Abstract
We construct N = 1 supergravity extensions of scalar field theories with higher-derivative kinetic terms. Special attention is paid to the auxiliary fields, whose elimination leads not only to corrections to the kinetic terms, but to new expressions for the potential energy as well. Our formalism allows one to write a supergravity extension of any higher-derivative scalar field theory and therefore has applications to both particle physics and cosmological model building. For instance, the ghost condensate vacuum spontaneously breaks local supersymmetry without the super-Higgs effect taking place. Supersymmetric cubic Galileons are shown to imply equations of motion of higher than second order, thus leading to the appearance of ghosts.
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Proceedings of the workshop “Breaking of supersymmetry and ultraviolet divergences in extended supergravity”, held in March 2013 at the INFN in Frascati. Michael Koehn: Speaker.
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In all examples in this paper, we will, for specificity, choose \(T_{ijk*l*}|\) to be proportional to \(\frac{1}{2}(g_{ik*}g_{jl*}+g_{il*}g_{jk*})\).
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The effective description in terms of the DBI action is valid at arbitrary velocity, but only as long as the proper acceleration of the branes is small.
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One could equally well assume that it also has higher-derivative kinetic terms, but that they are unimportant in the vacuum. For simplicity, we will not pursue this option here.
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This ghost was not seen in [18] because in that paper the perturbation analysis was performed solely around \(\bar{\xi } = constant\) backgrounds.
References
Y.A. Golfand, E.P. Likhtman, Extension of algebra of Poincare Group generators and violation of P invariance. JETP Lett. 13(8), 323 (1971)
D.V. Volkov, V.P. Akulov, Is the neutrino a goldstone particle? Phys. Lett. B 46(1), 109–110 (1973)
J. Wess, B. Zumino, Supergauge transformations in four dimensions. Nucl. Phys. B 70(1), 39–50 (1974)
R. Haag, J.T. Lopuszanski, M. Sohnius, All possible generators of supersymmetries of the S-matrix. Nucl. Phys. B 88(2), 257–274 (1975)
P. Langacker, Proton decay, grand unification, and supersymmetry, in Proceedings of AIP Conference (University of Pennsylvania, Philadelphia, Pennsylvania 19104, 1984). pp. 251–276
S. Dimopoulos, H. Georgi, Softly broken supersymmetry and SU(5). Nucl. Phys. B 193(1), 150–162 (1981)
S. Dimopoulos, S. Raby, F. Wilczek, Supersymmetry and the scale of unification. Phys. Rev. D 24(6), 1681–1683 (1981)
V. Braun, Y.H. He, B.A. Ovrut, T. Pantev, The exact MSSM spectrum from string theory. JHEP 05, 043 (2006)
A. Lukas, B.A. Ovrut, K.S. Stelle, D. Waldram, Universe as a domain wall. Phys. Rev. D 59(8), 86001 (1999)
E. Silverstein, D. Tong, Scalar speed limits and cosmology: acceleration from D-cceleration. Phys. Rev. D 70(1), 103505 (2004)
J. Khoury, B.A. Ovrut, P.J. Steinhardt, N. Turok, Ekpyrotic universe: colliding branes and the origin of the hot big bang. Phys. Rev. D 64(1), 123522 (2001)
