Abstract
We derive the general supertrace formula for a system with N chiral superfields and one nilpotent chiral superfield in global and local supersymmetry. The nilpotent multiplet is realized by taking the scalar-decoupling limit of a chiral superfield breaking supersymmetry spontaneously. As we show, however, the modified formula is not simply related to the scalar-decoupling limit of the supertrace in linearly-realized supersymmetry. We also show that the supertrace formula reduces to that of a linearly realized supersymmetric theory with a decoupled sGoldstino if the Goldstino is the fermion in the nilpotent multiplet.
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References
Z. Komargodski and N. Seiberg, From Linear SUSY to Constrained Superfields, JHEP 09 (2009) 066 [arXiv:0907.2441] [INSPIRE].
G. Dall’Agata and F. Farakos, Constrained superfields in Supergravity, JHEP 02 (2016) 101 [arXiv:1512.02158] [INSPIRE].
S. Ferrara, R. Kallosh, A. Van Proeyen and T. Wrase, Linear Versus Non-linear Supersymmetry, in General, JHEP 04 (2016) 065 [arXiv:1603.02653] [INSPIRE].
R. Kallosh, A. Karlsson, B. Mosk and D. Murli, Orthogonal Nilpotent Superfields from Linear Models, JHEP 05 (2016) 082 [arXiv:1603.02661] [INSPIRE].
G. Dall’Agata, E. Dudas and F. Farakos, On the origin of constrained superfields, JHEP 05 (2016) 041 [arXiv:1603.03416] [INSPIRE].
N. Cribiori, G. Dall’Agata and F. Farakos, From Linear to Non-linear SUSY and Back Again, JHEP 08 (2017) 117 [arXiv:1704.07387] [INSPIRE].
D.V. Volkov and V.P. Akulov, Possible universal neutrino interaction, JETP Lett. 16 (1972) 438 [INSPIRE].
D.V. Volkov and V.P. Akulov, Is the Neutrino a Goldstone Particle?, Phys. Lett. B 46 (1973) 109 [INSPIRE].
M. Roček, Linearizing the Volkov-Akulov Model, Phys. Rev. Lett. 41 (1978) 451 [INSPIRE].
E.A. Ivanov and A.A. Kapustnikov, General Relationship Between Linear and Nonlinear Realizations of Supersymmetry, J. Phys. A 11 (1978) 2375 [INSPIRE].
U. Lindström and M. Roček, Constrained local superfields, Phys. Rev. D 19 (1979) 2300 [INSPIRE].
R. Casalbuoni, S. De Curtis, D. Dominici, F. Feruglio and R. Gatto, Nonlinear Realization of Supersymmetry Algebra From Supersymmetric Constraint, Phys. Lett. B 220 (1989) 569 [INSPIRE].
P. McGuirk, G. Shiu and F. Ye, Soft branes in supersymmetry-breaking backgrounds, JHEP 07 (2012) 188 [arXiv:1206.0754] [INSPIRE].
R. Kallosh and T. Wrase, Emergence of Spontaneously Broken Supersymmetry on an Anti-D3-Brane in KKLT dS Vacua, JHEP 12 (2014) 117 [arXiv:1411.1121] [INSPIRE].
E.A. Bergshoeff, K. Dasgupta, R. Kallosh, A. Van Proeyen and T. Wrase, \( \overline{\mathrm{D}3} \) and dS, JHEP 05 (2015) 058 [arXiv:1502.07627] [INSPIRE].
R. Kallosh, F. Quevedo and A.M. Uranga, String Theory Realizations of the Nilpotent Goldstino, JHEP 12 (2015) 039 [arXiv:1507.07556] [INSPIRE].
B. Vercnocke and T. Wrase, Constrained superfields from an anti-D3-brane in KKLT, JHEP 08 (2016) 132 [arXiv:1605.03961] [INSPIRE].
R. Kallosh, B. Vercnocke and T. Wrase, String Theory Origin of Constrained Multiplets, JHEP 09 (2016) 063 [arXiv:1606.09245] [INSPIRE].
S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, de Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [INSPIRE].
I. Antoniadis, E. Dudas, S. Ferrara and A. Sagnotti, The Volkov-Akulov-Starobinsky supergravity, Phys. Lett. B 733 (2014) 32 [arXiv:1403.3269] [INSPIRE].
