Abstract
We initiate the study of how the insertion of magnetically charged states in 4d self-dual gauge theories impacts the 2d chiral algebras supported on the celestial sphere at asymptotic null infinity, from the point of view of the 4d/2d twistorial correspondence introduced by Costello and the second author. By reducing the 6d twistorial theory to a 3d holomorphic-topological theory with suitable boundary conditions, we can motivate certain non-perturbative enhancements of the celestial chiral algebra corresponding to extensions by modules arising from 3d boundary monopole operators. We also identify the insertion of 4d (non-abelian) monopoles with families of spectral flow automorphisms of the celestial chiral algebra.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Guevara, E. Himwich, M. Pate and A. Strominger, Holographic symmetry algebras for gauge theory and gravity, JHEP 11 (2021) 152 [arXiv:2103.03961] [INSPIRE].
A. Strominger, w1+∞ and the Celestial Sphere, arXiv:2105.14346 [INSPIRE].
A. Ball, S.A. Narayanan, J. Salzer and A. Strominger, Perturbatively exact w1+∞ asymptotic symmetry of quantum self-dual gravity, JHEP 01 (2022) 114 [arXiv:2111.10392] [INSPIRE].
R. Bhardwaj et al., Loop-level gluon OPEs in celestial holography, JHEP 11 (2022) 171 [arXiv:2208.14416] [INSPIRE].
R. Monteiro, Celestial chiral algebras, colour-kinematics duality and integrability, JHEP 01 (2023) 092 [arXiv:2208.11179] [INSPIRE].
K. Costello and N.M. Paquette, Celestial holography meets twisted holography: 4d amplitudes from chiral correlators, JHEP 10 (2022) 193 [arXiv:2201.02595] [INSPIRE].
K. Costello and N.M. Paquette, Associativity of One-Loop Corrections to the Celestial Operator Product Expansion, Phys. Rev. Lett. 129 (2022) 231604 [arXiv:2204.05301] [INSPIRE].
V.E. Fernández, One-loop corrections to the celestial chiral algebra from Koszul Duality, JHEP 04 (2023) 124 [arXiv:2302.14292] [INSPIRE].
R. Bittleston, On the associativity of 1-loop corrections to the celestial operator product in gravity, JHEP 01 (2023) 018 [arXiv:2211.06417] [INSPIRE].
K.J. Costello, Quantizing local holomorphic field theories on twistor space, arXiv:2111.08879 [INSPIRE].
K. Costello and S. Li, Anomaly cancellation in the topological string, Adv. Theor. Math. Phys. 24 (2020) 1723 [arXiv:1905.09269] [INSPIRE].
K. Costello, N.M. Paquette and A. Sharma, Top-Down Holography in an Asymptotically Flat Spacetime, Phys. Rev. Lett. 130 (2023) 061602 [arXiv:2208.14233] [INSPIRE].
K. Costello and D. Gaiotto, Twisted Holography, arXiv:1812.09257 [INSPIRE].
K. Costello and N.M. Paquette, Twisted Supergravity and Koszul Duality: A case study in AdS3, Commun. Math. Phys. 384 (2021) 279 [arXiv:2001.02177] [INSPIRE].
B. Bakalov and V. Kac, Field algebras, Int. Math. Res. Not. 2003 (2003) 123.
A. Strominger, Magnetic Corrections to the Soft Photon Theorem, Phys. Rev. Lett. 116 (2016) 031602 [arXiv:1509.00543] [INSPIRE].
D. Kapec and P. Mitra, Shadows and soft exchange in celestial CFT, Phys. Rev. D 105 (2022) 026009 [arXiv:2109.00073] [INSPIRE].
M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes, Commun. Math. Phys. 165 (1994) 311 [hep-th/9309140] [INSPIRE].
M. Aganagic, K. Costello, J. McNamara and C. Vafa, Topological Chern-Simons/Matter Theories, arXiv:1706.09977 [INSPIRE].
O. Aharony et al., Aspects of N = 2 supersymmetric gauge theories in three-dimensions, Nucl. Phys. B 499 (1997) 67 [hep-th/9703110] [INSPIRE].
K. Intriligator and N. Seiberg, Aspects of 3d N = 2 Chern-Simons-Matter Theories, JHEP 07 (2013) 079 [arXiv:1305.1633] [INSPIRE].
A. Gadde, S. Gukov and P. Putrov, Walls, Lines, and Spectral Dualities in 3d Gauge Theories, JHEP 05 (2014) 047 [arXiv:1302.0015] [INSPIRE].
A. Gadde, S. Gukov and P. Putrov, Fivebranes and 4-manifolds, Prog. Math. 319 (2016) 155 [arXiv:1306.4320] [INSPIRE].
T. Okazaki and S. Yamaguchi, Supersymmetric boundary conditions in three-dimensional N = 2 theories, Phys. Rev. D 87 (2013) 125005 [arXiv:1302.6593] [INSPIRE].
