Spinor-helicity formalism for massless fields in AdS 4 . Part II. Potentials
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Received: February 9, 2020 Accepted: May 15, 2020 Published: June 9, 2020
Balakrishnan Nagaraja and Dmitry Ponomarevb,c a
George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, University Drive, College Station, TX 77843, U.S.A. b Institute for Theoretical and Mathematical Physics, Lomonosov Moscow State University, Lomonosovsky avenue, Moscow, 119991, Russia c I.E. Tamm Theory Department, Lebedev Physical Institute, Leninsky avenue, Moscow, 119991, Russia
E-mail: [email protected], [email protected] Abstract: In a recent letter we suggested a natural generalization of the flat-space spinorhelicity formalism in four dimensions to anti-de Sitter space. In the present paper we give some technical details that were left implicit previously. For lower-spin fields we also derive potentials associated with the previously found plane-wave solutions for field strengths. We then employ these potentials to evaluate some three-point amplitudes. This analysis illustrates a typical computation of an amplitude without internal lines in our formalism. Keywords: Higher Spin Symmetry, Scattering Amplitudes, AdS-CFT Correspondence ArXiv ePrint: 1912.07494
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP06(2020)068
JHEP06(2020)068
Spinor-helicity formalism for massless fields in AdS4. Part II. Potentials
Contents 1
2 Spinor-helicity representation in flat space 2.1 Plane-wave solutions 2.2 Amplitudes from space-time integrals 2.3 Amplitudes from symmetries
3 4 6 7
3 Massless representations in AdS4
8
4 AdS4 geometry
9
5 Plane waves for field strengths
11
6 Plane waves for potentials 6.1 Spin 1 6.2 Spin 32 6.2.1 Fixing an ansatz 6.2.2 Solving for potentials 6.3 Spin 2 6.4 Higher-spin potentials
14 15 16 16 17 18 19
7 Scattering amplitudes from space-time integrals 7.1 Simple examples 7.2 Genuine three-point amplitudes 7.2.1 Spin 0 − 12 − 32 amplitude 7.2.2 Spin 0 − 0 − 2 amplitude
19 20 21 22 23
8 Three-point amplitudes from symmetries
25
9 Helicity-changing operators
26
10 Conclusion and outlook
28
A Notations and conventions
30
B AdS4 and spinors
32
C Details on spin
3 2
potential
34
D Details on spin 2 potential
36
E Details on amplitudes from symmetries
37
–i–
JHEP06(2020)068
1 Introduction
1
Introduction
1
These results were obtained employing the light-cone deformation procedure, which is closely connected to the spinor-helicity formalism [37–39].
–1–
JHEP06(2020)068
In recent years significant progress was achieved in amplitudes’ computations as well as in understanding of various hidden structures underlying them. This is especially true for theories of massless particles in four dimensions. For these theories one can choose convenient kinematic variables that lead to what is known as the spinor-helicity formalism. This formalism allows to compute amplitudes efficiently and produces them in an extremely compact form. This is typically illustrated by the Parke-Taylor formula [1], whic
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