Abstract
The \( \mathcal{N} \) = 1 and \( \mathcal{N} \) = 2 super-Schwarzian derivatives were originally introduced by physicists when computing a finite superconformal transformation of the super stress-energy tensor underlying a superconformal field theory. Mathematicians like to think of them as the cocycles describing central extensions of Lie superalgebras. In this work, a third possibility is discussed which consists in applying the method of nonlinear realizations to osp(1|2) and su(1, 1|1) superconformal algebras. It is demonstrated that the super-Schwarzians arise quite naturally, if one decides to keep the number of independent Goldstone superfields to a minimum.
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References
W. Fu, D. Gaiotto, J. Maldacena and S. Sachdev, Supersymmetric Sachdev-Ye-Kitaev models, Phys. Rev. D 95 (2017) 026009 [arXiv:1610.08917] [INSPIRE].
M. Berkooz, N. Brukner, V. Narovlansky and A. Raz, The double scaled limit of Super–Symmetric SYK models, arXiv:2003.04405 [INSPIRE].
D. Friedan, Notes on string theory and two-dimensional conformal field theory, in Unified string theories, M.B. Green and D.J. Gross eds., World Scientific, Singapore (1985).
J.D. Cohn, N = 2 super-Riemann surfaces, Nucl. Phys. B 284 (1987) 349 [INSPIRE].
K. Schoutens, O(n) extended superconformal field theory in superspace, Nucl. Phys. B 295 (1988) 634 [INSPIRE].
J.P. Michel and C. Duval, On the projective geometry of the supercircle: a unified construction of the super cross-ratio and Schwarzian derivative, Int. Math. Res. Not. (2008) 054 [arXiv:0710.1544].
S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 1., Phys. Rev. 177 (1969) 2239 [INSPIRE].
E.A. Ivanov and V.I. Ogievetsky, The inverse Higgs phenomenon in nonlinear realizations, Theor. Math. Phys. 25 (1975) 1050.
A. Galajinsky, Schwarzian mechanics via nonlinear realizations, Phys. Lett. B 795 (2019) 277 [arXiv:1905.01935] [INSPIRE].
E.A. Ivanov, S.O. Krivonos and V.M. Leviant, Geometric superfield approach to superconformal mechanics, J. Phys. A 22 (1989) 4201 [INSPIRE].
A. Galajinsky, A variant of Schwarzian mechanics, Nucl. Phys. B 936 (2018) 661 [arXiv:1809.00904] [INSPIRE].
S.J. Gates, Jr. and L. Rana, A proposal for \( {\mathcal{N}}_0 \)extended supersymmetry in integrable systems, Phys. Lett. B 369 (1996) 269 [hep-th/9510152] [INSPIRE].
S. Aoyama and Y. Honda, N = 4 super-Schwarzian theory on the coadjoint orbit and PSU(1, 1|2), JHEP 06 (2018) 070 [arXiv:1801.06800] [INSPIRE].
K.M. Apfeldorf and J. Gomis, Superconformal theories from pseudoparticle mechanics, Nucl. Phys. B 411 (1994) 745 [hep-th/9303085] [INSPIRE].
S. Filyukov and I. Masterov, On the Schwarzian counterparts of conformal mechanics, arXiv:2004.03304 [INSPIRE].
I. Masterov and B. Merzlikin, Superfield approach to higher derivative \( \mathcal{N} \) = 1 superconformal mechanics, JHEP 11 (2019) 165 [arXiv:1909.12574] [INSPIRE].
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Galajinsky, A. Super-Schwarzians via nonlinear realizations. J. High Energ. Phys. 2020, 27 (2020). https://doi.org/10.1007/JHEP06(2020)027
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DOI: https://doi.org/10.1007/JHEP06(2020)027