J. Khoury, B.A. Ovrut, N. Seiberg, P.J. Steinhardt, N. Turok, From big crunch to big bang. Phys. Rev. D 65(8), 86007 (2002)
E.I. Buchbinder, J. Khoury, B.A. Ovrut, New Ekpyrotic cosmology. Phys. Rev. D 76, 123503 (2007)
E.I. Buchbinder, J. Khoury, B.A. Ovrut, On the initial conditions in new ekpyrotic cosmology. JHEP 11(1), 076 (2007)
E.I. Buchbinder, J. Khoury, B.A. Ovrut, Non-gaussianities in new ekpyrotic cosmology. Phys. Rev. Lett. 100(1), 171302 (2008)
M. Koehn, J.L. Lehners, B.A. Ovrut, Higher-derivative chiral superfield actions coupled to N=1 supergravity. Phys. Rev. D 86(8), 85019 (2012)
J. Khoury, J.L. Lehners, B. Ovrut, Supersymmetric \(P(X,\phi )\) and the ghost condensate. Phys. Rev. D 83(1), 125031 (2011)
J. Khoury, J.L. Lehners, B.A. Ovrut, Supersymmetric galileons. Phys. Rev. D 84(4), 43521 (2011)
M. Koehn, J.L. Lehners, B.A. Ovrut, Dbi inflation in \({\cal N}=1\) supergravity. Phys. Rev. D 86, 123510 (2012)
G.W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space. Int. J. Theor. Phys. 10(6), 363–384 (1974)
A. Nicolis, R. Rattazzi, E. Trincherini, Galileon as a local modification of gravity. Phys. Rev. D 79(6), 064036 (2009)
C. Deffayet, X. Gao, D.A. Steer, G. Zahariade, From k-essence to generalized Galileons. Phys. Rev. D 84(6), 064039 (2011)
M. Koehn, J.L. Lehners, B.A. Ovrut, Supersymmetric cubic Galileons have ghosts. Phys. Rev. D 88(2), 023528 (2013)
M. Koehn, J.L. Lehners, B.A. Ovrut, Ghost condensate in N = 1 supergravity. Phys. Rev. D 87(6), 65022 (2013)
R. Donagi, B.A. Ovrut, D. Waldram, Moduli spaces of fivebranes on elliptic Calabi-Yau threefolds. J. High Energ. Phys 11(1), 030 (1999)
E. Buchbinder, R. Donagi, B. Ovrut, Vector bundle moduli and small instanton transitions. J. High Energ. Phys. 06(0), 054 (2002)
E.I. Buchbinder, R. Donagi, B.A. Ovrut, Vector bundle moduli superpotentials in heterotic superstrings and M-theory. J. High Energ. Phys. 07(0), 066 (2002)
C. Armendáriz-Picón, T. Damour, V. Mukhanov, k-Inflation. Phys. Lett. B 458(2), 209–218 (1999)
P. Steinhardt, N. Turok, Cosmic evolution in a cyclic universe. Phys. Rev. D 65(12) (2002)
J.L. Lehners, Ekpyrotic and cyclic cosmology. Phys. Rep. 465(6), 223–263 (2008)
M. Trodden, K. Hinterbichler, Generalizing Galileons. Class. Quant. Grav. 28(2), 204003 (2011)
N. Arkani-Hamed, H.S. Cheng, M.A. Luty, S. Mukohyama, Ghost condensation and a consistent infrared modification of gravity. JHEP 05, 074 (2004)
P. Creminelli, M.A. Luty, A. Nicolis, L. Senatore, Starting the Universe: stable violation of the null energy condition and non-standard cosmologies. J. High Energ. Phys. 12(1), 080 (2006)
J.L. Lehners, Cosmic bounces and cyclic universes. Class. Quant. Grav. 28(20), 204004 (2011)
J. Wess, J. Bagger, Supersymmetry and Supergravity (Princeton University Press, Princeton, NJ, 1992)
D. Baumann, D. Green, Signature of supersymmetry from the early universe. Phys. Rev. D 85(1), 103520 (2012)
D. Baumann, D. Green, Supergravity for effective theories. J. High Energ. Phys. 03, 001 (2012)
F. Farakos, A. Kehagias, Emerging potentials in higher-derivative gauged chiral models coupled to N=1 supergravity. J. High Energ. Phys. 11, 077 (2012)