T. Dimofte, D. Gaiotto and N.M. Paquette, Dual boundary conditions in 3d SCFT’s, JHEP 05 (2018) 060 [arXiv:1712.07654] [INSPIRE].
K. Costello, T. Dimofte and D. Gaiotto, Boundary Chiral Algebras and Holomorphic Twists, Commun. Math. Phys. 399 (2023) 1203 [arXiv:2005.00083] [INSPIRE].
K. Zeng, Monopole operators and bulk-boundary relation in holomorphic topological theories, SciPost Phys. 14 (2023) 153 [arXiv:2111.00955] [INSPIRE].
M. Bullimore et al., Vortices and Vermas, Adv. Theor. Math. Phys. 22 (2018) 803 [arXiv:1609.04406] [INSPIRE].
H. Nakajima, Towards a mathematical definition of Coulomb branches of 3-dimensional \( \mathcal{N} \) = 4 gauge theories, I, Adv. Theor. Math. Phys. 20 (2016) 595 [arXiv:1503.03676] [INSPIRE].
A. Braverman, M. Finkelberg and H. Nakajima, Towards a mathematical definition of Coulomb branches of 3-dimensional \( \mathcal{N} \) = 4 gauge theories, II, Adv. Theor. Math. Phys. 22 (2018) 1071 [arXiv:1601.03586] [INSPIRE].
M. Bullimore, T. Dimofte and D. Gaiotto, The Coulomb Branch of 3d \( \mathcal{N} \) = 4 Theories, Commun. Math. Phys. 354 (2017) 671 [arXiv:1503.04817] [INSPIRE].
S. Alekseev, M. Dedushenko and M. Litvinov, Chiral life on a slab, arXiv:2301.00038 [INSPIRE].
X. Zhu, An introduction to affine Grassmannians and the geometric Satake equivalence, arXiv:1603.05593.
A. Ballin, T. Creutzig, T. Dimofte and W. Niu, 3d mirror symmetry of braided tensor categories, arXiv:2304.11001 [INSPIRE].
A. Ballin and W. Niu, 3d Mirror Symmetry and the βγ VOA, arXiv:2202.01223 [https://doi.org/10.1142/S0219199722500699] [INSPIRE].
N. Garner and W. Niu, Line Operators in U(1|1) Chern-Simons Theory, arXiv:2304.05414 [INSPIRE].
T. Creutzig and D. Ridout, W-Algebras Extending Affine \( \hat{\mathfrak{gl}} \)(1|1), Springer Proc. Math. Stat. 36 (2013) 349 [arXiv:1111.5049] [INSPIRE].
T. Creutzig, S. Kanade and R. McRae, Tensor categories for vertex operator superalgebra extensions, arXiv:1705.05017 [INSPIRE].
T. Creutzig, R. McRae and J. Yang, Direct limit completions of vertex tensor categories, Commun. Contemp. Math. 24 (2022) 2150033 [arXiv:2006.09711] [INSPIRE].
O. Gwilliam and B.R. Williams, Higher Kac-Moody algebras and symmetries of holomorphic field theories, Adv. Theor. Math. Phys. 25 (2021) 129 [arXiv:1810.06534] [INSPIRE].
K. Zeng, Twisted Holography and Celestial Holography from Boundary Chiral Algebra, arXiv:2302.06693 [INSPIRE].
L. Donnay, S. Pasterski and A. Puhm, Goldilocks modes and the three scattering bases, JHEP 06 (2022) 124 [arXiv:2202.11127] [INSPIRE].
L. Freidel, D. Pranzetti and A.-M. Raclariu, A discrete basis for celestial holography, arXiv:2212.12469 [INSPIRE].
L.J. Mason and D. Skinner, The Complete Planar S-matrix of N = 4 SYM as a Wilson Loop in Twistor Space, JHEP 12 (2010) 018 [arXiv:1009.2225] [INSPIRE].
T. Adamo, M. Bullimore, L. Mason and D. Skinner, Scattering Amplitudes and Wilson Loops in Twistor Space, J. Phys. A 44 (2011) 454008 [arXiv:1104.2890] [INSPIRE].
W. Bu and E. Casali, The 4d/2d correspondence in twistor space and holomorphic Wilson lines, JHEP 11 (2022) 076 [arXiv:2208.06334] [INSPIRE].
J. Oh and Y. Zhou, Twisted holography of defect fusions, SciPost Phys. 10 (2021) 105 [arXiv:2103.00963] [INSPIRE].
D. Gaiotto and J. Oh, Aspects of Ω-deformed M-theory, arXiv:1907.06495 [INSPIRE].
D. Gaiotto and M. Rapcak, Miura operators, degenerate fields and the M2-M5 intersection, JHEP 01 (2022) 086 [arXiv:2012.04118] [INSPIRE].
D. Zwanziger, Angular distributions and a selection rule in charge-pole reactions, Phys. Rev. D 6 (1972) 458 [INSPIRE].
C. Csaki et al., Scattering amplitudes for monopoles: pairwise little group and pairwise helicity, JHEP 08 (2021) 029 [arXiv:2009.14213] [INSPIRE].
