Abstract
Scattering amplitudes have the potential to provide new insights to the study of supergravity theories with gauged R-symmetry and Minkowski vacua. Such gaugings break supersymmetry spontaneously, either partly or completely. In this paper, we develop a framework for double-copy constructions of Abelian and non-Abelian gaugings of \( \mathcal{N}=8 \) supergravity with these properties. They are generally obtained as the double copy of a spontaneously-broken (possibly supersymmeric) gauge theory and a theory with explicitly-broken supersymmetry. We first identify purely-adjoint deformations of \( \mathcal{N}=4 \) super-Yang-Millstheorythatpreservethedualitybetweencolorandkinematics. A combination of Higgsing and orbifolding yields the needed duality-satisfying gauge-theory factors with multiple matter representations. We present three explicit examples. Two are Cremmer-Scherk-Schwarz gaugings with unbroken \( \mathcal{N}=6,\;4 \) supersymmetry and U(1) gauge group. The third has unbroken \( \mathcal{N}=4 \) supersymmetry and SU(2) × U(1) gauge group. We also discuss examples in which the double-copy method gives theories with explicitly-broken supersymmetry.
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References
E. Cremmer and B. Julia, The SO(8) Supergravity, Nucl. Phys. B 159 (1979) 141 [INSPIRE].
B. de Wit and H. Nicolai, N = 8 Supergravity, Nucl. Phys. B 208 (1982) 323 [INSPIRE].
C.M. Hull, Noncompact Gaugings of N = 8 Supergravity, Phys. Lett. B 142 (1984) 39 [INSPIRE].
C.M. Hull and N.P. Warner, Noncompact Gaugings From Higher Dimensions, Class. Quant. Grav. 5 (1988) 1517 [INSPIRE].
C.M. Hull and N.P. Warner, The Structure of the Gauged N = 8 Supergravity Theories, Nucl. Phys. B 253 (1985) 650 [INSPIRE].
M. Günaydin, L.J. Romans and N.P. Warner, Gauged N = 8 Supergravity in Five-Dimensions, Phys. Lett. 154B (1985) 268 [INSPIRE].
M. Günaydin, L.J. Romans and N.P. Warner, IIB, or Not IIB: That Is the Question, Phys. Lett. 164B (1985) 309 [INSPIRE].
M. Günaydin, G. Sierra and P.K. Townsend, The Geometry of N = 2 Maxwell-Einstein Supergravity and Jordan Algebras, Nucl. Phys. B 242 (1984) 244 [INSPIRE].
M. Günaydin, G. Sierra and P.K. Townsend, Gauging the d = 5 Maxwell-Einstein Supergravity Theories: More on Jordan Algebras, Nucl. Phys. B 253 (1985) 573 [INSPIRE].
M. Günaydin, G. Sierra and P.K. Townsend, More on d = 5 Maxwell-Einstein Supergravity: Symmetric Spaces and Kinks, Class. Quant. Grav. 3 (1986) 763 [INSPIRE].
M. Günaydin and M. Zagermann, The gauging of five-dimensional, N = 2 Maxwell-Einstein supergravity theories coupled to tensor multiplets, Nucl. Phys. B 572 (2000) 131 [hep-th/9912027] [INSPIRE].
M. Günaydin and M. Zagermann, Gauging the full R symmetry group in five-dimensional, N = 2 Yang-Mills Einstein tensor supergravity, Phys. Rev. D 63 (2001) 064023 [hep-th/0004117] [INSPIRE].
M. Günaydin and M. Zagermann, The vacua of 5-D, N = 2 gauged Yang-Mills/Einstein tensor supergravity: Abelian case, Phys. Rev. D 62 (2000) 044028 [hep-th/0002228] [INSPIRE].
H. Nicolai and H. Samtleben, Maximal gauged supergravity in three-dimensions, Phys. Rev. Lett. 86 (2001) 1686 [hep-th/0010076] [INSPIRE].
H. Nicolai and H. Samtleben, Compact and noncompact gauged maximal supergravities in three-dimensions, JHEP 04 (2001) 022 [hep-th/0103032] [INSPIRE].
