Abstract
Higher-derivative operators are central elements of any effective field theory. In supersymmetric theories, these include operators with additional derivatives that appear explicitly in the superspace description. We develop a toolkit for coupling such super-symmetric effective field theories to supergravity. We explain how to write the action for minimal supergravity coupled to chiral superfields with arbitrary numbers of derivatives and curvature couplings. We discuss two examples in detail, showing how the component actions agree with the expectations from the linearized description in terms of a Ferrara-Zumino multiplet. In a companion paper [1], we apply the formalism to the effective theory of inflation.
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References
D. Baumann and D. Green, Signatures of supersymmetry from the early universe, arXiv:1109.0292 [INSPIRE].
Y. Golfand and E. Likhtman, Extension of the algebra of Poincaré group generators and violation of P invariance, JETP Lett. 13 (1971) 323 [Pisma Zh. Eksp. Teor. Fiz. 13 (1971) 452] [INSPIRE].
D. Volkov and V. Akulov, Is the neutrino a Goldstone particle?, Phys. Lett. B 46 (1973) 109 [INSPIRE].
J. Wess and B. Zumino, Supergauge transformations in four-dimensions, Nucl. Phys. B 70 (1974) 39 [INSPIRE].
G. ’t Hooft, Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking, NATO Adv. Study Inst. Ser. B Phys. 59 (1980) 135 [INSPIRE].
S. Weinberg, The quantum theory of fields. Volume 1: foundations, Cambridge University Press, Cambridge U.K. (1995).
S. Cecotti, S. Ferrara and L. Girardello, Structure of the scalar potential in general \( \mathcal{N} = {1} \) higher derivative supergravity in four-dimensions, Phys. Lett. B 187 (1987) 321 [INSPIRE].
S. Cecotti, S. Ferrara and L. Girardello, Flat potentials in higher derivative supergravity, Phys. Lett. B 187 (1987) 327 [INSPIRE].
N. Krasnikov, A. Kyiatkin and E. Poppitz, Structure of the effective potential in supersymmetric theories with higher order derivatives coupled to supergravity, Phys. Lett. B 222 (1989) 66 [INSPIRE].
E. Poppitz, A superfield derivation of the low-energy effective action in \( \mathcal{N} = {1} \) , \( \mathcal{N} = {2} \) supergravity theories, Phys. Lett. B 238 (1990) 323 [INSPIRE].
D. Butter and S.M. Kuzenko, New higher-derivative couplings in 4D \( \mathcal{N} = {2} \) supergravity, JHEP 03 (2011) 047 [arXiv:1012.5153] [INSPIRE].
C. Cheung, P. Creminelli, A. Fitzpatrick, J. Kaplan and L. Senatore, The effective field theory of inflation, JHEP 03 (2008) 014 [arXiv:0709.0293] [INSPIRE].
P. Creminelli, M.A. Luty, A. Nicolis and L. Senatore, Starting the universe: stable violation of the null energy condition and non-standard cosmologies, JHEP 12 (2006) 080 [hep-th/0606090] [INSPIRE].
L. Senatore and M. Zaldarriaga, The effective field theory of multifield inflation, arXiv:1009.2093 [INSPIRE].
J. Wess and J. Bagger, Supersymmetry and supergravity, Princeton University Press, Princeton U.S.A. (1992).
Z. Komargodski and N. Seiberg, From linear SUSY to constrained superfields, JHEP 09 (2009) 066 [arXiv:0907.2441] [INSPIRE].
S.J. Gates, M. Grisaru, M. Rocek and W. Siegel, Superspace or one thousand and onelessons in supersymmetry, Front. Phys. 58 (1983) 1 [hep-th/0108200] [INSPIRE].
L. Randall and R. Sundrum, Out of this world supersymmetry breaking, Nucl. Phys. B 557 (1999) 79 [hep-th/9810155] [INSPIRE].
C. Cheung, F. D’Eramo and J. Thaler, Supergravity computations without gravity complications, Phys. Rev. D 84 (2011) 085012 [arXiv:1104.2598] [INSPIRE].
R. Grimm, J. Wess and B. Zumino, A complete solution of the Bianchi identities in superspace, Nucl. Phys. B 152 (1979) 255 [INSPIRE].
N. Dragon, Torsion and curvature in extended supergravity, Z. Phys. C 2 (1979) 29 [INSPIRE].
G. Girardi, R. Grimm, M. Muller and J. Wess, Superspace geometry and the minimal, nonminimal, and new minimal supergravity multiplets, Z. Phys. C 26 (1984) 123 [INSPIRE].
K. Stelle and P.C. West, Minimal auxiliary fields for supergravity, Phys. Lett. B 74 (1978) 330 [INSPIRE].
S. Ferrara and P. van Nieuwenhuizen, The auxiliary fields of supergravity, Phys. Lett. B 74 (1978) 333 [INSPIRE].
C. Beasley and E. Witten, New instanton effects in string theory, JHEP 02 (2006) 060 [hep-th/0512039] [INSPIRE].
I. Antoniadis, E. Dudas and D. Ghilencea, Supersymmetric models with higher dimensional operators, JHEP 03 (2008) 045 [arXiv:0708.0383] [INSPIRE].
Z. Komargodski and N. Seiberg, Comments on supercurrent multiplets, supersymmetric field theories and supergravity, JHEP 07 (2010) 017 [arXiv:1002.2228] [INSPIRE].
G. Festuccia and N. Seiberg, Rigid supersymmetric theories in curved superspace, JHEP 06 (2011) 114 [arXiv:1105.0689] [INSPIRE].
T.T. Dumitrescu and N. Seiberg, Supercurrents and brane currents in diverse dimensions, JHEP 07 (2011) 095 [arXiv:1106.0031] [INSPIRE].
S. Weinberg, The quantum theory of fields. Volume 3: supersymmetry, Cambridge University Press, Cambridge U.K. (2000).
M. Magro, I. Sachs and S. Wolf, Superfield Noether procedure, Annals Phys. 298 (2002) 123 [hep-th/0110131] [INSPIRE].
S.M. Kuzenko, Variant supercurrents and Noether procedure, Eur. Phys. J. C 71 (2011) 1513 [arXiv:1008.1877] [INSPIRE].
L. Senatore, K.M. Smith and M. Zaldarriaga, Non-Gaussianities in single field inflation and their optimal limits from the WMAP 5-year data, JCAP 01 (2010) 028 [arXiv:0905.3746] [INSPIRE].
X. Chen and Y. Wang, Quasi-single field inflation and non-Gaussianities, JCAP 04 (2010) 027 [arXiv:0911.3380] [INSPIRE].
J. Khoury, J.-L. Lehners and B. Ovrut, Supersymmetric P(X,ϕ) and the ghost condensate, Phys. Rev. D 83 (2011) 125031 [arXiv:1012.3748] [INSPIRE].
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ArXiv ePrint: 1109.0293
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Baumann, D., Green, D. Supergravity for effective theories. J. High Energ. Phys. 2012, 1 (2012). https://doi.org/10.1007/JHEP03(2012)001
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DOI: https://doi.org/10.1007/JHEP03(2012)001