Abstract
This paper is an extension of our last 1D, \( \mathcal{N} \) = 4 supersymmetric SYK paper [1]. In this paper we introduced the complex linear supermultiplet (CLS), which is “usefully inequivalent” to the chiral supermultiplet. We construct three types of models based on the complex linear supermultiplet containing quartic interactions from modified CLS kinetic term, quartic interactions from 3-pt vertices integrated over the whole superspace, and 2(q − 1)-pt interactions generated via superpotentials respectively. A strong evidence for the inevitability of dynamical bosons for 1D, \( \mathcal{N} \) = 4 SYK is also presented.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.J. Gates Jr., Y. Hu and S.N.H. Mak, On 1D, N = 4 supersymmetric SYK-type models. Part I, JHEP 06 (2021) 158 [arXiv:2103.11899] [INSPIRE].
S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70 (1993) 3339 [cond-mat/9212030] [INSPIRE].
A. Kitaev, Hidden correlations in the Hawking radiation and thermal noise, in KITP fundamental physics prize symposium, 10 November 2014.
A. Kitaev, Hidden correlations in the Hawking radiation and thermal noise, https://online.kitp.ucsb.edu/online/joint98/kitaev/, University of California, Santa Barbara, CA, U.S.A., 12 February 2015.
A. Kitaev, A simple model of quantum holography (part 1), talk at KITP strings seminar and entanglement 2015 program, https://online.kitp.ucsb.edu/online/entangled15/kitaev/, University of California, Santa Barbara, CA, U.S.A., 7 April 2015.
A. Kitaev, A simple model of quantum holography (part 2), talk at KITP strings seminar and entanglement 2015 program, https://online.kitp.ucsb.edu/online/entangled15/kitaev2/, University of California, Santa Barbara, CA, U.S.A., 27 May 2015.
Y.A. Golfand and E.P. Likhtman, Extension of the algebra of Poincaré group generators and violation of p invariance, JETP Lett. 13 (1971) 323 [Pisma Zh. Eksp. Teor. Fiz. 13 (1971) 452] [INSPIRE].
J. Wess and B. Zumino, A Lagrangian model invariant under supergauge transformations, Phys. Lett. B 49 (1974) 52 [INSPIRE].
J. Wess and B. Zumino, Supergauge transformations in four-dimensions, Nucl. Phys. B 70 (1974) 39 [INSPIRE].
J. Wess, Fermi-Bose supersymmetry, lectures given at the Bonn summer school, Bonn, Germany (1974) [Lect. Notes Phys. 37 (1975) 352] [INSPIRE].
P. Fayet, Fermi-Bose hypersymmetry, Nucl. Phys. B 113 (1976) 135 [INSPIRE].
J. Wess and B. Zumino, Supergauge invariant extension of quantum electrodynamics, Nucl. Phys. B 78 (1974) 1 [INSPIRE].
S. Ferrara and B. Zumino, Supergauge invariant Yang-Mills theories, Nucl. Phys. B 79 (1974) 413 [INSPIRE].
W. Siegel, Gauge spinor superfield as a scalar multiplet, Phys. Lett. B 85 (1979) 333 [INSPIRE].
T. Hübsch, Linear and chiral superfields are usefully inequivalent, Class. Quant. Grav. 16 (1999) L51 [hep-th/9903175] [INSPIRE].
S.J. Gates Jr., Superspace formulation of new nonlinear sigma models, Nucl. Phys. B 238 (1984) 349 [INSPIRE].
W.E. Thirring, A soluble relativistic field theory?, Annals Phys. 3 (1958) 91 [INSPIRE].
Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. I, Phys. Rev. 122 (1961) 345 [INSPIRE].
Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. II, Phys. Rev. 124 (1961) 246 [INSPIRE].
D.J. Gross and A. Neveu, Dynamical symmetry breaking in asymptotically free field theories, Phys. Rev. D 10 (1974) 3235 [INSPIRE].
W. Siegel and S.J. Gates Jr., Superfield supergravity, Nucl. Phys. B 147 (1979) 77 [INSPIRE].
S.J. Gates Jr. and W. Siegel, Variant superfield representations, Nucl. Phys. B 187 (1981) 389 [INSPIRE].
