Superconformal mechanics and nonlinear supersymmetry

Journal of High Energy Physics

Volumn 7, Issue 10, 2003, Pages 1787-1802

  Leiva, Carlos ^a   Plyushchay, Mikhail S ^a,b  

^a UNIVERSIDAD DE SANTIAGO DE CHILE   (Chile)

^b INSTITUTE FOR HIGH ENERGY PHYSICS   (Russian Federation)

Author keywords

Conformal and W Symmetry; Extended Supersymmetry; Global Symmetries

Indexed keywords

EID: 23044437600     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2003/10/069     Document Type: Article

References (50)

1. V. de Alfaro, S. Fubini and G. Furlan, Conformal invariance in quantum mechanics, Nuovo Cim. A34 (1976) 569.
2. V. P. Akulov and A. I. Pashnev, Quantum superconformal model in (1,2) space, Theor. Math. Phys. 56 (1983) 862.
3. S. Fubini and E. Rabinovici, Superconformal quantum mechanics, Nucl. Phys. B 245 (1984) 17.
4. E. A. Ivanov, S. O. Krivonos and V. M. Leviant, Geometry of conformal mechanics, J. Phys. A 22 (1989) 345;
5. Geometric superfield approach to superconformal mechanics, J. Phys. A 22 (1989) 4201.
6. P. Claus et al., Black holes and superconformal mechanics, Phys. Rev. Lett. 81 (1998) 4553 [hep-th/9804177].
7. J.A. de Azcarraga, J.M. Izquierdo, J.C. Perez Bueno and P.K. Townsend, Superconformal mechanics and nonlinear realizations, Phys. Rev. D 59 (1999) 084015 [hep-th/9810230].
8. R. Kallosh, Black holes and quantum mechanics, hep-th/9902007.
9. G.W. Gibbons and P.K. Townsend, Black holes and Calogero models, Phys. Lett. B 454 (1999) 187 [hep-th/9812034].
10. J. Michelson and A. Strominger, The geometry of (super)conformal quantum mechanics, Commun. Math. Phys. 213 (2000) 1 [hep-th/9907191].
11. J. Kumar, Conformal mechanics and the Virasoro algebra, J. High Energy Phys. 04 (1999) 006 [hep-th/9901139].
12. S. Cacciatori, D. Klemm and D. Zanon, W(infinity) algebras, conformal mechanics and black holes, Class. and Quant. Grav. 17 (2000) 1731 [hep-th/9910065].
13. N. Wyllard, (Super)conformal many-body quantum mechanics with extended supersymmetry, J. Math. Phys. 41 (2000) 2826 [hep-th/9910160].
14. R. Britto-Pacumio, J. Michelson, A. Strominger and A. Volovich, Lectures on superconformal quantum mechanics and multi-black hole moduli spaces, hep-th/9911066.
15. E.E. Donets, A. Pashnev, V.O. Rivelles, D.P. Sorokin and M. Tsulaia, N = 4 superconformal mechanics and the potential structure of AdS spaces, Phys. Lett. B 484 (2000) 337 [hep-th/0004019].
16. G. Papadopoulos, Conformal and superconformal mechanics, Class. and Quant. Grav. 17 (2000) 3715 [hep-th/0002007].
17. M.S. Plyushchay, Monopole Chern-Simons term: charge-monopole system as a particle with spin, Nucl. Phys. B 589 (2000) 413 [hep-th/0004032].
18. M. Cadoni, P. Carta and S. Mignemi, A realization of the infinite-dimensional symmetries of conformal mechanics, Phys. Rev. D 62 (2000) 086002 [hep-th/0004107].
19. A. Marcus, Superconformal mechanics and the super Virasoro algebra, J. High Energy Phys. 02 (2001) 043 [hep-th/0101017].
20. E. Deotto, G. Furlan and E. Gozzi, A new supersymmetric extension of conformal mechanics, Phys. Lett. B 481 (2000) 315 [hep-th/0204108].
21. I. Bandos, E. Ivanov, J. Lukierski and D. Sorokin, On the superconformal flatness of AdS superspaces, J. High Energy Phys. 06 (2002) 040 [hep-th/0205104].
22. E. Ivanov, S. Krivonos and J. Niederle, Conformal and superconformal mechanics revisited, hep-th/0210196;
23. 1, canonical transformations and superconformal mechanics, Phys. Lett. B 555 (2003) 99 [hep-th/0212204];
24. E. Ivanov, S. Krivonos and O. Lechtenfeld, New variant of N = 4 superconformal mechanics, J. High Energy Phys. 03 (2003) 014 [hep-th/0212303].
