Effective field theories, soft theorems and ambitwistor strings

The research will be in the area of scattering amplitudes, (ambitwistor) string theory and conformal infinity. Scattering amplitudes form the S-matrix that describes the scattering of particles from the infinite past to the infinite future. Conformal infinity gives a method to understand the infinite past and future as initial and final data hypersurfaces giving a geometric insight into the construction of the S-matrix and its properties, including symmetries. In particular it has recently been shown by Strominger and collaborators that there is a clear relationship between these asymptotic symmetries and soft theorems for scattering amplitudes [1]. Recent work of the supervisor [2] shows that this has a particularly transparent and geometric representation in ambitwistor string theories. Furthermore, ambitwistor string theories have recently been extended to encompass effective field theories such as DBI, nonlinear sigma models, etc., that have particularly enhanced soft behaviour.

Soft behaviour is particularly problematic in the construction of the S-matrix, and indeed many pure mathematicians will say that rigourously speaking the S-matrix for massless theories does not exist (or is trivial) and is subject to a number of no-go theorems. However, physicists have been computing the S-matrix for such theories for years using methods such as dimensional regularization to make sense of divergences that occur and have a detailed understanding of key structures such as the exponentiation of infrared divergences. These are essential for calculations of cross sections at CERN. Resolution of any of these issues would have a major potential impact both on the mathematics of these theories and on their physical applications.

- Aims and objectives:
The overarching aims are to understand underlying mathematical structures and to resolve key theoretical issues in the construction of the S-matrix centred around infrared problems including soft limits and the conformal representations of the S-matrix.

I. To create a dictionary between the field theory based technology of Strominger et. al., and the ambitwistor string framework developed by the supervisor and collaborators.
II. To compare the action of asymptotic symmetries in the two frameworks.
III. To understand infrared sectors within the ambitwistor framework.
IV. To gain an understanding of how physicist's approaches confront the issues of scattering between different infrared sectors.
V. There will be novel effects in effective field theories with enhanced soft behaviour and so these will provide a testing ground.

- Novelty of the research methodology:
The use of ambitiwistor strings is unique to the group in Oxford and collaborators and provides powerful new techniques not widely used in the rest of the community ([3], [4]). Effective field theories should exhibit novel behaviours relative to more conventional theories.


[1] A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, arXiv:1703.05448.
[2] Y. Geyer, A. E. Lipstein, and L. Mason, Ambitwistor strings at null infinity and subleading soft limits, Class. Quantum Gravity 32, 055003 (2014), arXiv:1406.1462.
[3] L. Mason and D. Skinner, Heterotic twistor-string theory, Nucl. Phys. B795 (2008) 105, arXiv:0708.2276.
[4] L. Mason and D. Skinner, Ambitwistor strings and the scattering equations, JHEP 07 (2014) 048, arXiv:1311.2564.


This project falls within the EPSRC Mathematical Sciences research area, and in particular the sub-area of Mathematical Physics.
No companies or collaborators will be involved.