Abstract
We present for the first time a ghost-free higher-derivative chiral model with a propagating auxiliary F-term field (highest component of the chiral multiplet). We obtain this model by removing a ghost in a higher derivative chiral model, with Higgsing it in terms of an auxiliary vector superfield. Depending on the sign of the quadratic derivative term of the chiral superfield, the model contains two ghost free branches of the parameter regions. We find that supersymmetry is spontaneously broken in one branch while it is preserved in the other branch. As a consequence of dynamical F-term field, a conserved U(1) charge corresponding to the number density of F appears, which can be regarded as a generalization of the R-symmetry.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R.P. Woodard, Avoiding dark energy with 1/r modifications of gravity, Lect. Notes Phys. 720 (2007) 403 [astro-ph/0601672] [INSPIRE].
G.W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space, Int. J. Theor. Phys. 10 (1974) 363 [INSPIRE].
T. Kobayashi, M. Yamaguchi and J. Yokoyama, Generalized G-inflation: Inflation with the most general second-order field equations, Prog. Theor. Phys. 126 (2011) 511 [arXiv:1105.5723] [INSPIRE].
C. Charmousis, E.J. Copeland, A. Padilla and P.M. Saffin, General second order scalar-tensor theory, self tuning and the Fab Four, Phys. Rev. Lett. 108 (2012) 051101 [arXiv:1106.2000] [INSPIRE].
J. Bagger and A. Galperin, A new Goldstone multiplet for partially broken supersymmetry, Phys. Rev. D 55 (1997) 1091 [hep-th/9608177] [INSPIRE].
J. Bagger and A. Galperin, The tensor Goldstone multiplet for partially broken supersymmetry, Phys. Lett. B 412 (1997) 296 [hep-th/9707061] [INSPIRE].
M. Roček and A.A. Tseytlin, Partial breaking of global D = 4 supersymmetry, constrained superfields and three-brane actions, Phys. Rev. D 59 (1999) 106001 [hep-th/9811232] [INSPIRE].
S.M. Kuzenko and S.A. McCarthy, Nonlinear selfduality and supergravity, JHEP 02 (2003) 038 [hep-th/0212039] [INSPIRE].
S.M. Kuzenko and S.A. McCarthy, On the component structure of N = 1 supersymmetric nonlinear electrodynamics, JHEP 05 (2005) 012 [hep-th/0501172] [INSPIRE].
F. Farakos, C. Germani, A. Kehagias and E.N. Saridakis, A New Class of Four-Dimensional N = 1 Supergravity with Non-minimal Derivative Couplings, JHEP 05(2012) 050 [arXiv:1202.3780] [INSPIRE].
M. Koehn, J.-L. Lehners and B.A. Ovrut, Higher-Derivative Chiral Superfield Actions Coupled to N = 1 Supergravity, Phys. Rev. D 86 (2012) 085019 [arXiv:1207.3798] [INSPIRE].
H. Abe, Y. Sakamura and Y. Yamada, Matter coupled Dirac-Born-Infeld action in four-dimensional N = 1 conformal supergravity, Phys. Rev. D 92 (2015) 025017 [arXiv:1504.01221] [INSPIRE].
S. Aoki and Y. Yamada, DBI action of real linear superfield in 4D \( \mathcal{N}=1 \) conformal supergravity, JHEP 06 (2016) 168 [arXiv:1603.06770] [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].
F. Farakos, C. Germani and A. Kehagias, On ghost-free supersymmetric galileons, JHEP 11 (2013) 045 [arXiv:1306.2961] [INSPIRE].
S. Sasaki, M. Yamaguchi and D. Yokoyama, Supersymmetric DBI inflation, Phys. Lett. B 718 (2012) 1 [arXiv:1205.1353] [INSPIRE].
M. Koehn, J.-L. Lehners and B.A. Ovrut, DBI Inflation in N = 1 Supergravity, Phys. Rev. D 86 (2012) 123510 [arXiv:1208.0752] [INSPIRE].
R. Gwyn and J.-L. Lehners, Non-Canonical Inflation in Supergravity, JHEP 05 (2014) 050 [arXiv:1402.5120] [INSPIRE].
S. Aoki and Y. Yamada, Inflation in supergravity without Kähler potential, Phys. Rev. D 90 (2014) 127701 [arXiv:1409.4183] [INSPIRE].
S. Aoki and Y. Yamada, Impacts of supersymmetric higher derivative terms on inflation models in supergravity, JCAP 07 (2015) 020 [arXiv:1504.07023] [INSPIRE].
H. Abe, Y. Sakamura and Y. Yamada, Massive vector multiplet inflation with Dirac-Born-Infeld type action, Phys. Rev. D 91 (2015) 125042 [arXiv:1505.02235] [INSPIRE].
C. Adam, J.M. Queiruga, J. Sanchez-Guillen and A. Wereszczynski, N = 1 supersymmetric extension of the baby Skyrme model, Phys. Rev. D 84 (2011) 025008 [arXiv:1105.1168] [INSPIRE].
