, arXiv:1909.01358 [INSPIRE].
N. Arkani-Hamed et al., Grassmannian Geometry of Scattering Amplitudes, Cambridge University Press, Cambridge U.K. (2016).
N. Arkani-Hamed and J. Trnka, Into the amplituhedron, JHEP 12 (2014) 182 [arXiv:1312.7878] [INSPIRE].
N. Arkani-Hamed and J. Trnka, The amplituhedron, JHEP 10 (2014) 030 [arXiv:1312.2007] [INSPIRE].
N. Arkani-Hamed, A. Hodges and J. Trnka, Positive amplitudes in the amplituhedron, JHEP 08 (2015) 030 [arXiv:1412.8478] [INSPIRE].
N. Arkani-Hamed, H. Thomas and J. Trnka, Unwinding the amplituhedron in binary, JHEP 01 (2018) 016 [arXiv:1704.05069] [INSPIRE].
N. Arkani-Hamed, C. Langer, A. Yelleshpur Srikant and J. Trnka, Deep into the amplituhedron: amplitude singularities at all loops and legs, Phys. Rev. Lett. 122 (2019) 051601 [arXiv:1810.08208] [INSPIRE].
D. Damgaard, L. Ferro, T. Lukowski and M. Parisi, The momentum amplituhedron, JHEP 08 (2019) 042 [arXiv:1905.04216] [INSPIRE].
E. Herrmann, C. Langer, J. Trnka and M. Zheng, Positive geometry, local triangulations, and the dual of the Amplituhedron, JHEP 01 (2021) 035 [arXiv:2009.05607] [INSPIRE].
N. Arkani-Hamed, Y. Bai, S. He and G. Yan, Scattering forms and the positive geometry of kinematics, color and the worldsheet, JHEP 05 (2018) 096 [arXiv:1711.09102] [INSPIRE].
Z. Bern, E. Herrmann, S. Litsey, J. Stankowicz and J. Trnka, Evidence for a nonplanar amplituhedron, JHEP 06 (2016) 098 [arXiv:1512.08591] [INSPIRE].
N. Arkani-Hamed, S. He and T. Lam, Stringy canonical forms, JHEP 02 (2021) 069 [arXiv:1912.08707] [INSPIRE].
J. Trnka, Towards the gravituhedron: new expressions for NMHV gravity amplitudes, JHEP 04 (2021) 253 [arXiv:2012.15780] [INSPIRE].
M. Jagadale and A. Laddha, Towards positive geometry of multi scalar field amplitudes: accordiohedron and effective field theory, arXiv:2104.04915 [INSPIRE].
K. Kampf, J. Novotny and J. Trnka, Recursion relations for tree-level amplitudes in the SU(N) nonlinear sigma model, Phys. Rev. D 87 (2013) 081701 [arXiv:1212.5224] [INSPIRE].
K. Kampf, J. Novotny and J. Trnka, Tree-level amplitudes in the nonlinear sigma model, JHEP 05 (2013) 032 [arXiv:1304.3048] [INSPIRE].
J. Bijnens, K. Kampf and M. Sjö, Higher-order tree-level amplitudes in the nonlinear sigma model, JHEP 11 (2019) 074 [Erratum ibid. 03 (2021) 066] [arXiv:1909.13684] [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].
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. Elvang, M. Hadjiantonis, C.R.T. Jones and S. Paranjape, Soft bootstrap and supersymmetry, JHEP 01 (2019) 195 [arXiv:1806.06079] [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].
I. Low and Z. Yin, New flavor-kinematics dualities and extensions of nonlinear Sigma models, Phys. Lett. B 807 (2020) 135544 [arXiv:1911.08490] [INSPIRE].
I. Low, L. Rodina and Z. Yin, Double copy in higher derivative operators of Nambu-Goldstone bosons, Phys. Rev. D 103 (2021) 025004 [arXiv:2009.00008] [INSPIRE].
E. Casali, Y. Geyer, L. Mason, R. Monteiro and K.A. Roehrig, New ambitwistor string theories, JHEP 11 (2015) 038 [arXiv:1506.08771] [INSPIRE].
C. Cheung, C.-H. Shen and C. Wen, Unifying relations for scattering amplitudes, JHEP 02 (2018) 095 [arXiv:1705.03025] [INSPIRE].
Y.-t. Huang and C. Wen, Soft theorems from anomalous symmetries, JHEP 12 (2015) 143 [arXiv:1509.07840] [INSPIRE].
P. Di Vecchia, R. Marotta, M. Mojaza and J. Nohle, New soft theorems for the gravity dilaton and the Nambu-Goldstone dilaton at subsubleading order, Phys. Rev. D 93 (2016) 085015 [arXiv:1512.03316] [INSPIRE].
M. Bianchi, A.L. Guerrieri, Y.-t. Huang, C.-J. Lee and C. Wen, Exploring soft constraints on effective actions, JHEP 10 (2016) 036 [arXiv:1605.08697] [INSPIRE].
M.B. Green and C. Wen, Modular forms and SL(2, ℤ)-covariance of type IIB superstring theory, JHEP 06 (2019) 087 [arXiv:1904.13394] [INSPIRE].
Y. Wang and X. Yin, Supervertices and non-renormalization conditions in maximal supergravity theories, arXiv:1505.05861 [INSPIRE].
K. Kampf, J. Novotny, M. Shifman and J. Trnka, New soft theorems for Goldstone boson amplitudes, Phys. Rev. Lett. 124 (2020) 111601 [arXiv:1910.04766] [INSPIRE].