I.L. Buchbinder, S.M. Kuzenko, Nonlocal action for supertrace anomalies in superspace of N=1 supergravity. Phys. Lett. B 202(2), 233–237 (1988)
I. Buchbinder, S. Kuzenko, J. Yarevskaya, Supersymmetric effective potential: superfield approach. Nucl. Phys. B 411(2), 665–692 (1994)
A.T. Banin, I.L. Buchbinder, N.G. Pletnev, Quantum properties of the four-dimensional generic chiral superfield model. Phys. Rev. D 74(4), 045010 (2006)
F. Brandt, Anomaly candidates and invariants of D = 4, N = 1 supergravity theories. Class. Quant. Grav. 11(4), 849–863 (1994)
F. Brandt, Local BRST cohomology in minimal D = 4, N = 1 supergravity. Ann. Phys. 259, 253–312 (1997)
I. Antoniadis, E. Dudas, D.M. Ghilencea, Supersymmetric models with higher dimensional operators. J. High Energ. Phys. 03, 045 (2008)
R.G. Leigh, Dirac-Born action from Dirichlet Sigma model. Mod. Phys. Lett. A 4(2), 2767–2772 (1989)
J. Khoury, B.A. Ovrut, J. Stokes, The worldvolume action of kink solitons in AdS spacetime. JHEP 08, 015 (2012)
B.A. Ovrut, J. Stokes, Heterotic kink solitons and their worldvolume action. JHEP 09, 065 (2012)
G. Dvali, S.H.H. Tye, Brane inflation. Phys. Lett. B 450(1), 72–82 (1999)
E. Lima, B. Ovrut, J. Park, Five-brane superpotentials in heterotic M-theory. Nucl. Phys. B 626(1), 113–164 (2002)
S. Kachru, R. Kallosh, A. Linde, J. Maldacena, L. McAllister, S.P. Trivedi, Towards inflation in string theory. J. Cosmol. Astropart. Phys. 10(1), 013 (2003)
J. Gray, A. Lukas, B. Ovrut, Perturbative antibrane potentials in heterotic M theory. Phys. Rev. D 76(6), 066007 (2007)
M. Alishahiha, E. Silverstein, D. Tong, DBI in the sky: non-Gaussianity from inflation with a speed limit. Phys. Rev. D 70(1), 123505 (2004)
M. Rocek, A.A. Tseytlin, Partial breaking of global D = 4 supersymmetry, constrained superfields, and 3-brane actions. Phys. Rev. D 59(1), 106001 (1999)
M. Kawasaki, M. Yamaguchi, T. Yanagida, Natural chaotic inflation in supergravity. Phys. Rev. Lett. 85(1), 3572–3575 (2000)
R. Kallosh, A. Linde, T. Rube, General inflaton potentials in supergravity. Phys. Rev. D 83(4), 043507 (2011)
D. Baumann, L. McAllister, A microscopic limit on gravitational waves from D-brane inflation. Phys. Rev. D 75(1), 123508 (2007)
J.E. Lidsey, I. Huston, Gravitational wave constraints on Dirac Born Infeld inflation. J. Cosmol. Astropart. Phys. 07, 002 (2007)
T. Kobayashi, S. Mukohyama, S. Kinoshita, Constraints on wrapped Dirac-Born-Infeld inflation in a warped throat. J. Cosmol. Astropart. Phys. 01, 028 (2008)
R. Bean, X. Chen, H. Peiris, Comparing infrared Dirac-Born-Infeld brane inflation to observations. Phys. Rev. D 77(2), 023527 (2008)
D. Langlois, S. Renaux-Petel, D.A. Steer, T. Tanaka, Primordial perturbations and non-Gaussianities in DBI and general multifield inflation. Phys. Rev. D 78(6), 63523 (2008)
T. Kidani, K. Koyama, S. Mizuno, Non-Gaussianities in multifield DBI inflation with a waterfall phase transition. Phys. Rev. D 86(8), 083503 (2012)
B.A. Ovrut, P.J. Steinhardt, Supersymmetry and inflation: a new approach. Phys. Lett. B 133(3), 161–168 (1983)
A. Nicolis, R. Rattazzi, E. Trincherini, Energy’s and amplitudes’ positivity. J. High Energ. Phys. 05, 095 (2010)
