Abstract
We construct new models of “curved” SU(4|1) supersymmetric mechanics based on two versions of the off-shell multiplet (8, 8, 0) which are “mirror” to each other. The worldline realizations of the supergroup SU(4|1) are treated as a deformation of flat \( \mathcal{N}=8 \), d = 1 supersymmetry. Using SU(4|1) chiral superfields, we derive invariant actions for the first-type (8, 8, 0) multiplet, which parametrizes special Kähler manifolds. Since we are not aware of a manifestly SU(4|1) covariant superfield formalism for the second-type (8, 8, 0) multiplet, we perform a general construction of SU(4|1) invariant actions for both multiplet types in terms of SU(2|1) superfields. An important class of such actions enjoys superconformal OSp(8|2) invariance. We also build off-shell actions for the SU(4|1) multiplets (6, 8, 2) and (7, 8, 1) through appropriate substitutions for the component fields in the (8, 8, 0) actions. The (6, 8, 2) actions are shown to respect superconformal SU(4|1, 1) invariance.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. Festuccia and N. Seiberg, Rigid Supersymmetric Theories in Curved Superspace, JHEP 06 (2011) 114 [arXiv:1105.0689] [INSPIRE].
S. Bellucci and A. Nersessian, (Super)oscillator on CP N and constant magnetic field, Phys. Rev. D 67 (2003) 065013 [Erratum ibid. D 71 (2005) 089901] [hep-th/0211070] [INSPIRE].
C. Römelsberger, Counting chiral primaries in N = 1, d = 4 superconformal field theories, Nucl. Phys. B 747 (2006) 329 [hep-th/0510060] [INSPIRE].
A.V. Smilga, Weak supersymmetry, Phys. Lett. B 585 (2004) 173 [hep-th/0311023] [INSPIRE].
A. Pashnev and F. Toppan, On the classification of \( \mathcal{N} \) -extended supersymmetric quantum mechanical systems, J. Math. Phys. 42 (2001) 5257 [hep-th/0010135] [INSPIRE].
E. Ivanov and S. Sidorov, Deformed Supersymmetric Mechanics, Class. Quant. Grav. 31 (2014) 075013 [arXiv:1307.7690] [INSPIRE].
E. Ivanov and S. Sidorov, Super Kähler oscillator from SU(2|1) superspace, J. Phys. A 47 (2014) 292002 [arXiv:1312.6821] [INSPIRE].
E. Ivanov, S. Sidorov and F. Toppan, Superconformal mechanics in SU(2|1) superspace, Phys. Rev. D 91 (2015) 085032 [arXiv:1501.05622] [INSPIRE].
E. Ivanov and S. Sidorov, SU(2|1) mechanics and harmonic superspace, Class. Quant. Grav. 33 (2016) 055001 [arXiv:1507.00987] [INSPIRE].
S. Fedoruk and E. Ivanov, Gauged spinning models with deformed supersymmetry, JHEP 11 (2016) 103 [arXiv:1610.04202] [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, O. Lechtenfeld and S. Sidorov, Quantum SU(2|1) supersymmetric Calogero-Moser spinning systems, JHEP 04 (2018) 043 [arXiv:1801.00206] [INSPIRE].
E. Ivanov, O. Lechtenfeld and S. Sidorov, SU(2|2) supersymmetric mechanics, JHEP 11 (2016) 031 [arXiv:1609.00490] [INSPIRE].
S. Bellucci, E. Ivanov, S. Krivonos and O. Lechtenfeld, N = 8 superconformal mechanics, Nucl. Phys. B 684 (2004) 321 [hep-th/0312322] [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].
S. Bellucci, E. Ivanov and A. Sutulin, N = 8 mechanics in SU(2) × SU(2) harmonic superspace, Nucl. Phys. B 722 (2005) 297 [Erratum ibid. B 747 (2006) 464] [hep-th/0504185] [INSPIRE].
E. Ivanov, O. Lechtenfeld and A. Sutulin, Hierarchy of N = 8 Mechanics Models, Nucl. Phys. B 790 (2008) 493 [arXiv:0705.3064] [INSPIRE].
S. Bellucci, S. Krivonos and A. Nersessian, N = 8 supersymmetric mechanics on special Kähler manifolds, Phys. Lett. B 605 (2005) 181 [hep-th/0410029] [INSPIRE].
E.A. Ivanov and A.V. Smilga, Symplectic σ-models in superspace, Nucl. Phys. B 694 (2004) 473 [hep-th/0402041] [INSPIRE].
D.-E. Diaconescu and R. Entin, A Nonrenormalization theorem for the d = 1, N = 8 vector multiplet, Phys. Rev. D 56 (1997) 8045 [hep-th/9706059] [INSPIRE].
F. Toppan, On Chiral and Nonchiral 1D Supermultiplets, in Proceedings, 13th Regional Conference on Mathematical Physics, Antalya, Turkey, October 27–31, 2010, pp. 227–237 (2012) [DOI:https://doi.org/10.1142/9789814417532_0017] [arXiv:1105.2016] [INSPIRE].