N. Arkani-Hamed, L. Rodina and J. Trnka, Locality and unitarity of scattering amplitudes from singularities and gauge invariance, Phys. Rev. Lett. 120 (2018) 231602 [arXiv:1612.02797] [INSPIRE].
L. Rodina, Uniqueness from locality and BCFW shifts, JHEP 09 (2019) 078 [arXiv:1612.03885] [INSPIRE].
L. Rodina, Uniqueness from gauge invariance and the Adler zero, JHEP 09 (2019) 084 [arXiv:1612.06342] [INSPIRE].
L. Rodina, Scattering amplitudes from soft theorems and infrared behavior, Phys. Rev. Lett. 122 (2019) 071601 [arXiv:1807.09738] [INSPIRE].
J.J.M. Carrasco and L. Rodina, UV considerations on scattering amplitudes in a web of theories, Phys. Rev. D 100 (2019) 125007 [arXiv:1908.08033] [INSPIRE].
J.J.M. Carrasco, L. Rodina, Z. Yin and S. Zekioglu, Simple encoding of higher derivative gauge and gravity counterterms, Phys. Rev. Lett. 125 (2020) 251602 [arXiv:1910.12850] [INSPIRE].
L. Dai, I. Low, T. Mehen and A. Mohapatra, Operator counting and soft blocks in chiral perturbation theory, Phys. Rev. D 102 (2020) 116011 [arXiv:2009.01819] [INSPIRE].
L. Rodina and Z. Yin, Exploring the landscape for soft theorems of nonlinear Sigma models, arXiv:2102.08396 [INSPIRE].
J.J.M. Carrasco, L. Rodina and S. Zekioglu, Composing effective prediction at five points, JHEP 06 (2021) 169 [arXiv:2104.08370] [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].
J. Bonifacio, K. Hinterbichler, L.A. Johnson and A. Joyce, Shift-symmetric spin-1 theories, JHEP 09 (2019) 029 [arXiv:1906.10692] [INSPIRE].
P. Benincasa and F. Cachazo, Consistency conditions on the S-matrix of massless particles, arXiv:0705.4305 [INSPIRE].
H. Elvang, M. Hadjiantonis, C.R.T. Jones and S. Paranjape, On the supersymmetrization of Galileon theories in four dimensions, Phys. Lett. B 781 (2018) 656 [arXiv:1712.09937] [INSPIRE].
K. Hinterbichler and A. Joyce, Hidden symmetry of the Galileon, Phys. Rev. D 92 (2015) 023503 [arXiv:1501.07600] [INSPIRE].
J. Novotny, Geometry of special Galileons, Phys. Rev. D 95 (2017) 065019 [arXiv:1612.01738] [INSPIRE].
G. Bossard and H. Nicolai, Counterterms vs. dualities, JHEP 08 (2011) 074 [arXiv:1105.1273] [INSPIRE].
J. Novotný, Self-duality, helicity conservation and normal ordering in nonlinear QED, Phys. Rev. D 98 (2018) 085015 [arXiv:1806.02167] [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].
H. Elvang, M. Hadjiantonis, C.R.T. Jones and S. Paranjape, Electromagnetic duality and D3-brane scattering amplitudes beyond leading order, JHEP 04 (2021) 173 [arXiv:2006.08928] [INSPIRE].
C. Deffayet, A.E. Gümrükçüoğlu, S. Mukohyama and Y. Wang, A no-go theorem for generalized vector Galileons on flat spacetime, JHEP 04 (2014) 082 [arXiv:1312.6690] [INSPIRE].
J. Bonifacio, K. Hinterbichler, L.A. Johnson, A. Joyce and R.A. Rosen, Matter couplings and equivalence principles for soft scalars, JHEP 07 (2020) 056 [arXiv:1911.04490] [INSPIRE].
H. Lüo and C. Wen, Recursion relations from soft theorems, JHEP 03 (2016) 088 [arXiv:1512.06801] [INSPIRE].
H. Elvang, C.R.T. Jones and S.G. Naculich, Soft photon and graviton theorems in effective field theory, Phys. Rev. Lett. 118 (2017) 231601 [arXiv:1611.07534] [INSPIRE].
K. Kampf and J. Novotný, Scattering amplitudes and soft theorems in multi-flavor Galileon theories, JHEP 12 (2020) 056 [arXiv:2009.07940] [INSPIRE].
C. de Rham, M. Fasiello and A.J. Tolley, Galileon duality, Phys. Lett. B 733 (2014) 46 [arXiv:1308.2702] [INSPIRE].
K. Kampf and J. Novotny, Unification of Galileon dualities, JHEP 10 (2014) 006 [arXiv:1403.6813] [INSPIRE].
D. Roest, The special Galileon as Goldstone of diffeomorphisms, JHEP 01 (2021) 096 [arXiv:2004.09559] [INSPIRE].
L. Heisenberg, Generalised Proca theories, in the proceedings of the 52nd Rencontres de Moriond on Gravitation, March 25–April 1, La Thuile, Italy (2017) [arXiv:1705.05387] [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: 2104.10693
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
Kampf, K., Novotný, J., Přeučil, F. et al. Multi-spin soft bootstrap and scalar-vector Galileon. J. High Energ. Phys. 2021, 153 (2021). https://doi.org/10.1007/JHEP07(2021)153
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2021)153