B. de Wit, H. Samtleben and M. Trigiante, On Lagrangians and gaugings of maximal supergravities, Nucl. Phys. B 655 (2003) 93 [hep-th/0212239] [INSPIRE].
B. de Wit, H. Samtleben and M. Trigiante, The maximal D = 5 supergravities, Nucl. Phys. B 716 (2005) 215 [hep-th/0412173] [INSPIRE].
B. de Wit and H. Samtleben, Gauged maximal supergravities and hierarchies of nonAbelian vector-tensor systems, Fortsch. Phys. 53 (2005) 442 [hep-th/0501243] [INSPIRE].
H. Samtleben, Lectures on Gauged Supergravity and Flux Compactifications, Class. Quant. Grav. 25 (2008) 214002 [arXiv:0808.4076] [INSPIRE].
M. Trigiante, Gauged Supergravities, Phys. Rept. 680 (2017) 1 [arXiv:1609.09745] [INSPIRE].
F. Catino, G. Dall’Agata, G. Inverso and F. Zwirner, On the moduli space of spontaneously broken N = 8 supergravity, JHEP 09 (2013) 040 [arXiv:1307.4389] [INSPIRE].
G. Dall’Agata and G. Inverso, On the Vacua of N = 8 Gauged Supergravity in 4 Dimensions, Nucl. Phys. B 859 (2012) 70 [arXiv:1112.3345] [INSPIRE].
G. Dall’Agata, G. Inverso and M. Trigiante, Evidence for a family of SO(8) gauged supergravity theories, Phys. Rev. Lett. 109 (2012) 201301 [arXiv:1209.0760] [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. Johansson and A. Ochirov, Pure Gravities via Color-Kinematics Duality for Fundamental Matter, JHEP 11 (2015) 046 [arXiv:1407.4772] [INSPIRE].
Z. Bern, C. Boucher-Veronneau and H. Johansson, N ≥ 4 Supergravity Amplitudes from Gauge Theory at One Loop, Phys. Rev. D 84 (2011) 105035 [arXiv:1107.1935] [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. Chiodaroli, Q. Jin and R. Roiban, Color/kinematics duality for general abelian orbifolds of N = 4 super Yang-Mills theory, JHEP 01 (2014) 152 [arXiv:1311.3600] [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].
M. Chiodaroli, M. Günaydin, H. Johansson and R. Roiban, Complete construction of magical, symmetric and homogeneous N = 2 supergravities as double copies of gauge theories, Phys. Rev. Lett. 117 (2016) 011603 [arXiv:1512.09130] [INSPIRE].
H. Johansson, G. Kälin and G. Mogull, Two-loop supersymmetric QCD and half-maximal supergravity amplitudes, JHEP 09 (2017) 019 [arXiv:1706.09381] [INSPIRE].
M. Ben-Shahar and M. Chiodaroli, One-loop amplitudes for \( \mathcal{N}= 2 \) homogeneous supergravities, JHEP 03 (2019) 153 [arXiv:1812.00402] [INSPIRE].
H. Johansson and J. Nohle, Conformal Gravity from Gauge Theory, arXiv:1707.02965 [INSPIRE].
H. Johansson, G. Mogull and F. Teng, Unraveling conformal gravity amplitudes, JHEP 09 (2018) 080 [arXiv:1806.05124] [INSPIRE].
G. Chen and Y.-J. Du, Amplitude Relations in Non-linear σ-model, JHEP 01 (2014) 061 [arXiv:1311.1133] [INSPIRE].
G. Chen, Y.-J. Du, S. Li and H. Liu, Note on off-shell relations in nonlinear σ-model, JHEP 03 (2015) 156 [arXiv:1412.3722] [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].
Y.-J. Du and C.-H. Fu, Explicit BCJ numerators of nonlinear simga model, JHEP 09 (2016) 174 [arXiv:1606.05846] [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].
G. Chen, S. Li and H. Liu, Off-shell BCJ Relation in Nonlinear σ-model, arXiv:1609.01832 [INSPIRE].
C. Cheung and C.-H. Shen, Symmetry for Flavor-Kinematics Duality from an Action, Phys. Rev. Lett. 118 (2017) 121601 [arXiv:1612.00868] [INSPIRE].
