Ambitwistor Strings and Soft Theorems

Arthur Lipstein

Arthur Lipstein is a Postdoctoral Research Associate at University of Hamburg/DESY.

Ambitwistor string theories are a family of chiral (holomorphic) string theories whose target space is the space of complexified null geodesics in a general space-time. Like conventional strings, they are critical in 10 dimensions and describe supergravity, but unlike conventional strings, they do not admit a tower of higher massive modes (and are correspondingly not thought to be ultraviolet finite). They provide a natural generalization of the twistor-strings of Witten, Berkovits and Skinner to arbitrary dimension and their correlators give rise to the beautiful formulae for gravitational and Yang-Mills scattering amplitudes in all dimensions recently discovered by Cachazo, He and Yuan (CHY). Ambitwistor strings were also used to obtain new formulae in four dimensions by the authors of this article.

In a recent series of papers, Strominger and collaborators proposed a new way of understanding soft limits of gravitational scattering amplitudes in terms of asymptotic symmetries of space-time. In particular, they conjectured that the BMS group (which preserves the conformal structure of null infinity in four dimensions) is a symmetry of the gravitational S-matrix, and showed that the associated Ward identity is Weinberg’s soft graviton theorem, which provides a universal formula for the leading behaviour of scattering amplitudes when the energy of an external graviton goes to zero. The key insight in Strominger’s argument is that soft gravitons can be thought of as the Goldstone bosons associated with spontaneously broken BMS symmetries. Cachazo and Strominger subsequently used this approach to suggest new theorems for the subleading terms in the soft limit.

In our CQG paper, Yvonne Geyer, Lionel Mason, and I used ambitwistor string theory to prove the soft theorems from the perspective of conformal field theory, and extend them to describe gravity and Yang-Mills theory in arbitrary dimensions following the work of Schwab and Volovich, who used the CHY formulae. The main idea of our paper is that when the momentum of a vertex operator in ambitwistor string theory becomes soft, the leading and subleading terms in the expansion of the vertex operator correspond to Hamiltonians of the world sheet conformal field theory that generate diffeomorphisms of null infinity and give rise to the leading and subleading soft theorems when inserted into correlation functions. In four dimensions, these Hamiltonians correspond to Hamiltonians first found by Roger Penrose for the scattering of null geodesics through space-time.

In summary, our paper combines many exciting recent developments in the fields of scattering amplitudes and twistor string theory to obtain new insights into soft theorems and their relation to symmetries of the gravitational S-matrix. In particular, our work implies that the soft graviton theorems arise from a spontaneously broken diffeormorphism group which acts in any dimension D and is generally not a conformal transformation of the D-2 sphere at null infinity, and is therefore more general than the extended BMS group. Furthermore, we have shown that there is a similar story for Yang-Mills theory. Since the study of ambitwistor string theory is still in its early stages, there are many directions to explore such as extending the framework to loop level and to more general space-time backgrounds.

Read the full article in Classical and Quantum Gravity:
Ambitwistor strings at null infinity and (subleading) soft limits
Yvonne Geyer, Arthur E Lipstein and Lionel Mason
Yvonne Geyer et al 2015 Class. Quantum Grav. 32 055003

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