M.B. Green, J.H. Schwarz and E. Witten, Superstring Theory: Volume 1, Cambridge University Press (1987) [INSPIRE].
M.B. Green, J.H. Schwarz and E. Witten, Superstring Theory: Volume 2, Cambridge University Press (1988) [INSPIRE].
A. Galperin, E. Ivanov, S. Kalitsyn, V. Ogievetsky and E. Sokatchev, Unconstrained N = 2 Matter, Yang-Mills and Supergravity Theories in Harmonic Superspace, Class. Quant. Grav. 1 (1984) 469 [Erratum ibid. 2 (1985) 127] [INSPIRE].
F. Delduc and E. Ivanov, N = 4 mechanics of general (4, 4, 0) multiplets, Nucl. Phys. B 855 (2012) 815 [arXiv:1107.1429] [INSPIRE].
S. Fedoruk, E. Ivanov and A. Smilga, \( \mathcal{N}=4 \) mechanics with diverse (4, 4, 0) multiplets: Explicit examples of hyper-Kähler with torsion, Clifford Kähler with torsion and octonionic Kähler with torsion geometries, J. Math. Phys. 55 (2014) 052302 [arXiv:1309.7253] [INSPIRE].
N. Kim and J.-H. Park, Superalgebra for M-theory on a pp wave, Phys. Rev. D 66 (2002) 106007 [hep-th/0207061] [INSPIRE].
L. Motl, A. Neitzke and M.M. Sheikh-Jabbari, Heterotic plane wave matrix models and giant gluons, JHEP 06 (2003) 058 [hep-th/0306051] [INSPIRE].
C.T. Asplund, F. Denef and E. Dzienkowski, Massive quiver matrix models for massive charged particles in AdS, JHEP 01 (2016) 055 [arXiv:1510.04398] [INSPIRE].
E. Ivanov, L. Mezincescu, A. Pashnev and P.K. Townsend, Odd coset quantum mechanics, Phys. Lett. B 566 (2003) 175 [hep-th/0301241] [INSPIRE].
M. Goykhman, E. Ivanov and S. Sidorov, Super Landau Models on Odd Cosets, Phys. Rev. D 87 (2013) 025026 [arXiv:1208.3418] [INSPIRE].
E. Ivanov, S. Kalitsyn, A.V. Nguyen and V. Ogievetsky, Harmonic Superspaces of Extended Supersymmetry. The Calculus of Harmonic Variables, J. Phys. A 18 (1985) 3433 [INSPIRE].
N.L. Holanda and F. Toppan, Four types of (super)conformal mechanics: D-module reps and invariant actions, J. Math. Phys. 55 (2014) 061703 [arXiv:1402.7298] [INSPIRE].
Z. Kuznetsova and F. Toppan, D-module Representations of N = 2, 4, 8 Superconformal Algebras and Their Superconformal Mechanics, J. Math. Phys. 53 (2012) 043513 [arXiv:1112.0995] [INSPIRE].
D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N = 4 super Yang-Mills, JHEP 04 (2002) 013[hep-th/0202021] [INSPIRE].
K. Dasgupta, M.M. Sheikh-Jabbari and M. Van Raamsdonk, Matrix perturbation theory for M-theory on a PP wave, JHEP 05 (2002) 056 [hep-th/0205185] [INSPIRE].
K. Dasgupta, M.M. Sheikh-Jabbari and M. Van Raamsdonk, Protected multiplets of M-theory on a plane wave, JHEP 09 (2002) 021 [hep-th/0207050] [INSPIRE].
F. Delduc and E. Ivanov, Gauging N = 4 Supersymmetric Mechanics, Nucl. Phys. B 753 (2006) 211 [hep-th/0605211] [INSPIRE].
S. Fedoruk, E. Ivanov and O. Lechtenfeld, Supersymmetric Calogero models by gauging, Phys. Rev. D 79 (2009) 105015 [arXiv:0812.4276] [INSPIRE].
S. Khodaee and F. Toppan, Critical scaling dimension of D-module representations of N = 4, 7, 8 Superconformal Algebras and constraints on Superconformal Mechanics, J. Math. Phys. 53 (2012) 103518 [arXiv:1208.3612] [INSPIRE].
F. Toppan, Critical D-module reps for finite superconformal algebras and their superconformal mechanics, in 29th International Colloquium on Group-Theoretical Methods in Physics (GROUP 29), Tianjin, China, August 20–26, 2012 (2013) [arXiv:1302.3459] [INSPIRE].
N. Aizawa, Z. Kuznetsova and F. Toppan, The quasi-nonassociative exceptional F(4) deformed quantum oscillator, J. Math. Phys. 59 (2018) 022101 [arXiv:1711.02923] [INSPIRE].
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: 1807.11804
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Ivanov, E., Lechtenfeld, O. & Sidorov, S. Deformed \( \mathcal{N}=8 \) mechanics of (8, 8, 0) multiplets. J. High Energ. Phys. 2018, 193 (2018). https://doi.org/10.1007/JHEP08(2018)193
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2018)193