S. Stieberger, Open & Closed vs. Pure Open String Disk Amplitudes, arXiv:0907.2211 [INSPIRE].
N.E.J. Bjerrum-Bohr, P.H. Damgaard and P. Vanhove, Minimal Basis for Gauge Theory Amplitudes, Phys. Rev. Lett. 103 (2009) 161602 [arXiv:0907.1425] [INSPIRE].
N.E.J. Bjerrum-Bohr, P.H. Damgaard, T. Sondergaard and P. Vanhove, Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes, JHEP 06 (2010) 003 [arXiv:1003.2403] [INSPIRE].
C.R. Mafra, O. Schlotterer and S. Stieberger, Explicit BCJ Numerators from Pure Spinors, JHEP 07 (2011) 092 [arXiv:1104.5224] [INSPIRE].
J.J.M. Carrasco, C.R. Mafra and O. Schlotterer, Semi-abelian Z-theory: NLSM+ϕ 3 from the open string, JHEP 08 (2017) 135 [arXiv:1612.06446] [INSPIRE].
S. He, R. Monteiro and O. Schlotterer, String-inspired BCJ numerators for one-loop MHV amplitudes, JHEP 01 (2016) 171 [arXiv:1507.06288] [INSPIRE].
C.R. Mafra and O. Schlotterer, Double-Copy Structure of One-Loop Open-String Amplitudes, Phys. Rev. Lett. 121 (2018) 011601 [arXiv:1711.09104] [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].
C.-H. Fu, P. Vanhove and Y. Wang, A Vertex Operator Algebra Construction of the Colour-Kinematics Dual numerator, JHEP 09 (2018) 141 [arXiv:1806.09584] [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].
Y.-J. Du and F. Teng, BCJ numerators from reduced Pfaffian, JHEP 04 (2017) 033 [arXiv:1703.05717] [INSPIRE].
N.E.J. Bjerrum-Bohr, J.L. Bourjaily, P.H. Damgaard and B. Feng, Manifesting Color-Kinematics Duality in the Scattering Equation Formalism, JHEP 09 (2016) 094 [arXiv:1608.00006] [INSPIRE].
L. Mason and D. Skinner, Ambitwistor strings and the scattering equations, JHEP 07 (2014) 048 [arXiv:1311.2564] [INSPIRE].
A. Anastasiou, L. Borsten, M.J. Duff, L.J. Hughes and S. Nagy, Yang-Mills origin of gravitational symmetries, Phys. Rev. Lett. 113 (2014) 231606 [arXiv:1408.4434] [INSPIRE].
A. Anastasiou, L. Borsten, M.J. Hughes and S. Nagy, Global symmetries of Yang-Mills squared in various dimensions, JHEP 01 (2016) 148 [arXiv:1502.05359] [INSPIRE].
A. Anastasiou et al., Twin supergravities from Yang-Mills theory squared, Phys. Rev. D 96 (2017) 026013 [arXiv:1610.07192] [INSPIRE].
A. Anastasiou, L. Borsten, M.J. Duff, A. Marrani, S. Nagy and M. Zoccali, Are all supergravity theories Yang-Mills squared?, Nucl. Phys. B 934 (2018) 606 [arXiv:1707.03234] [INSPIRE].
A. Anastasiou, L. Borsten, M.J. Duff, S. Nagy and M. Zoccali, Gravity as Gauge Theory Squared: A Ghost Story, Phys. Rev. Lett. 121 (2018) 211601 [arXiv:1807.02486] [INSPIRE].
Z. Bern, A. De Freitas and H.L. Wong, On the coupling of gravitons to matter, Phys. Rev. Lett. 84 (2000) 3531 [hep-th/9912033] [INSPIRE].
M. Chiodaroli, M. Günaydin, H. Johansson and R. Roiban, Scattering amplitudes in \( \mathcal{N}=2 \) Maxwell-Einstein and Yang-Mills/Einstein supergravity, JHEP 01 (2015) 081 [arXiv:1408.0764] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations, JHEP 01 (2015) 121 [arXiv:1409.8256] [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].
S. Stieberger and T.R. Taylor, New relations for Einstein-Yang-Mills amplitudes, Nucl. Phys. B 913 (2016) 151 [arXiv:1606.09616] [INSPIRE].