C. de Rham, A.J. Tolley, DBI and the Galileon reunited. J. Cosmol. Astropart. Phys. 05, 015 (2010)
K. Hinterbichler, M. Trodden, D. Wesley, Multifield Galileons and higher codimension branes. Phys. Rev. D 82(1), 124018 (2010)
G. Goon, K. Hinterbichler, M. Trodden, Symmetries for Galileons and DBI scalars on curved space. J. Cosmol. Astropart. Phys. 07, 017 (2011)
C. Deffayet, S. Deser, G. Esposito-Farese, Arbitrary p-form Galileons. Phys. Rev. D 82(6), 61501 (2010)
A. Padilla, P.M. Saffi, S.Y. Zhou, Bi-galileon theory I: motivation and formulation. J. High Energ. Phys. 12, 031 (2010)
M. Ostrogradsky, Sur les racines égales des polynomes entiers. Mem. Ac. St. Petersbourg, IV 4, 385 (1850)
F.P. Silva, K. Koyama, Self-accelerating universe in Galileon cosmology. Phys. Rev. D 80(1), 121301(R) (2009)
A. De Felice, S. Tsujikawa, Cosmology of a Covariant Galileon field. Phys. Rev. Lett. 105(1), 111301 (2010)
N. Chow, J. Khoury, Galileon cosmology. Phys. Rev. D 80(2), 024037 (2009)
A.I. Vainshtein, To the problem of nonvanishing gravitation mass. Phys. Lett. B 39(3), 393–394 (1972)
C. Deffayet, G. Dvali, G. Gabadadze, A. Vainshtein, Nonperturbative continuity in graviton mass versus perturbative discontinuity. Phys. Rev. D 65(4), 044026 (2002)
K. Hinterbichler, A. Joyce, J. Khoury, G.E.J. Miller, Dirac-Born-Infeld Genesis: an improved violation of the null energy condition. Phys. Rev. Lett. 110(2), 241303 (2013)
P. Creminelli, A. Nicolis, E. Trincherini, Galilean genesis: an alternative to inflation. J. Cosmol. Astropart. Phys. 11(1), 021 (2010)
J.L. Lehners, S. Renaux-Petel, Multifield cosmological perturbations at third order and the ekpyrotic trispectrum. Phys. Rev. D 80(6), 063503 (2009)
J.L. Lehners, Ekpyrotic nongaussianity: a review. Adv. Astron. 2010, 1–20 (2010)
Y.F. Cai, D.A. Easso, R. Brandenberger, Towards a nonsingular bouncing cosmology. J. Cosmol. Astropart. Phys. 08, 020 (2012)
J.L. Lehners, Eternal inflation with noninflationary pocket universes. Phys. Rev. D 86(4), 43518 (2012)
M.C. Johnson, J.L. Lehners, Cycles in the multiverse. Phys. Rev. D 85(1), 103509 (2012)
Z.G. Liu, Y.S. Piao, Galilean Islands in eternally inflating background (2013). arXiv.org
Acknowledgments
M. Koehn would like to thank Stefano Bellucci for the invitation to the workshop “Breaking of supersymmetry and ultraviolet divergences in extended supergravity” at the INFN in Frascati in March 2013, where the content of these proceedings was presented. M. Koehn and J. L. Lehners gratefully acknowledge the support of the European Research Council via the Starting Grant numbered 256994. B. A. Ovrut is supported in part by the DOE under contract No. DE-AC02-76-ER-03071 and the NSF under grant No. 1001296.
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Koehn, M., Lehners, JL., Ovrut, B.A. (2014). Scalars with Higher Derivatives in Supergravity and Cosmology. In: Bellucci, S. (eds) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity. Springer Proceedings in Physics, vol 153. Springer, Cham. https://doi.org/10.1007/978-3-319-03774-5_7
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