Abstract
We construct \( \mathcal{N}=1 \) supersymmetric nonlocal theories in four dimension. We discuss higher derivative extensions of chiral and vector superfields, and write down generic forms of Kähler potential and superpotential up to quadratic order. We derive the condition in which an auxiliary field remains non-dynamical, and the dynamical scalars and fermions are free from the ghost degrees of freedom. We also investigate the nonlocal effects on the supersymmetry breaking and find that supertrace (mass) formula is significantly modified even at the tree level.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Yu. A. Golfand and E.P. 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].
R. Haag, J.T. Lopuszanski and M. Sohnius, All possible generators of supersymmetries of the S matrix, Nucl. Phys. B 88 (1975) 257 [INSPIRE].
S.P. Martin, A supersymmetry primer, Adv. Ser. Direct. High Energy Phys. 18 (1998) 1 [Adv. Ser. Direct. High Energy Phys. 21 (2010) 1] [hep-ph/9709356] [INSPIRE].
M. Ostrogradsky, Mémoires sur les équations différentielles, relatives au problème des isopérimètres (in French), Mem. Acad. St. Petersbourg 6 (1850) 385 [INSPIRE].
R.P. Woodard, Avoiding dark energy with 1/r modifications of gravity, Lect. Notes Phys. 720 (2007) 403 [astro-ph/0601672] [INSPIRE].
R.P. Woodard, Ostrogradsky’s theorem on Hamiltonian instability, Scholarpedia 10 (2015) 32243 [arXiv:1506.02210] [INSPIRE].
A. Nicolis, R. Rattazzi and E. Trincherini, The Galileon as a local modification of gravity, Phys. Rev. D 79 (2009) 064036 [arXiv:0811.2197] [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.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].
J. Khoury, J.-L. Lehners and B.A. Ovrut, Supersymmetric Galileons, Phys. Rev. D 84 (2011) 043521 [arXiv:1103.0003] [INSPIRE].
M. Nitta and S. Sasaki, Higher derivative corrections to manifestly supersymmetric nonlinear realizations, Phys. Rev. D 90 (2014) 105002 [arXiv:1408.4210] [INSPIRE].
A. Addazi and G. Esposito, Nonlocal quantum field theory without acausality and nonunitarity at quantum level: is SUSY the key?, Int. J. Mod. Phys. A 30 (2015) 1550103 [arXiv:1502.01471] [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].
A. Pais and G.E. Uhlenbeck, On field theories with nonlocalized action, Phys. Rev. 79 (1950) 145 [INSPIRE].
K.S. Stelle, Renormalization of higher derivative quantum gravity, Phys. Rev. D 16 (1977) 953 [INSPIRE].
E. Tomboulis, Renormalizability and asymptotic freedom in quantum gravity, Phys. Lett. B 97 (1980) 77 [INSPIRE].
E.T. Tomboulis, Renormalization and asymptotic freedom in quantum gravity, in Quantum theory of gravity, S.M. Christensen ed., (1983), pg. 251 [INSPIRE].
J.W. Moffat, Finite nonlocal gauge field theory, Phys. Rev. D 41 (1990) 1177 [INSPIRE].
E.T. Tomboulis, Superrenormalizable gauge and gravitational theories, hep-th/9702146 [INSPIRE].
T. Biswas, A. Mazumdar and W. Siegel, Bouncing universes in string-inspired gravity, JCAP 03 (2006) 009 [hep-th/0508194] [INSPIRE].
N. Barnaby and N. Kamran, Dynamics with infinitely many derivatives: the initial value problem, JHEP 02 (2008) 008 [arXiv:0709.3968] [INSPIRE].
N. Barnaby and N. Kamran, Dynamics with infinitely many derivatives: variable coefficient equations, JHEP 12 (2008) 022 [arXiv:0809.4513] [INSPIRE].
L. Modesto, Super-renormalizable quantum gravity, Phys. Rev. D 86 (2012) 044005 [arXiv:1107.2403] [INSPIRE].
T. Biswas, E. Gerwick, T. Koivisto and A. Mazumdar, Towards singularity and ghost free theories of gravity, Phys. Rev. Lett. 108 (2012) 031101 [arXiv:1110.5249] [INSPIRE].
