Abstract
We discuss the Bosonic sector of a class of supersymmetric non-Lorentzian five-dimensional gauge field theories with an SU(1, 3) conformal symmetry. These actions have a Lagrange multiplier which imposes a novel Ω-deformed anti-self-dual gauge field constraint. Using a generalised ’t Hooft ansatz we find the constraint equation linearizes allowing us to construct a wide class of explicit solutions. These include finite action configurations that describe worldlines of anti-instantons which can be created and annihilated. We also describe the dynamics on the constraint surface.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
W. Nahm, Supersymmetries and their Representations, Nucl. Phys. B 135 (1978) 149 [INSPIRE].
E. Witten, Some comments on string dynamics, in STRINGS 95: Future Perspectives in String Theory (1995), pp. 501–523 [hep-th/9507121] [INSPIRE].
A. Strominger, Open p-branes, Phys. Lett. B 383 (1996) 44 [hep-th/9512059] [INSPIRE].
N. Seiberg, Nontrivial fixed points of the renormalization group in six-dimensions, Phys. Lett. B 390 (1997) 169 [hep-th/9609161] [INSPIRE].
N. Lambert, A. Lipstein and P. Richmond, Non-Lorentzian M5-brane Theories from Holography, JHEP 08 (2019) 060 [arXiv:1904.07547] [INSPIRE].
N. Lambert and T. Orchard, Non-Lorentzian Avatars of (1, 0) Theories, arXiv:2011.06968 [INSPIRE].
O. Aharony, M. Berkooz, S. Kachru, N. Seiberg and E. Silverstein, Matrix description of interacting theories in six-dimensions, Adv. Theor. Math. Phys. 1 (1998) 148 [hep-th/9707079] [INSPIRE].
O. Aharony, M. Berkooz, S. Kachru and E. Silverstein, Matrix description of (1, 0) theories in six-dimensions, Phys. Lett. B 420 (1998) 55 [hep-th/9709118] [INSPIRE].
N. Lambert, A. Lipstein, R. Mouland and P. Richmond, Five-Dimensional Non-Lorentzian Conformal Field Theories and their Relation to Six-Dimensions, JHEP 03 (2021) 053 [arXiv:2012.00626] [INSPIRE].
N. Lambert, A. Lipstein, R. Mouland and P. Richmond, Bosonic symmetries of (2, 0) DLCQ field theories, JHEP 01 (2020) 166 [arXiv:1912.02638] [INSPIRE].
S. Vandoren and P. van Nieuwenhuizen, Lectures on instantons, arXiv:0802.1862 [INSPIRE].
N. Aronszajn and W.F. Donoghue, On exponential representations of analytic functions in the upper half-plane with positive imaginary part, Journal d’Analyse Mathematique 5 (1956) 321.
N. Lambert, C. Papageorgakis and M. Schmidt-Sommerfeld, Instanton Operators in Five-Dimensional Gauge Theories, JHEP 03 (2015) 019 [arXiv:1412.2789] [INSPIRE].
Y. Tachikawa, Instanton operators and symmetry enhancement in 5d supersymmetric gauge theories, PTEP 2015 (2015) 043B06 [arXiv:1501.01031] [INSPIRE].
O. Bergman and D. Rodriguez-Gomez, A Note on Instanton Operators, Instanton Particles, and Supersymmetry, JHEP 05 (2016) 068 [arXiv:1601.00752] [INSPIRE].
N. Lambert, A. Lipstein, R. Mouland and P. Richmond, Five-Dimensional Path Integrals for Six-Dimensional Conformal Field Theories, arXiv:2109.04829 [INSPIRE].
G. Arutyunov and E. Sokatchev, Implications of superconformal symmetry for interacting (2, 0) tensor multiplets, Nucl. Phys. B 635 (2002) 3 [hep-th/0201145] [INSPIRE].
P.J. Heslop, Aspects of superconformal field theories in six dimensions, JHEP 07 (2004) 056 [hep-th/0405245] [INSPIRE].
L. Rastelli and X. Zhou, Holographic Four-Point Functions in the (2, 0) Theory, JHEP 06 (2018) 087 [arXiv:1712.02788] [INSPIRE].
P. Heslop and A.E. Lipstein, M-theory Beyond The Supergravity Approximation, JHEP 02 (2018) 004 [arXiv:1712.08570] [INSPIRE].
S.M. Chester and E. Perlmutter, M-Theory Reconstruction from (2, 0) CFT and the Chiral Algebra Conjecture, JHEP 08 (2018) 116 [arXiv:1805.00892] [INSPIRE].
T. Abl, P. Heslop and A.E. Lipstein, Recursion relations for anomalous dimensions in the 6d (2, 0) theory, JHEP 04 (2019) 038 [arXiv:1902.00463] [INSPIRE].
L.F. Alday and X. Zhou, All Tree-Level Correlators for M-theory on AdS7 × S4, Phys. Rev. Lett. 125 (2020) 131604 [arXiv:2006.06653] [INSPIRE].
L.F. Alday, S.M. Chester and H. Raj, 6d (2, 0) and M-theory at 1-loop, JHEP 01 (2021) 133 [arXiv:2005.07175] [INSPIRE].
N. Lambert and P. Richmond, (2, 0) Supersymmetry and the Light-Cone Description of M5-branes, JHEP 02 (2012) 013 [arXiv:1109.6454] [INSPIRE].
R. Mouland, Supersymmetric soliton σ-models from non-Lorentzian field theories, JHEP 04 (2020) 129 [arXiv:1911.11504] [INSPIRE].
D. Tong, TASI lectures on solitons: Instantons, monopoles, vortices and kinks, in Theoretical Advanced Study Institute in Elementary Particle Physics: Many Dimensions of String Theory, (2005) [hep-th/0509216] [INSPIRE].
N. Dorey, T.J. Hollowood, V.V. Khoze, M.P. Mattis and S. Vandoren, Multi-instanton calculus and the AdS/CFT correspondence in N = 4 superconformal field theory, Nucl. Phys. B 552 (1999) 88 [hep-th/9901128] [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: 2105.02008
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
Lambert, N., Lipstein, A., Mouland, R. et al. Instanton worldlines in five-dimensional Ω-deformed gauge theory. J. High Energ. Phys. 2021, 86 (2021). https://doi.org/10.1007/JHEP09(2021)086
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2021)086