Abstract
Superparticle models with OSp(N |2) supersymmetry group are studied. We first consider the N = 4 case and construct the models with κ-symmetry on the coset spaces of the OSp(N |2) supergroup. In addition, within the canonical formalism we present an OSp(4|2) superparticle model with semi-dynamical angular variables. For generic N we construct a superparticle model on AdS2 × SN −1 with the reduced κ-symmetry. It is demonstrated that the Hamiltonian of this model has the same structure as the one for the N = 4 casebecauseadditionalfermionscontributetothesecond-classconstraintsonly.
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M. Cadoni, P. Carta, D. Klemm and S. Mignemi, AdS 2 gravity as conformally invariant mechanical system, Phys. Rev. D 63 (2001) 125021 [hep-th/0009185] [INSPIRE].
M. Astorino, S. Cacciatori, D. Klemm and D. Zanon, AdS 2 supergravity and superconformal quantum mechanics, Annals Phys. 304 (2003) 128 [hep-th/0212096] [INSPIRE].
C. Chamon, R. Jackiw, S.-Y. Pi and L. Santos, Conformal quantum mechanics as the CFT 1 dual to AdS 2, Phys. Lett. B 701 (2011) 503 [arXiv:1106.0726] [INSPIRE].
D. Grumiller et al., Menagerie of AdS 2 boundary conditions, JHEP 10 (2017) 203 [arXiv:1708.08471] [INSPIRE].
M. Cardenas et al., Boundary theories for dilaton supergravity in 2D, JHEP 11 (2018) 077 [arXiv:1809.07208] [INSPIRE].
G.W. Gibbons and P.K. Townsend, Black holes and Calogero models, Phys. Lett. B 454 (1999) 187 [hep-th/9812034] [INSPIRE].
P. Claus et al., Black holes and superconformal mechanics, Phys. Rev. Lett. 81 (1998) 4553 [hep-th/9804177] [INSPIRE].
N. Wyllard, (Super)conformal many body quantum mechanics with extended supersymmetry, J. Math. Phys. 41 (2000) 2826 [hep-th/9910160] [INSPIRE].
C.M. Hull, The geometry of supersymmetric quantum mechanics, hep-th/9910028 [INSPIRE].
G. Papadopoulos, Conformal and superconformal mechanics, Class. Quant. Grav. 17 (2000) 3715 [hep-th/0002007] [INSPIRE].
J.-G. Zhou, Super 0-brane and GS superstring actions on AdS 2 × S 2, Nucl. Phys. B 559 (1999) 92 [hep-th/9906013] [INSPIRE].
M. Kreuzer and J.-G. Zhou, Killing gauge for the 0-brane on AdS 2 × S 2 coset superspace, Phys. Lett. B 472 (2000) 309 [hep-th/9910067] [INSPIRE].
S. Bellucci, A. Galajinsky, E. Ivanov and S. Krivonos, AdS 2 /CF T 1 , canonical transformations and superconformal mechanics, Phys. Lett. B 555 (2003) 99 [hep-th/0212204] [INSPIRE].
E. Ivanov, S. Krivonos and O. Lechtenfeld, N = 4, d = 1 supermultiplets from nonlinear realizations of D(2, 1; α), Class. Quant. Grav. 21 (2004) 1031 [hep-th/0310299] [INSPIRE].
A. Anabalon, J. Gomis, K. Kamimura and J. Zanelli, N = 4 superconformal mechanics as a non linear realization, JHEP 10 (2006) 068 [hep-th/0607124] [INSPIRE].
A. Galajinsky, Particle dynamics on AdS 2 × S 2 background with two-form flux, Phys. Rev. D 78 (2008) 044014 [arXiv:0806.1629] [INSPIRE].
S. Bellucci and S. Krivonos, Potentials in N = 4 superconformal mechanics, Phys. Rev. D 80 (2009) 065022 [arXiv:0905.4633] [INSPIRE].
A. Galajinsky, Particle dynamics near extreme Kerr throat and supersymmetry, JHEP 11 (2010) 126 [arXiv:1009.2341] [INSPIRE].
S. Fedoruk, E. Ivanov and O. Lechtenfeld, New D(2, 1; α) mechanics with spin variables, JHEP 04 (2010) 129 [arXiv:0912.3508] [INSPIRE].
S. Krivonos and O. Lechtenfeld, Many-particle mechanics with D(2, 1; α) superconformal symmetry, JHEP 02 (2011) 042 [arXiv:1012.4639] [INSPIRE].
S. Fedoruk, E. Ivanov and O. Lechtenfeld, Superconformal mechanics, J. Phys. A 45 (2012) 173001 [arXiv:1112.1947] [INSPIRE].