S.J. Gates Jr., M.T. Grisaru, M. Roček and W. Siegel, Superspace or one thousand and one lessons in supersymmetry, Front. Phys. 58 (1983) 1 [hep-th/0108200] [INSPIRE].
B.B. Deo and S.J. Gates Jr., Comments on nonminimal N = 1 scalar multiplets, Nucl. Phys. B 254 (1985) 187 [INSPIRE].
I.L. Buchbinder and S.M. Kuzenko, Ideas and methods of supersymmetry and supergravity: or a walk through superspace, CRC press, Boca Raton, FL, U.S.A. (1998) [ISBN-13:978-0750305068].
S.M. Kuzenko, Projective superspace as a double punctured harmonic superspace, Int. J. Mod. Phys. A 14 (1999) 1737 [hep-th/9806147] [INSPIRE].
S.J. Gates Jr. and S.M. Kuzenko, The CNM hypermultiplet nexus, Nucl. Phys. B 543 (1999) 122 [hep-th/9810137] [INSPIRE].
S.J. Gates Jr., T. Hübsch and S.M. Kuzenko, CNM models, holomorphic functions and projective superspace C maps, Nucl. Phys. B 557 (1999) 443 [hep-th/9902211] [INSPIRE].
S.J. Gates Jr. and S.M. Kuzenko, 4D, N = 2 supersymmetric off-shell sigma models on the cotangent bundles of Kähler manifolds, Fortsch. Phys. 48 (2000) 115 [hep-th/9903013] [INSPIRE].
S.J. Gates Jr., T. Hübsch and S.M. Kuzenko, CNM models, holomorphic functions and projective superspace C maps, Nucl. Phys. B 557 (1999) 443 [hep-th/9902211] [INSPIRE].
S.J. Gates Jr., S. Penati and G. Tartaglino-Mazzucchelli, 6D supersymmetric nonlinear sigma-models in 4D, N = 1 superspace, JHEP 09 (2006) 006 [hep-th/0604042] [INSPIRE].
S.J. Gates Jr., S. Penati and G. Tartaglino-Mazzucchelli, 6D supersymmetry, projective superspace and 4D, N = 1 superfields, JHEP 05 (2006) 051 [hep-th/0508187] [INSPIRE].
M. Arai and M. Nitta, Hyper-Kähler sigma models on (co)tangent bundles with SO(n) isometry, Nucl. Phys. B 745 (2006) 208 [hep-th/0602277] [INSPIRE].
M. Arai, S.M. Kuzenko and U. Lindström, Hyper-Kähler sigma models on cotangent bundles of Hermitian symmetric spaces using projective superspace, JHEP 02 (2007) 100 [hep-th/0612174] [INSPIRE].
M. Arai, S.M. Kuzenko and U. Lindström, Polar supermultiplets, Hermitian symmetric spaces and hyper-Kähler metrics, JHEP 12 (2007) 008 [arXiv:0709.2633] [INSPIRE].
S.M. Kuzenko and J. Novak, Chiral formulation for hyper-Kähler sigma-models on cotangent bundles of symmetric spaces, JHEP 12 (2008) 072 [arXiv:0811.0218] [INSPIRE].
S.M. Kuzenko, Lectures on nonlinear sigma-models in projective superspace, J. Phys. A 43 (2010) 443001 [arXiv:1004.0880] [INSPIRE].
S.J. Gates Jr. and L. Rana, Manifest (4, 0) supersymmetry, sigma models and the ADHM instanton construction, Phys. Lett. B 345 (1995) 233 [hep-th/9411091] [INSPIRE].
R. Dhanawittayapol, S.J. Gates Jr. and L. Rana, A canticle on (4, 0) supergravity scalar multiplet systems for a ‘cognoscente’, Phys. Lett. B 389 (1996) 264 [hep-th/9606108] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2110.15562
Rights and permissions
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.
About this article
Cite this article
James Gates, S., Hu, Y. & Mak, SN.H. On 1D, \( \mathcal{N} \) = 4 supersymmetric SYK-type models. Part II. J. High Energ. Phys. 2022, 148 (2022). https://doi.org/10.1007/JHEP03(2022)148
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2022)148