On-shell methods for form factors in $$\mathcal{N}=4$$ N = 4 SYM and their applications
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July 2020 Vol. 63 No. 7: 270001 https://doi.org/10.1007/s11433-019-1507-0
On-shell methods for form factors in N = 4 SYM and their applications Gang Yang1,2* 1
CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China; 2 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China Received November 17, 2019; accepted January 7, 2020; published online March 10, 2020
Form factors are quantities that involve both asymptotic on-shell states and gauge invariant operators. They provide a natural bridge between on-shell amplitudes and off-shell correlation functions of operators, thus allowing us to use modern on-shell amplitude techniques to probe into the off-shell side of quantum field theory. In particular, form factors have been successfully used in computing the cusp (soft) anomalous dimensions and anomalous dimensions of general local operators. This review is intended to provide a pedagogical introduction to some of these developments. We will first review some amplitudes background using four-point amplitudes as main examples. Then we generalize these techniques to form factors, including (1) tree-level form factors, (2) Sudakov form factor and infrared singularities, and (3) form factors of general operators and their anomalous dimensions. Although most examples we consider are in N = 4 super-Yang-Mill theory, the on-shell methods are universal and are expected to be applicable to general gauge theories. form factors, helicity amplitudes, unitarity method, supersymmetry PACS number(s): Citation:
13.40.Gp, 11.80.Cr, 11.55.Bq, 12.60.Jv
G. Yang, On-shell methods for form factors in N = 4 SYM and their applications, Sci. China-Phys. Mech. Astron. 63, 270001 (2020), https://doi.org/10.1007/s11433-019-1507-0
Contents 1 Introduction
270001-2
2 Preliminary: Four-point tree amplitudes
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2.1 N=4 super Yang-Mills theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270001-4 2.2 Four-point amplitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270001-5 2.3 Color-kinematics duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270001-6 2.4 Spinor helicity formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270001-7 2.5 On-shell unitarity cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270001-9 *Corresponding author (email: [email protected]) c Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020 ⃝
phys.scichina.com
link.springer.com
G. Yang
Sci. China-Phys. Mech. Astron.
July (2020) Vol. 63 No.
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