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Soft bootstrap and supersymmetry. (English) Zbl 1409.81146

Summary: The soft bootstrap is an on-shell method to constrain the landscape of effective field theories (EFTs) of massless particles via the consistency of the low-energy S-matrix. Given assumptions on the on-shell data (particle spectra, linear symmetries, and low-energy theorems), the soft bootstrap is an efficient algorithm for determining the possible consistency of an EFT with those properties. The implementation of the soft bootstrap uses the recently discovered method of soft subtracted recursion. We derive a precise criterion for the validity of these recursion relations and show that they fail exactly when the assumed symmetries can be trivially realized by independent operators in the effective action. We use this to show that the possible pure (real and complex) scalar, fermion, and vector exceptional EFTs are highly constrained. Next, we prove how the soft behavior of states in a supermultiplet must be related and illustrate the results in extended supergravity. We demonstrate the power of the soft bootstrap in two applications. First, for the \( \mathcal{N}=1\) and \( \mathcal{N}=2\) \(\mathbb C {\mathbb{P}}^1\) nonlinear sigma models, we show that on-shell constructibility establishes the emergence of accidental IR symmetries. This includes a new on-shell perspective on the interplay between \( \mathcal{N}=2\) supersymmetry, low-energy theorems, and electromagnetic duality. We also show that \( \mathcal{N}=2\) supersymmetry requires 3-point interactions with the photon that make the soft behavior of the scalar \(O(1)\) instead of vanishing, despite the underlying symmetric coset. Second, we study Galileon theories, including aspects of supersymmetrization, the possibility of a vector-scalar Galileon EFT, and the existence of higher-derivative corrections preserving the enhanced special Galileon symmetry. The latter is addressed both by soft bootstrap and by application of double-copy/KLT relations applied to higher-derivative corrections of chiral perturbation theory.

MSC:

81T60 Supersymmetric field theories in quantum mechanics
81U20 \(S\)-matrix theory, etc. in quantum theory

References:

[1] S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 1., Phys. Rev.177 (1969) 2239 [INSPIRE].
[2] C.G. Callan Jr., S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 2., Phys. Rev.177 (1969) 2247 [INSPIRE].
[3] D.V. Volkov, Phenomenological Lagrangians, Fiz. Elem. Chast. Atom. Yadra4 (1973) 3 [INSPIRE].
[4] H. Georgi, On-shell effective field theory, Nucl. Phys.B 361 (1991) 339 [INSPIRE]. · doi:10.1016/0550-3213(91)90244-R
[5] C. Arzt, Reduced effective Lagrangians, Phys. Lett.B 342 (1995) 189 [hep-ph/9304230] [INSPIRE].
[6] 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]. · doi:10.1103/PhysRevLett.114.221602
[7] 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]. · doi:10.1103/PhysRevLett.116.041601
[8] C. Cheung, K. Kampf, J. Novotny, C.-H. Shen and J. Trnka, A Periodic Table of Effective Field Theories, JHEP02 (2017) 020 [arXiv:1611.03137] [INSPIRE]. · Zbl 1377.81123 · doi:10.1007/JHEP02(2017)020
[9] 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]. · Zbl 1207.81088 · doi:10.1016/j.nuclphysb.2005.02.030
[10] 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]. · doi:10.1103/PhysRevLett.94.181602
[11] K. Risager, A Direct proof of the CSW rules, JHEP12 (2005) 003 [hep-th/0508206] [INSPIRE]. · doi:10.1088/1126-6708/2005/12/003
[12] H. Elvang, D.Z. Freedman and M. Kiermaier, Proof of the MHV vertex expansion for all tree amplitudes in N = 4 SYM theory, JHEP06 (2009) 068 [arXiv:0811.3624] [INSPIRE]. · doi:10.1088/1126-6708/2009/06/068
[13] T. Cohen, H. Elvang and M. Kiermaier, On-shell constructibility of tree amplitudes in general field theories, JHEP04 (2011) 053 [arXiv:1010.0257] [INSPIRE]. · Zbl 1250.81072 · doi:10.1007/JHEP04(2011)053
[14] C. Cheung, C.-H. Shen and J. Trnka, Simple Recursion Relations for General Field Theories, JHEP06 (2015) 118 [arXiv:1502.05057] [INSPIRE]. · Zbl 1388.81257 · doi:10.1007/JHEP06(2015)118
[15] L. Susskind and G. Frye, Algebraic aspects of pionic duality diagrams, Phys. Rev.D 1 (1970) 1682 [INSPIRE].
