Light-ray wave functions and integrability

Creators: Homrich, Alexandre^{1, 2}; Simmons-Duffin, David³; Vieira, Pedro^{1, 4}

1. Perimeter Institute
2. University of California, Santa Barbara
3. California Institute of Technology
4. ICTP South American Institute for Fundamental Research

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Abstract

Using integrability, we construct (to leading order in perturbation theory) the explicit form of twist-three light-ray operators in planar = 4 SYM. This construction allows us to directly compute analytically continued CFT data at complex spin. We derive analytically the “magic” decoupling zeroes previously observed numerically. Using the Baxter equation, we also show that certain Regge trajectories merge together into a single unifying Riemann surface. Perhaps more surprisingly, we find that this unification of Regge trajectories is not unique. If we organize twist-three operators differently into what we call “cousin trajectories” we find infinitely more possible continuations. We speculate about which of these remarkable features of twist-three operators might generalize to other operators, other regimes and other theories.

Copyright and License

© The Authors. 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.

Article funded by SCOAP3.

Acknowledgement

We thank Carlos Bercini, Simon Caron-Huot, Cyuan-Han Chang, Davide Gaiotto, Kolya Gromov, David Gross, Petr Kravchuk, Martin Kruczenski, Harish Murali, Ian Moult, Enrico Olivucci and Paul Ryan for helpful discussions. Research at the Perimeter Institute is supported in part by the Government of Canada through NSERC and by the Province of Ontario through MRI. This work was support in part by the ICTP-SAIFR FAPESP grant 2016/01343-7 and FAPESP grant 2017/03303-1. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. This research was supported in part by grant NSF PHY-2309135 to the Kavli Institute for Theoretical Physics (KITP). This work was additionally supported by grants from the Simons Foundation (Simons Collaboration on the Nonperturbative Bootstrap (DSD: #488657, PV: #488661) and Simons Collaboration on Confinement and QCD Strings (AH:#994312)).

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