Abstract
Strominger and collaborators recently proposed that soft theorems for gauge and gravity amplitudes can be interpreted as Ward identities of a 2d CFT at null infinity. In this paper, we will consider a specific realization of this CFT known as ambitwistor string theory, which describes 4d Yang-Mills and gravity with any amount of supersymmetry. Using 4d ambtwistor string theory, we derive soft theorems in the form of an infinite series in the soft momentum which are valid to subleading order in gauge theory and sub-subleading order in gravity. Furthermore, we describe how the algebra of soft limits can be encoded in the braiding of soft vertex operators on the worldsheet and point out a simple relation between soft gluon and soft graviton vertex operators which suggests an interesting connection to color-kinematics duality. Finally, by considering ambitwistor string theory on a genus one worldsheet, we compute the 1-loop correction to the subleading soft graviton theorem due to infrared divergences.
Highlights
Null infinity in four dimensional asymptotically flat spacetimes [19,20,21], and the soft photon theorems are associated with spontaneouly gauge symmetry at null infinity [22,23,24]
We describe how the algebra of soft limits can be encoded in the braiding of soft vertex operators on the worldsheet and point out a simple relation between soft gluon and soft graviton vertex operators which suggests an interesting connection to color-kinematics duality
The key features of these models are that their spectra only contain field theory degrees of freedom and their correlation functions produce scattering amplitudes in the form discovered by Cachazo, He, and Yuan (CHY) [29,30,31,32], notably they are expressed as worldsheet integrals which localize onto solutions of the scattering equations
Summary
4d ambitwistor string theories were studied in [27, 43]. They are closely related to the twistor string theories of Witten [44], Berkovits [45], and Skinner [46]. And vertex operators are defined for both positive and negative helicity particles This makes 4d ambitwistor strings a lot more flexible than ordinary twistor strings, in that they can describe 4d Yang-Mills theory and gravity with any amount of supersymmetry, and the resulting amplitudes are much simpler, depending on very few moduli. The fields have the following OPE’s: λα (σ)μβ The spectrum of this model contains both (super)Yang-Mills theory and conformal (super)gravity. Πki=1δ2 tiλ (σi) − λi Πnj=k+1δ2 (tj λ (σj ) − λj ) These delta functions localize the worldsheet integrals onto solutions of the 4d scattering equations refined by helicity: λiλ (σi) = 0, i = 1, . We describe various properties of these equations in appendix A
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