[16] A. Galli and E. Galli, Implications of certain algebraic aspects of dual resonance models, Phys. Rev.D 2 (1970) 1081 [INSPIRE].
[17] A. Galli and E. Galli, Further comments on the relations between dual models and chiral symmetry breaking, Phys. Rev.D 4 (1971) 1253 [INSPIRE].
[18] Z. Yin, The Infrared Structure of Exceptional Scalar Theories, arXiv:1810.07186 [INSPIRE]. · Zbl 1414.81164
[19] D. Simmons-Duffin, The Conformal Bootstrap, in Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings (TASI 2015), Boulder, CO, U.S.A., June 1-26, 2015, pp. 1-74 (2017) [https://doi.org/10.1142/9789813149441_0001] [arXiv:1602.07982] [INSPIRE]. · Zbl 1359.81165
[20] D. Poland, S. Rychkov and A. Vichi, The Conformal Bootstrap: Theory, Numerical Techniques and Applications, Rev. Mod. Phys.91 (2019) 015002 [arXiv:1805.04405] [INSPIRE]. · doi:10.1103/RevModPhys.91.015002
[21] I. Low and A.V. Manohar, Spontaneously broken space-time symmetries and Goldstone’s theorem, Phys. Rev. Lett.88 (2002) 101602 [hep-th/0110285] [INSPIRE]. · doi:10.1103/PhysRevLett.88.101602
[22] K. Hinterbichler and A. Joyce, Hidden symmetry of the Galileon, Phys. Rev.D 92 (2015) 023503 [arXiv:1501.07600] [INSPIRE].
[23] F. Farakos, C. Germani and A. Kehagias, On ghost-free supersymmetric galileons, JHEP11 (2013) 045 [arXiv:1306.2961] [INSPIRE]. · Zbl 1342.83471
[24] 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]. · Zbl 1398.81240 · doi:10.1016/j.physletb.2018.04.032
[25] R. Klein, E. Malek, D. Roest and D. Stefanyszyn, No-go theorem for a gauge vector as a spacetime Goldstone mode, Phys. Rev.D 98 (2018) 065001 [arXiv:1806.06862] [INSPIRE].
[26] K. Kampf, J. Novotny and J. Trnka, Tree-level Amplitudes in the Nonlinear σ-model, JHEP05 (2013) 032 [arXiv:1304.3048] [INSPIRE]. · Zbl 1392.81139 · doi:10.1007/JHEP05(2013)032
[27] H. Lüo and C. Wen, Recursion relations from soft theorems, JHEP03 (2016) 088 [arXiv:1512.06801] [INSPIRE]. · doi:10.1007/JHEP03(2016)088
[28] H. Elvang and Y.-t. Huang, Scattering Amplitudes, arXiv:1308.1697 [INSPIRE]. · Zbl 1332.81010
[29] H. Elvang and Y.-t. Huang, Scattering Amplitudes in Gauge Theory and Gravity, Cambridge University Press (2015) [INSPIRE]. · Zbl 1332.81010
[30] J.M. Henn and J.C. Plefka, Scattering Amplitudes in Gauge Theories, Lect. Notes Phys.883 (2014) 1 [INSPIRE]. · Zbl 1315.81005
[31] L.J. Dixon, A brief introduction to modern amplitude methods, in Proceedings, 2012 European School of High-Energy Physics (ESHEP 2012), La Pommeraye, Anjou, France, June 06-19, 2012, pp. 31-67 (2014) [https://doi.org/10.5170/CERN-2014-008.31] [arXiv:1310.5353] [INSPIRE].