T. Biswas and N. Okada, Towards LHC physics with nonlocal Standard Model, Nucl. Phys. B 898 (2015) 113 [arXiv:1407.3331] [INSPIRE].
S. Talaganis, T. Biswas and A. Mazumdar, Towards understanding the ultraviolet behavior of quantum loops in infinite-derivative theories of gravity, Class. Quant. Grav. 32 (2015) 215017 [arXiv:1412.3467] [INSPIRE].
E.T. Tomboulis, Nonlocal and quasilocal field theories, Phys. Rev. D 92 (2015) 125037 [arXiv:1507.00981] [INSPIRE].
T. Biswas, A.S. Koshelev and A. Mazumdar, Consistent higher derivative gravitational theories with stable de Sitter and anti-de Sitter backgrounds, arXiv:1606.01250 [INSPIRE].
T. Biswas, A.S. Koshelev and A. Mazumdar, Gravitational theories with stable (anti-)de Sitter backgrounds, Fundam. Theor. Phys. 183 (2016) 97 [arXiv:1602.08475] [INSPIRE].
S. Talaganis and A. Mazumdar, High-energy scatterings in infinite-derivative field theory and ghost-free gravity, Class. Quant. Grav. 33 (2016) 145005 [arXiv:1603.03440] [INSPIRE].
R. Pius and A. Sen, Cutkosky rules for superstring field theory, arXiv:1604.01783 [INSPIRE].
K. Ohmori, A review on tachyon condensation in open string field theories, hep-th/0102085 [INSPIRE].
W. Taylor and B. Zwiebach, D-branes, tachyons and string field theory, hep-th/0311017 [INSPIRE].
Y. Okawa, Analytic methods in open string field theory, Prog. Theor. Phys. 128 (2012) 1001 [INSPIRE].
N. Moeller and B. Zwiebach, Dynamics with infinitely many time derivatives and rolling tachyons, JHEP 10 (2002) 034 [hep-th/0207107] [INSPIRE].
P.G.O. Freund and M. Olson, Non-Archimedean strings, Phys. Lett. B 199 (1987) 186 [INSPIRE].
G. Calcagni and L. Modesto, Nonlocality in string theory, J. Phys. A 47 (2014) 355402 [arXiv:1310.4957] [INSPIRE].
P.G.O. Freund and E. Witten, Adelic string amplitudes, Phys. Lett. B 199 (1987) 191 [INSPIRE].
L. Brekke, P.G.O. Freund, M. Olson and E. Witten, Non-Archimedean string dynamics, Nucl. Phys. B 302 (1988) 365 [INSPIRE].
D. Ghoshal and A. Sen, Tachyon condensation and brane descent relations in p-adic string theory, Nucl. Phys. B 584 (2000) 300 [hep-th/0003278] [INSPIRE].
J.A. Minahan, Quantum corrections in p-adic string theory, hep-th/0105312 [INSPIRE].
S. Giaccari and L. Modesto, Classical and quantum nonlocal supergravity, arXiv:1605.03906 [INSPIRE].
J. Wess and J. Bagger, SUSY and supergravity, Princeton Univ. Pr., Princeton U.S.A. (1992).
J. Edholm, A.S. Koshelev and A. Mazumdar, Universality of testing ghost-free gravity, arXiv:1604.01989 [INSPIRE].
I. Ellwood and W. Taylor, Open string field theory without open strings, Phys. Lett. B 512 (2001) 181 [hep-th/0103085] [INSPIRE].
T. Kimura, A. Mazumdar, T. Noumi and M. Yamaguchi, in preparation.
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: 1608.01652
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
Kimura, T., Mazumdar, A., Noumi, T. et al. Nonlocal \( \mathcal{N}=1 \) supersymmetry. J. High Energ. Phys. 2016, 22 (2016). https://doi.org/10.1007/JHEP10(2016)022
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2016)022