C. Adam, J.M. Queiruga, J. Sanchez-Guillen and A. Wereszczynski, Extended Supersymmetry and BPS solutions in baby Skyrme models, JHEP 05 (2013) 108 [arXiv:1304.0774] [INSPIRE].
M. Nitta and S. Sasaki, BPS States in Supersymmetric Chiral Models with Higher Derivative Terms, Phys. Rev. D 90 (2014) 105001 [arXiv:1406.7647] [INSPIRE].
S. Bolognesi and W. Zakrzewski, Baby Skyrme Model, Near-BPS Approximations and Supersymmetric Extensions, Phys. Rev. D 91 (2015) 045034 [arXiv:1407.3140] [INSPIRE].
J.M. Queiruga, Baby Skyrme model and fermionic zero modes, arXiv:1606.02869 [INSPIRE].
M. Nitta and S. Sasaki, Classifying BPS States in Supersymmetric Gauge Theories Coupled to Higher Derivative Chiral Models, Phys. Rev. D 91 (2015) 125025 [arXiv:1504.08123] [INSPIRE].
I.L. Buchbinder, S. Kuzenko and Z. Yarevskaya, Supersymmetric effective potential: Superfield approach, Nucl. Phys. B 411 (1994) 665 [INSPIRE].
I.L. Buchbinder and S.M. Kuzenko, Ideas and methods of supersymmetry and supergravity: Or a walk through superspace, IOP, Bristol, U.K. (1998), pg. 656 [INSPIRE].
S.M. Kuzenko and S.J. Tyler, The one-loop effective potential of the Wess-Zumino model revisited, JHEP 09 (2014) 135 [arXiv:1407.5270] [INSPIRE].
A.T. Banin, I.L. Buchbinder and N.G. Pletnev, On quantum properties of the four-dimensional generic chiral superfield model, Phys. Rev. D 74 (2006) 045010 [hep-th/0606242] [INSPIRE].
D. Nemeschansky and R. Rohm, Anomaly Constraints On Supersymmetric Effective Lagrangians, Nucl. Phys. B 249 (1985) 157 [INSPIRE].
S.J. Gates Jr., Why auxiliary fields matter: The strange case of the 4-D, N = 1 supersymmetric QCD effective action, Phys. Lett. B 365 (1996) 132 [hep-th/9508153] [INSPIRE].
S.J. Gates Jr., Why auxiliary fields matter: The strange case of the 4-D, N = 1 supersymmetric QCD effective action. 2, Nucl. Phys. B 485 (1997) 145 [hep-th/9606109] [INSPIRE].
S.J. Gates Jr., M.T. Grisaru, M.E. Knutt and S. Penati, The superspace WZNW action for 4-D, N = 1 supersymmetric QCD, Phys. Lett. B 503 (2001) 349 [hep-ph/0012301] [INSPIRE].
S.J. Gates Jr., M.T. Grisaru, M.E. Knutt, S. Penati and H. Suzuki, Supersymmetric gauge anomaly with general homotopic paths, Nucl. Phys. B 596 (2001) 315 [hep-th/0009192] [INSPIRE].
S.J. Gates Jr., M.T. Grisaru and S. Penati, Holomorphy, minimal homotopy and the 4-D, N = 1 supersymmetric Bardeen-Gross-Jackiw anomaly, Phys. Lett. B 481(2000) 397 [hep-th/0002045] [INSPIRE].
M. Nitta, A Note on supersymmetric WZW term in four dimensions, Mod. Phys. Lett. A 15 (2000) 2327 [hep-th/0101166] [INSPIRE].
M. Nitta and S. Sasaki, Higher Derivative Corrections to Manifestly Supersymmetric Nonlinear Realizations, Phys. Rev. D 90 (2014) 105002 [arXiv:1408.4210] [INSPIRE].
M. Eto, T. Fujimori, M. Nitta, K. Ohashi and N. Sakai, Higher Derivative Corrections to Non-Abelian Vortex Effective Theory, Prog. Theor. Phys. 128 (2012) 67 [arXiv:1204.0773] [INSPIRE].
C. Adam, J.M. Queiruga, J. Sanchez-Guillen and A. Wereszczynski, Supersymmetric K field theories and defect structures, Phys. Rev. D 84 (2011) 065032 [arXiv:1107.4370] [INSPIRE].
C. Adam, J.M. Queiruga, J. Sanchez-Guillen and A. Wereszczynski, BPS bounds in supersymmetric extensions of K field theories, Phys. Rev. D 86 (2012) 105009 [arXiv:1209.6060] [INSPIRE].
L. Freyhult, The supersymmetric extension of the Faddeev model, Nucl. Phys. B 681 (2004) 65 [hep-th/0310261] [INSPIRE].
E.A. Bergshoeff, R.I. Nepomechie and H.J. Schnitzer, Supersymmetric Skyrmions in Four-dimensions, Nucl. Phys. B 249 (1985) 93 [INSPIRE].