[32] 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]. · doi:10.1103/PhysRevLett.118.231601
[33] Y. Nambu and G. Jona-Lasinio, Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. 1., Phys. Rev.122 (1961) 345 [INSPIRE].
[34] C. Cheung and C.-H. Shen, private communications.
[35] 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]. · doi:10.1103/PhysRevLett.120.261602
[36] C. de Rham and G. Gabadadze, Selftuned Massive Spin-2, Phys. Lett.B 693 (2010) 334 [arXiv:1006.4367] [INSPIRE]. · doi:10.1016/j.physletb.2010.08.043
[37] C. de Rham and G. Gabadadze, Generalization of the Fierz-Pauli Action, Phys. Rev.D 82 (2010) 044020 [arXiv:1007.0443] [INSPIRE].
[38] K. Hinterbichler, Theoretical Aspects of Massive Gravity, Rev. Mod. Phys.84 (2012) 671 [arXiv:1105.3735] [INSPIRE]. · doi:10.1103/RevModPhys.84.671
[39] M.T. Grisaru, H.N. Pendleton and P. van Nieuwenhuizen, Supergravity and the S Matrix, Phys. Rev.D 15 (1977) 996 [INSPIRE].
[40] M.T. Grisaru and H.N. Pendleton, Some Properties of Scattering Amplitudes in Supersymmetric Theories, Nucl. Phys.B 124 (1977) 81 [INSPIRE]. · doi:10.1016/0550-3213(77)90277-2
[41] H. Elvang, D.Z. Freedman and M. Kiermaier, Solution to the Ward Identities for Superamplitudes, JHEP10 (2010) 103 [arXiv:0911.3169] [INSPIRE]. · Zbl 1291.81243 · doi:10.1007/JHEP10(2010)103
[42] R.H. Boels and W. Wormsbecher, Spontaneously broken conformal invariance in observables, arXiv:1507.08162 [INSPIRE].
[43] 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].
[44] M. Bianchi, A.L. Guerrieri, Y.-t. Huang, C.-J. Lee and C. Wen, Exploring soft constraints on effective actions, JHEP10 (2016) 036 [arXiv:1605.08697] [INSPIRE]. · Zbl 1390.81248 · doi:10.1007/JHEP10(2016)036
[45] N. Bobev, H. Elvang and T.M. Olson, Dilaton effective action with N = 1 supersymmetry, JHEP04 (2014) 157 [arXiv:1312.2925] [INSPIRE]. · doi:10.1007/JHEP04(2014)157
[46] N. Craig, H. Elvang, M. Kiermaier and T. Slatyer, Massive amplitudes on the Coulomb branch of N = 4 SYM, JHEP12 (2011) 097 [arXiv:1104.2050] [INSPIRE]. · Zbl 1306.81088 · doi:10.1007/JHEP12(2011)097
[47] S. Weinberg, Infrared photons and gravitons, Phys. Rev.140 (1965) B516 [INSPIRE]. · doi:10.1103/PhysRev.140.B516
[48] H. Elvang and M. Kiermaier, Stringy KLT relations, global symmetries and E7(7)violation, JHEP10 (2010) 108 [arXiv:1007.4813] [INSPIRE]. · Zbl 1291.81308 · doi:10.1007/JHEP10(2010)108
[49] J. Broedel and L.J. Dixon, R4counterterm and E7(7)symmetry in maximal supergravity, JHEP05 (2010) 003 [arXiv:0911.5704] [INSPIRE]. · Zbl 1288.81131 · doi:10.1007/JHEP05(2010)003
[50] I. Low and Z. Yin, The Infrared Structure of Nambu-Goldstone Bosons, JHEP10 (2018) 078 [arXiv:1804.08629] [INSPIRE]. · Zbl 1402.83099 · doi:10.1007/JHEP10(2018)078
