The SAGEX review on scattering amplitudes Chapter 6: Ambitwistor Strings and Amplitudes from the Worldsheet

Abstract

Starting with Witten’s twistor string, chiral string theories have emerged that describe field theory amplitudes without the towers of massive states of conventional strings. These models are known as ambitwistor strings due to their target space; the space of complexified null geodesics, also called ambitwistor space. Correlators in these string theories directly yield compact formulæ for tree-level amplitudes and loop integrands, in the form of worldsheet integrals fully localized on solutions to constraints known as the scattering equations. In this chapter, we discuss two incarnations of the ambitwistor string: a ‘vector representation’ starting in space-time and structurally resembling the RNS superstring, and a four-dimensional twistorial version closely related to, but distinct from Witten’s original model. The RNS-like models exist for several theories, with ‘heterotic’ and type II models describing super-Yang-Mills and 10d supergravities respectively, and they manifest the double copy relations directly at the level of the worldsheet models. In the second half of the chapter, we explain how the underlying models lead to diverse applications, ranging from extensions to new sectors of theories, loop amplitudes and to scattering on curved backgrounds. We conclude with a brief discussion of connections to conventional strings and celestial holography.

Twistorial monopoles & chiral algebras

“…The twistorial studies discussed above are in fact recent contributions in a long history of work exploring the quantization of holomorphic BF and Chern-Simons theories on twistor (and ambitwistor) space, recently summarized in [69]; see also [70] for earlier connections to asymptotic symmetries. It will be fascinating to flesh out further connections between twisted holography, celestial holography, and (ambi)twistor string theory, as well as the 3d holomorphic-topological perspective espoused in this note.…”

The SAGEX review on scattering amplitudes*

“…2.6. Ambitwistor strings and amplitudes from the worldsheet [6] From its beginning, string theory has highlighted otherwise hidden worldsheet structures underlying scattering amplitudes although for better or worse, it is a theory that goes far beyond conventional field theory. Much more recently, starting with Witten's twistor string, chiral string theories have emerged that yield field theory amplitudes alone without the extra towers of massive modes of conventional strings.…”

Yang-Mills form factors on self-dual backgrounds

“…There is by now a long tradition of exploiting the integrability of the self-dual sector to provide non-perturbative results such as the construction of instantons and monopoles [4]. These structures are also intimately related to the rich structures discovered in scattering amplitudes, from the famous Parke-Taylor formula for the tree-level MHV scattering of gluons [5,6], to the more general constructions of [7][8][9][10][11][12][13][14][15][16][17], see [18][19][20][21][22] for reviews. The role of integrability was made explicit in studies of scattering amplitudes using twistor actions defined on twistor space that JHEP08(2023)165 allow the direct exploitation of the integrability of the self-dual sectors of Yang-Mills and gravity theories.…”