S. Ferrara, R. Kallosh and A. Linde, Cosmology with Nilpotent Superfields, JHEP 10 (2014) 143 [arXiv:1408.4096] [INSPIRE].
R. Kallosh and A. Linde, Inflation and Uplifting with Nilpotent Superfields, JCAP 01 (2015) 025 [arXiv:1408.5950] [INSPIRE].
G. Dall’Agata and F. Zwirner, On sgoldstino-less supergravity models of inflation, JHEP 12 (2014) 172 [arXiv:1411.2605] [INSPIRE].
R. Kallosh, A. Linde and M. Scalisi, Inflation, de Sitter Landscape and Super-Higgs effect, JHEP 03 (2015) 111 [arXiv:1411.5671] [INSPIRE].
S. Ferrara, L. Girardello and F. Palumbo, A General Mass Formula in Broken Supersymmetry, Phys. Rev. D 20 (1979) 403 [INSPIRE].
E. Cremmer, S. Ferrara, L. Girardello and A. Van Proeyen, Yang-Mills Theories with Local Supersymmetry: Lagrangian, Transformation Laws and SuperHiggs Effect, Nucl. Phys. B 212 (1983) 413 [INSPIRE].
M.T. Grisaru, M. Roček and A. Karlhede, The Superhiggs Effect in Superspace, Phys. Lett. B 120 (1983) 110 [INSPIRE].
S. Ferrara and A. Van Proeyen, Mass Formulae for Broken Supersymmetry in Curved Space-Time, Fortsch. Phys. 64 (2016) 896 [arXiv:1609.08480] [INSPIRE].
E.A. Bergshoeff, D.Z. Freedman, R. Kallosh and A. Van Proeyen, Pure de Sitter Supergravity, Phys. Rev. D 92 (2015) 085040 [Erratum ibid. D 93 (2016) 069901] [arXiv:1507.08264] [INSPIRE].
F. Hasegawa and Y. Yamada, Component action of nilpotent multiplet coupled to matter in 4 dimensional \( \mathcal{N}=1 \) supergravity, JHEP 10 (2015) 106 [arXiv:1507.08619] [INSPIRE].
R. Kallosh, Matter-coupled de Sitter Supergravity, Theor. Math. Phys. 187 (2016) 695 [arXiv:1509.02136] [INSPIRE].
R. Kallosh and T. Wrase, de Sitter Supergravity Model Building, Phys. Rev. D 92 (2015) 105010 [arXiv:1509.02137] [INSPIRE].
M. Schillo, E. van der Woerd and T. Wrase, The general de Sitter supergravity component action, Fortsch. Phys. 64 (2016) 292 [arXiv:1511.01542] [INSPIRE].
I. Antoniadis, E. Dudas and D.M. Ghilencea, Goldstino and sgoldstino in microscopic models and the constrained superfields formalism, Nucl. Phys. B 857 (2012) 65 [arXiv:1110.5939] [INSPIRE].
I. Antoniadis and D.M. Ghilencea, Low-scale SUSY breaking and the (s)goldstino physics, Nucl. Phys. B 870 (2013) 278 [arXiv:1210.8336] [INSPIRE].
V. Balasubramanian, P. Berglund, J.P. Conlon and F. Quevedo, Systematics of moduli stabilisation in Calabi-Yau flux compactifications, JHEP 03 (2005) 007 [hep-th/0502058] [INSPIRE].
D.Z. Freedman, D. Roest and A. van Proeyen, A Geometric Formulation of Supersymmetry, Fortsch. Phys. 65 (2017) 1600106 [arXiv:1609.07362] [INSPIRE].
D.Z. Freedman, D. Roest and A. Van Proeyen, Off-shell Poincaré Supergravity, JHEP 02 (2017) 102 [arXiv:1701.05216] [INSPIRE].
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Murli, D., Yamada, Y. Supertrace formulae for nonlinearly realized supersymmetry. J. High Energ. Phys. 2018, 112 (2018). https://doi.org/10.1007/JHEP04(2018)112
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DOI: https://doi.org/10.1007/JHEP04(2018)112