[51] B. Zumino, Supersymmetry and Kähler Manifolds, Phys. Lett.B 87 (1979) 203 [INSPIRE]. · doi:10.1016/0370-2693(79)90964-X
[52] D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press, Cambridge, U.K. (2012) [INSPIRE]. · Zbl 1245.83001 · doi:10.1017/CBO9781139026833
[53] M. Bando, T. Kuramoto, T. Maskawa and S. Uehara, Structure of Nonlinear Realization in Supersymmetric Theories, Phys. Lett.B 138 (1984) 94 [INSPIRE]. · Zbl 1022.81760 · doi:10.1016/0370-2693(84)91880-X
[54] H. Elvang, Y.-t. Huang and C. Peng, On-shell superamplitudes in N < 4 SYM, JHEP09 (2011) 031 [arXiv:1102.4843] [INSPIRE]. · Zbl 1301.81120
[55] A. Laddha and P. Mitra, Asymptotic Symmetries and Subleading Soft Photon Theorem in Effective Field Theories, JHEP05 (2018) 132 [arXiv:1709.03850] [INSPIRE]. · doi:10.1007/JHEP05(2018)132
[56] M. Heydeman, J.H. Schwarz and C. Wen, M5-Brane and D-brane Scattering Amplitudes, JHEP12 (2017) 003 [arXiv:1710.02170] [INSPIRE]. · Zbl 1383.81166 · doi:10.1007/JHEP12(2017)003
[57] G. Goon, K. Hinterbichler, A. Joyce and M. Trodden, Galileons as Wess-Zumino Terms, JHEP06 (2012) 004 [arXiv:1203.3191] [INSPIRE]. · doi:10.1007/JHEP06(2012)004
[58] C. de Rham and A.J. Tolley, DBI and the Galileon reunited, JCAP05 (2010) 015 [arXiv:1003.5917] [INSPIRE]. · doi:10.1088/1475-7516/2010/05/015
[59] J. Beltran Jimenez and L. Heisenberg, Derivative self-interactions for a massive vector field, Phys. Lett.B 757 (2016) 405 [arXiv:1602.03410] [INSPIRE]. · Zbl 1360.83046 · doi:10.1016/j.physletb.2016.04.017
[60] A. Padilla, D. Stefanyszyn and T. Wilson, Probing Scalar Effective Field Theories with the Soft Limits of Scattering Amplitudes, JHEP04 (2017) 015 [arXiv:1612.04283] [INSPIRE]. · Zbl 1378.81147 · doi:10.1007/JHEP04(2017)015
[61] F. Cachazo, S. He and E.Y. Yuan, Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM, JHEP07 (2015) 149 [arXiv:1412.3479] [INSPIRE]. · Zbl 1388.83196 · doi:10.1007/JHEP07(2015)149
[62] J. Broedel and L.J. Dixon, Color-kinematics duality and double-copy construction for amplitudes from higher-dimension operators, JHEP10 (2012) 091 [arXiv:1208.0876] [INSPIRE]. · doi:10.1007/JHEP10(2012)091
[63] G. Chen and Y.-J. Du, Amplitude Relations in Non-linear σ-model, JHEP01 (2014) 061 [arXiv:1311.1133] [INSPIRE]. · Zbl 1390.81194 · doi:10.1007/JHEP01(2014)061
[64] K. Kampf, J. Novotny and J. Trnka, Recursion relations for tree-level amplitudes in the SU(N) nonlinear σ-model, Phys. Rev.D 87 (2013) 081701 [arXiv:1212.5224] [INSPIRE].
[65] J.J.M. Carrasco, C.R. Mafra and O. Schlotterer, Abelian Z-theory: NLSM amplitudes and α′-corrections from the open string, JHEP06 (2017) 093 [arXiv:1608.02569] [INSPIRE]. · Zbl 1380.83251 · doi:10.1007/JHEP06(2017)093
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