C. Csáki et al., Dressed vs. pairwise states, and the geometric phase of monopoles and charges, JHEP 02 (2023) 211 [arXiv:2209.03369] [INSPIRE].
M. van Beest et al., Monopoles, Scattering, and Generalized Symmetries, arXiv:2306.07318 [INSPIRE].
L. Donnay, A. Puhm and A. Strominger, Conformally Soft Photons and Gravitons, JHEP 01 (2019) 184 [arXiv:1810.05219] [INSPIRE].
E. Crawley, A. Guevara, E. Himwich and A. Strominger, Self-Dual Black Holes in Celestial Holography, arXiv:2302.06661 [INSPIRE].
P.P. Kulish and L.D. Faddeev, Asymptotic conditions and infrared divergences in quantum electrodynamics, Theor. Math. Phys. 4 (1970) 745 [INSPIRE].
V. Chung, Infrared Divergence in Quantum Electrodynamics, Phys. Rev. 140 (1965) B1110 [INSPIRE].
N. Arkani-Hamed, M. Pate, A.-M. Raclariu and A. Strominger, Celestial amplitudes from UV to IR, JHEP 08 (2021) 062 [arXiv:2012.04208] [INSPIRE].
S. Choi and R. Akhoury, Soft Photon Hair on Schwarzschild Horizon from a Wilson Line Perspective, JHEP 12 (2018) 074 [arXiv:1809.03467] [INSPIRE].
G. Sparling, Dynamically broken symmetry and global yang-mills in minkowski space, Further Advances in Twistor Theory 1 (1977) 171.
R. Penrose and G. Sparling, The Twistor Quadrille: A Line Bundle Based on the Coulomb Field, in Advances in Twistor Theory, L.J. Mason, L.P. Hughston, P.Z. Kobak and K. Pulverer eds., CRC Press (1979).
R.S. Ward and R.O. Wells, Twistor geometry and field theory, Cambridge University Press (1991) [https://doi.org/10.1017/CBO9780511524493] [INSPIRE].
A. Guevara, Reconstructing Classical Spacetimes from the S-Matrix in Twistor Space, arXiv:2112.05111 [INSPIRE].
T.N. Bailey, Twistors and Fields With Sources on Worldlines, Proceedings of the Royal Society of London Series A 397 (1985) 143.
M. Bullimore and A. Ferrari, Twisted Hilbert Spaces of 3d Supersymmetric Gauge Theories, JHEP 08 (2018) 018 [arXiv:1802.10120] [INSPIRE].
S. Banerjee, P. Pandey and P. Paul, Conformal properties of soft operators: Use of null states, Phys. Rev. D 101 (2020) 106014 [arXiv:1902.02309] [INSPIRE].
S. Banerjee and P. Pandey, Conformal properties of soft-operators. Part II. Use of null-states, JHEP 02 (2020) 067 [arXiv:1906.01650] [INSPIRE].
S. Pasterski, A. Puhm and E. Trevisani, Celestial diamonds: conformal multiplets in celestial CFT, JHEP 11 (2021) 072 [arXiv:2105.03516] [INSPIRE].
Y. Geyer and L. Mason, The SAGEX review on scattering amplitudes Chapter 6: Ambitwistor Strings and Amplitudes from the Worldsheet, J. Phys. A 55 (2022) 443007 [arXiv:2203.13017] [INSPIRE].
Y. Geyer, A.E. Lipstein and L. Mason, Ambitwistor strings at null infinity and (subleading) soft limits, Class. Quant. Grav. 32 (2015) 055003 [arXiv:1406.1462] [INSPIRE].
R. Bittleston, A. Sharma and D. Skinner, Quantizing the non-linear graviton, arXiv:2208.12701 [INSPIRE].
T. Adamo, L. Mason and A. Sharma, Celestial w1+∞ Symmetries from Twistor Space, SIGMA 18 (2022) 016 [arXiv:2110.06066] [INSPIRE].
L. Mason, Gravity from holomorphic discs and celestial Lw1+∞ symmetries, arXiv:2212.10895 [INSPIRE].
G. Sparling, The non-linear graviton representing the analogue of schwarzschild or kerr black holes, Twistor Newslett. 1 (1976) 14.
Acknowledgments
We are grateful to K. Costello, T. Creutzig, S. Pasterski, and especially L. Mason and A. Sharma for very helpful conversations and correspondences. NP also thanks Perimeter Institute for hospitality while this work was being completed. NG and NP are supported by funds from the Department of Physics and the College of Arts & Sciences at the University of Washington. NP is also supported by the DOE Early Career Research Program under award DE-SC0022924, and by the Visiting Fellowship program at the Perimeter Institute of Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.
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: 2305.00049
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
Garner, N., Paquette, N.M. Twistorial monopoles & chiral algebras. J. High Energ. Phys. 2023, 88 (2023). https://doi.org/10.1007/JHEP08(2023)088
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2023)088