BCJ Identities in Pure Spinor Superspace

Abstract

This thesis focuses upon work advancing the methods by which scattering amplitudes in string and field theory may be described. Through the pure spinor formalism, rapid developments have been made in this area and numerous new results have been found. Further, when amplitudes are constructed so as to satisfy BCJ identities further simplifications become apparent, and the double copy procedure relating amplitudes in super Yang-Mills and supergravity may be applied. It is this context within which this thesis falls. The work which follows can broadly be split into two categories.

The first relates to the construction of a BCJ gauge, within which amplitudes automatically satisfy BCJ identities. Such has previously been described in a small subset of cases, and we use these results to find general methods for its construction. This is done in terms of a new combinatorial map, which we describe and rigorously prove identities satisfied by it. As a consequence of this, we are then able to relate the BCJ gauge constructed using these methods to arbitrary rank with the standard Lorenz gauge by a finite gauge transformation.

The second set of work relates to the construction of amplitudes at one loop in field theory. We describe a procedure by which one may extract from genus one string correlators their corresponding results in field theory. The results are shown to satisfy BCJ
identities automatically. Subtleties related to the symmetries of these results are then discussed, and an overview of why we are unable to then apply the double copy procedure is detailed. This resolves an outstanding problem related to the construction of higher point one loop amplitudes so as to satisfy BCJ identities, and raises new questions related to the application of the double copy in loop amplitudes.

More information

Identifiers

ORCID for Elliot, Nicholas Bridges: orcid.org/0000-0001-6422-0801

ORCID for Carlos Mafra: orcid.org/0000-0001-9842-9654

Catalogue record

Export record