S.B. Gudnason, M. Nitta and S. Sasaki, A supersymmetric Skyrme model, JHEP 02 (2016) 074 [arXiv:1512.07557] [INSPIRE].
M. Gomes, J.R. Nascimento, A.Yu. Petrov and A.J. da Silva, On the effective potential in higher-derivative superfield theories, Phys. Lett. B 682 (2009) 229 [arXiv:0908.0900] [INSPIRE].
F.S. Gama, M. Gomes, J.R. Nascimento, A.Yu. Petrov and A.J. da Silva, On the higher-derivative supersymmetric gauge theory, Phys. Rev. D 84 (2011) 045001 [arXiv:1101.0724] [INSPIRE].
F.S. Gama, M. Gomes, J.R. Nascimento, A.Yu. Petrov and A.J. da Silva, On the one-loop effective potential in the higher-derivative four-dimensional chiral superfield theory with a nonconventional kinetic term, Phys. Lett. B 733 (2014) 247 [arXiv:1401.5414] [INSPIRE].
T. Kimura, A. Mazumdar, T. Noumi and M. Yamaguchi, Nonlocal N = 1 Supersymmetry, arXiv:1608.01652 [INSPIRE].
I. Antoniadis, E. Dudas and D.M. Ghilencea, Supersymmetric Models with Higher Dimensional Operators, JHEP 03 (2008) 045 [arXiv:0708.0383] [INSPIRE].
E. Dudas and D.M. Ghilencea, Effective operators in SUSY, superfield constraints and searches for a UV completion, JHEP 06 (2015) 124 [arXiv:1503.08319] [INSPIRE].
S. Cecotti, Higher derivative supergravity is equivalent to standard supergravity coupled to matter. 1, Phys. Lett. B 190 (1987) 86 [INSPIRE].
F. Farakos, A. Kehagias and A. Riotto, On the Starobinsky Model of Inflation from Supergravity, Nucl. Phys. B 876 (2013) 187 [arXiv:1307.1137] [INSPIRE].
S.V. Ketov, On the supersymmetrization of inflation in f(R) gravity, PTEP 2013 (2013) 123B04 [arXiv:1309.0293] [INSPIRE].
S. Ferrara, R. Kallosh and A. Van Proeyen, On the Supersymmetric Completion of R + R 2 Gravity and Cosmology, JHEP 11 (2013) 134 [arXiv:1309.4052] [INSPIRE].
S.V. Ketov and T. Terada, Old-minimal supergravity models of inflation, JHEP 12 (2013) 040 [arXiv:1309.7494] [INSPIRE].
A. D’Adda, M. Lüscher and P. Di Vecchia, A 1/n Expandable Series of Nonlinear σ-models with Instantons, Nucl. Phys. B 146 (1978) 63 [INSPIRE].
K. Higashijima and M. Nitta, Supersymmetric nonlinear σ-models as gauge theories, Prog. Theor. Phys. 103 (2000) 635 [hep-th/9911139] [INSPIRE].
M. Nitta, Auxiliary field methods in supersymmetric nonlinear σ-models, Nucl. Phys. B 711 (2005) 133 [hep-th/0312025] [INSPIRE].
F. Farakos, S. Ferrara, A. Kehagias and M. Porrati, Supersymmetry Breaking by Higher Dimension Operators, Nucl. Phys. B 879 (2014) 348 [arXiv:1309.1476] [INSPIRE].
F. Farakos and R. von Unge, Complex Linear Effective Theory and Supersymmetry Breaking Vacua, Phys. Rev. D 91 (2015) 045024 [arXiv:1403.0935] [INSPIRE].
F. Farakos, O. Hulík, P. Kočí and R. von Unge, Non-minimal scalar multiplets, supersymmetry breaking and dualities, JHEP 09 (2015) 177 [arXiv:1507.01885] [INSPIRE].
S.M. Kuzenko and S.J. Tyler, Complex linear superfield as a model for Goldstino, JHEP 04 (2011) 057 [arXiv:1102.3042] [INSPIRE].
S.M. Kuzenko and S.J. Tyler, Comments on the complex linear Goldstino superfield, arXiv:1507.04593 [INSPIRE].
M. Kaku and P.K. Townsend, Poincaré Supergravity As Broken Superconformal Gravity, Phys. Lett. B 76 (1978) 54 [INSPIRE].
T. Kugo and S. Uehara, Conformal and Poincaré Tensor Calculi in N = 1 Supergravity, Nucl. Phys. B 226 (1983) 49 [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1608.01843
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Fujimori, T., Nitta, M. & Yamada, Y. Ghostbusters in higher derivative supersymmetric theories: who is afraid of propagating auxiliary fields?. J. High Energ. Phys. 2016, 106 (2016). https://doi.org/10.1007/JHEP09(2016)106
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2016)106