Abstract
In this paper we derive Ward-Takahashi identities from the path integral of supersymmetric five-dimensional field theories with an SU(1, 3) spacetime symmetry in the presence of instantons. We explicitly show how SU(1, 3) is enhanced to SU(1, 3) × U(1) where the additional U(1) acts non-perturbatively. Solutions to such Ward-Takahashi identities were previously obtained from correlators of six-dimensional Lorentzian conformal field theories but where the instanton number was replaced by the momentum along a null direction. Here we study the reverse procedure whereby we construct correlation functions out of towers of five-dimensional operators which satisfy the Ward-Takahashi identities of a six-dimensional conformal field theory. This paves the way to computing observables in six dimensions using five-dimensional path integral techniques. We also argue that, once the instanton sector is included into the path integral, the coupling of the five-dimensional Lagrangian must be quantised, leaving no free continuous parameters.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
F. Bastianelli, S. Frolov and A. A. Tseytlin, Three point correlators of stress tensors in maximally supersymmetric conformal theories in D = 3 and D = 6, Nucl. Phys. B 578 (2000) 139 [hep-th/9911135] [INSPIRE].
F. Bastianelli and R. Zucchini, Three point functions for a class of chiral operators in maximally supersymmetric CFT at large N , Nucl. Phys. B 574 (2000) 107 [hep-th/9909179] [INSPIRE].
B. Eden, S. Ferrara and E. Sokatchev, (2, 0) superconformal OPEs in D = 6, selection rules and nonrenormalization theorems, JHEP 11 (2001) 020 [hep-th/0107084] [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].
C. Beem, M. Lemos, L. Rastelli and B. C. van Rees, The (2, 0) superconformal bootstrap, Phys. Rev. D 93 (2016) 025016 [arXiv:1507.05637] [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].
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, S. M. Chester and H. Raj, 6d (2, 0) and M-theory at 1-loop, JHEP 01 (2021) 133 [arXiv:2005.07175] [INSPIRE].
C. Beem, L. Rastelli and B. C. van Rees, \( \mathcal{W} \) symmetry in six dimensions, JHEP 05 (2015) 017 [arXiv:1404.1079] [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].
O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [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, A. Lipstein, R. Mouland and P. Richmond, Bosonic symmetries of (2, 0) DLCQ field theories, JHEP 01 (2020) 166 [arXiv:1912.02638] [INSPIRE].
N. Lambert and T. Orchard, Non-Lorentzian Avatars of (1, 0) Theories, arXiv:2011.06968 [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, Instanton worldlines in five-dimensional Ω-deformed gauge theory, JHEP 09 (2021) 086 [arXiv:2105.02008] [INSPIRE].
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].
R. Mouland, Non-Lorentzian supersymmetric models and M-theory branes, Ph.D. Thesis, King’s College London (2021) [arXiv:2109.04416] [INSPIRE].
C. N. Pope, A. Sadrzadeh and S. R. Scuro, Timelike Hopf duality and type IIA* string solutions, Class. Quant. Grav. 17 (2000) 623 [hep-th/9905161] [INSPIRE].
N. Lambert and R. Mouland, Non-Lorentzian RG flows and Supersymmetry, JHEP 06 (2019) 130 [arXiv:1904.05071] [INSPIRE].
N. Lambert, C. Papageorgakis and M. Schmidt-Sommerfeld, M5-Branes, D4-branes and Quantum 5D super-Yang-Mills, JHEP 01 (2011) 083 [arXiv:1012.2882] [INSPIRE].
M. R. Douglas, On D = 5 super Yang-Mills theory and (2, 0) theory, JHEP 02 (2011) 011 [arXiv:1012.2880] [INSPIRE].
M. F. Atiyah, N. J. Hitchin, V. G. Drinfeld and Y. I. Manin, Construction of Instantons, Phys. Lett. A 65 (1978) 185 [INSPIRE].
V. Borokhov, A. Kapustin and X.-k. Wu, Topological disorder operators in three-dimensional conformal field theory, JHEP 11 (2002) 049 [hep-th/0206054] [INSPIRE].
T. Hartman, S. Jain and S. Kundu, Causality Constraints in Conformal Field Theory, JHEP 05 (2016) 099 [arXiv:1509.00014] [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: 2109.04829
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. Five-dimensional path integrals for six-dimensional conformal field theories. J. High Energ. Phys. 2022, 151 (2022). https://doi.org/10.1007/JHEP02(2022)151
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2022)151