S. Fedoruk and E. Ivanov, New realizations of the supergroup D(2, 1; α) in \( \mathcal{N}=4 \) superconformal mechanics, JHEP 10 (2015) 087 [arXiv:1507.08584] [INSPIRE].
A. Galajinsky, \( \mathcal{N}=4 \) superconformal mechanics from the SU(2) perspective, JHEP 02 (2015) 091 [arXiv:1412.4467] [INSPIRE].
A. Galajinsky, Couplings in D(2, 1; α) superconformal mechanics from the SU(2) perspective, JHEP 03 (2017) 054 [arXiv:1702.01955] [INSPIRE].
D. Chernyavsky, Super 0-brane action on the coset space of D(2, 1; α) supergroup, JHEP 09 (2017) 054 [arXiv:1707.00437] [INSPIRE].
D. Chernyavsky, SU(1, 1|N ) superconformal mechanics with fermionic gauge symmetry, JHEP 04 (2018) 009 [arXiv:1803.00343] [INSPIRE].
T. Okazaki, Membrane quantum mechanics, Nucl. Phys. B 890 (2014) 400 [arXiv:1410.8180] [INSPIRE].
N.B. Copland, S.M. Ko and J.-H. Park, Superconformal Yang-Mills quantum mechanics and Calogero model with OSp(N |2, R) symmetry, JHEP 07 (2012) 076 [arXiv:1205.3869] [INSPIRE].
M. Heinze, B. Hoare, G. Jorjadze and L. Megrelidze, Orbit method quantization of the AdS 2 superparticle, J. Phys. A 48 (2015) 315403 [arXiv:1504.04175] [INSPIRE].
M. Heinze and G. Jorjadze, Quantization of the AdS3 superparticle on OSP(1|2)2 /SL(2, ℝ), Nucl. Phys. B 915 (2017) 44 [arXiv:1610.03519] [INSPIRE].
S. Bellucci, E. Ivanov, S. Krivonos and O. Lechtenfeld, ABC of N = 8, d = 1 supermultiplets, Nucl. Phys. B 699 (2004) 226 [hep-th/0406015] [INSPIRE].
A. Galajinsky and O. Lechtenfeld, Superconformal SU(1, 1|n) mechanics, JHEP 09 (2016) 114 [arXiv:1606.05230] [INSPIRE].
S. Fedoruk, E. Ivanov and O. Lechtenfeld, OSp(4|2) superconformal mechanics, JHEP 08 (2009) 081 [arXiv:0905.4951] [INSPIRE].
S. Krivonos, O. Lechtenfeld and A. Sutulin, N -extended supersymmetric Calogero models, Phys. Lett. B 784 (2018) 137 [arXiv:1804.10825] [INSPIRE].
E. Ivanov and S. Sidorov, Deformed supersymmetric mechanics, Class. Quant. Grav. 31 (2014) 075013 [arXiv:1307.7690] [INSPIRE].
S. Fedoruk, E. Ivanov and S. Sidorov, Deformed supersymmetric quantum mechanics with spin variables, JHEP 01 (2018) 132 [arXiv:1710.02130] [INSPIRE].
S. Fedoruk, E. Ivanov and O. Lechtenfeld, Supersymmetric Calogero models by gauging, Phys. Rev. D 79 (2009) 105015 [arXiv:0812.4276] [INSPIRE].
R.R. Metsaev and A.A. Tseytlin, Superparticle and superstring in AdS 3 × S 3 Ramond-Ramond background in light cone gauge, J. Math. Phys. 42 (2001) 2987 [hep-th/0011191] [INSPIRE].
R.R. Metsaev and A.A. Tseytlin, Type IIB superstring action in AdS 5 × S 5 background, Nucl. Phys. B 533 (1998) 109 [hep-th/9805028] [INSPIRE].
N. Alonso-Alberca, E. Lozano-Tellechea and T. Ortin, Geometric construction of Killing spinors and supersymmetry algebras in homogeneous space-times, Class. Quant. Grav. 19 (2002) 6009 [hep-th/0208158] [INSPIRE].
P. Pasti, D.P. Sorokin and M. Tonin, On gauge fixed superbrane actions in AdS superbackgrounds, Phys. Lett. B 447 (1999) 251 [hep-th/9809213] [INSPIRE].
S. Bellucci and S. Krivonos, Supersymmetric mechanics in superspace, Lect. Notes Phys. 698 (2006) 49 [hep-th/0602199] [INSPIRE].
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Chernyavsky, D. On OSp(N |2) superconformal mechanics. J. High Energ. Phys. 2019, 170 (2019). https://doi.org/10.1007/JHEP02(2019)170
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DOI: https://doi.org/10.1007/JHEP02(2019)170