M. Chiodaroli, Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities, in J. Brüning and M. Staudacher (Eds.), Space-Time-Matter: Analytic and Geometric Structures, De Gruyter (2018), pp. 266-287, [https://doi.org/10.1515/9783110452150-011] [arXiv:1607.04129] [INSPIRE].
D. Nandan, J. Plefka, O. Schlotterer and C. Wen, Einstein-Yang-Mills from pure Yang-Mills amplitudes, JHEP 10 (2016) 070 [arXiv:1607.05701] [INSPIRE].
C. Cheung, C.-H. Shen and C. Wen, Unifying Relations for Scattering Amplitudes, JHEP 02 (2018) 095 [arXiv:1705.03025] [INSPIRE].
M. Chiodaroli, M. Günaydin, H. Johansson and R. Roiban, Explicit Formulae for Yang-Mills-Einstein Amplitudes from the Double Copy, JHEP 07 (2017) 002 [arXiv:1703.00421] [INSPIRE].
Y.-J. Du, B. Feng and F. Teng, Expansion of All Multitrace Tree Level EYM Amplitudes, JHEP 12 (2017) 038 [arXiv:1708.04514] [INSPIRE].
F. Teng and B. Feng, Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame, JHEP 05 (2017) 075 [arXiv:1703.01269] [INSPIRE].
M. Chiodaroli, M. Günaydin, H. Johansson and R. Roiban, Spontaneously Broken Yang-Mills-Einstein Supergravities as Double Copies, JHEP 06 (2017) 064 [arXiv:1511.01740] [INSPIRE].
J. Scherk and J.H. Schwarz, Spontaneous Breaking of Supersymmetry Through Dimensional Reduction, Phys. Lett. 82B (1979) 60 [INSPIRE].
J. Scherk and J.H. Schwarz, How to Get Masses from Extra Dimensions, Nucl. Phys. B 153 (1979) 61 [INSPIRE].
E. Cremmer, J. Scherk and J.H. Schwarz, Spontaneously Broken N = 8 Supergravity, Phys. Lett. 84B (1979) 83 [INSPIRE].
G. Dall’Agata and F. Zwirner, Quantum corrections to broken N = 8 supergravity, JHEP 09 (2012) 078 [arXiv:1205.4711] [INSPIRE].
B. de Wit and A. Van Proeyen, Special geometry, cubic polynomials and homogeneous quaternionic spaces, Commun. Math. Phys. 149 (1992) 307 [hep-th/9112027] [INSPIRE].
M. Chiodaroli, M. Günaydin, H. Johansson and R. Roiban, Gauged Supergravities and Spontaneous Supersymmetry Breaking from the Double Copy Construction, Phys. Rev. Lett. 120 (2018) 171601 [arXiv:1710.08796] [INSPIRE].
H. Johansson and A. Ochirov, Color-Kinematics Duality for QCD Amplitudes, JHEP 01 (2016) 170 [arXiv:1507.00332] [INSPIRE].
Z. Bern, J.J.M. Carrasco, L.J. Dixon, H. Johansson and R. Roiban, Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes, Phys. Rev. D 85 (2012) 105014 [arXiv:1201.5366] [INSPIRE].
L. Andrianopoli, R. D’Auria, S. Ferrara and M.A. Lledó, Gauging of flat groups in four-dimensional supergravity, JHEP 07 (2002) 010 [hep-th/0203206] [INSPIRE].
E. Malek and H. Samtleben, Ten-dimensional origin of Minkowski vacua in N =8 supergravity, Phys. Lett. B 776 (2018) 64 [arXiv:1710.02163] [INSPIRE].
N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the Simplest Quantum Field Theory?, JHEP 09 (2010) 016 [arXiv:0808.1446] [INSPIRE].
H. Elvang and Y. Huang, Scattering Amplitudes in Gauge Theory and Gravity, Cambridge University Press, (2015), [https://doi.org/10.1017/CBO9781107706620].
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Chiodaroli, M., Günaydin, M., Johansson, H. et al. Non-Abelian gauged supergravities as double copies. J. High Energ. Phys. 2019, 99 (2019). https://doi.org/10.1007/JHEP06(2019)099
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DOI: https://doi.org/10.1007/JHEP06(2019)099