25. C. Leiva and M.S. Plyushchay, Conformal symmetry of relativistic and nonrelativistic systems and AdS/CFT correspondence, Ann. Phys. (NY) 307 (2003) 372 [hep-th/0301244].
26. O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111].
27. A.A. Andrianov, M.V. Ioffe and V.P. Spiridonov, Higher derivative supersymmetry and the Witten index, Phys. Lett. A 174 (1993) 273 [hep-th/9303005];
28. A.A. Andrianov, M.V. Ioffe and D.N. Nishnianidze, Polynomial SUSY in quantum mechanics and second derivative Darboux transformation, Phys. Lett. A 201 (1995) 103 [hep-th/9404120];
29. A.A. Andrianov, F. Cannata, J.P. Dedonder and M.V. Ioffe, Second order derivative supersymmetry, Q deformations and scattering problem, Int. J. Mod. Phys. A 10 (1995) 2683 [hep-th/9404061].
30. B.F. Samsonov, New features in supersymmetry breakdown in quantum mechanics, Mod. Phys. Lett. A 11 (1996) 1563 [quant-ph/9611012].
31. D.J. Fernandez C, SUSUSY quantum mechanics, Int. J. Mod. Phys. A 12 (1997) 171 [quant-ph/9609009].
32. A.A. Andrianov, F. Cannata, M. Ioffe and D. Nishnianidze, Systems with higher-order shape invariance: spectral and algebraic properties, Phys. Lett. A 266 (2000) 341 [quant-ph/9902057].
33. M. Plyushchay, Supersymmetries in pure parabosonic systems, Int. J. Mod. Phys. A 15 (2000) 3679 [hep-th/9903130].
34. S.M. Klishevich and M.S. Plyushchay, Nonlinear super symmetry, quantum anomaly and quasi-exactly solvable systems, Nucl. Phys. B 606 (2001) 583 [hep-th/0012023].
35. H. Aoyama, M. Sato and T. Tanaka, General forms of a N-fold supersymmetric family, Phys. Lett. B 503 (2001) 423 [quant-ph/0012065];
36. N-fold supersymmetry in quantum mechanics: general formalism, Nucl. Phys. B 619 (2001) 105 [quant-ph/0106037];
37. H. Aoyama, N. Nakayama, M. Sato and T. Tanaka, sl(2) construction of type-A N-fold supersymmetry, Phys. Lett. B 519 (2001) 260 [hep-th/0107048].
38. S.M. Klishevich and M.S. Plyushchay, Nonlinear holomorphic supersymmetry, Dolan-Grady relations and Onsager algebra, Nucl. Phys. B 628 (2002) 217 [hep-th/0112158].
39. S.M. Klishevich and M.S. Plyushchay, Nonlinear supersymmetry on the plane in magnetic field and quasi-exactly solvable systems, Nucl. Phys. B 616 (2001) 403 [hep-th/0105135];
40. Nonlinear holomorphic supersymmetry on Riemann surfaces, Nucl. Phys. B 640 (2002) 481 [hep-th/0202077].
41. S.M. Klishevich and M.S. Plyushchay, Dolan-Grady relations and noncommutative quasi-exactly solvable systems, J. Phys. A 36 (2003) 11299 [hep-th/0212117].
42. P. Dorey, C. Dunning and R. Tateo, Spectral equivalences from Bethe ansatz equations, J. Phys. A 34 (2001) 5679 [hep-th/0103051].
43. F. Cannata, M.V. Ioffe and D.N. Nishnianidze, New methods for two-dimensional Schrödinger equation: SUSY-separation of variables and shape invariance, J. Phys. A 35 (2002) 1389 [hep-th/0201080].
44. A.A. Andrianov and A.V. Sokolov, Nonlinear supersymmetry in quantum mechanics: algebraic properties and differential representation, Nucl. Phys. B 660 (2003) 25 [hep-th/0301062].
45. E. Witten, Dynamical breaking of supersymmetry, Nucl. Phys. B 188 (1981) 513.
46. D.Z. Freedman and P.F. Mende, An exactly solvable N particle system in supersymmetric quantum mechanics, Nucl. Phys. B 344 (1990) 317.
47. S. Bellucci, A. Galajinsky and S. Krivonos, New many-body superconformal models as reductions of simple composite systems, Phys. Rev. D 68 (2003) 064010 [hep-th/0304087].
48. E. D'Hoker and L. Vinet, Supersymmetry of the Pauli equation in the presence of a magnetic monopole, Phys. Lett. B 137 (1984) 72.
49. M.S. Plyushchay, On the nature of fermion-monopole supersymmetry, Phys. Lett. B 485 (2000) 187 [hep-th/0005122].
50. A. Anabalon and M.S. Plyushchay, Interaction via reduction and nonlinear superconformal symmetry, Phys. Lett. B 572 (2003) 202 [hep-th/0306210].