Ambitwistor strings in ambitwistor space

Carabine, Nicholas

December 2017

Thesis or dissertation

© 2017 Nicholas Carabine. All rights reserved. No part of this publication may be reproduced without the written permission of the copyright holder.

This thesis is a recount of the research I undertook in the academic year 2016-2017 and the background work I learned from reading and attending lecture courses. Sections 2 and 3 are background sections providing an introduction to the concepts and methods that will be encountered in the research sections later on in the thesis.

The research covered in this thesis is the process of producing the BRST charge for a String theory in Ambitwistor space. The string theory being investigated originates from [1] theory which is a particle theory and [2] which is a string theory in Ambitwistor space. Whilst the link between these two papers may not seem obvious at first but the particle actions these papers are based from are the same. However for the sake of simplicity supersymmetry, which appears in both [1] and [2], is not covered.

The reason for the investigation of Ambitwistor string theory stems from Witten's initial paper on the subject [3] which showed led to a formula for tree-level 4 dimensional Yang-Mills amplitudes. And more recently Ambitwistor string theories of the form in [2] provide a way of producing amplitudes for Yang-Mills and gravitational amplitudes, known as the CHY Amplitudes,which were first shown in[4], [5] [6] and [7] which are a compact formulae for tree-level scattering amplitudes. It has been shown that the Ambitwistor String theory in [2] is able to produce expressions for higher order loop amplitudes [8], [9], [10], [11] and [12] to name just a few examples. From this point we seek to expand upon a theory that should be physically identical to the Ambitwistor string in [2] but representing it in Ambitwistor variables as has been done for the superparticle in [1].

The difficulty with representing the string theory in this way comes from the gauge symmetry being reducible. This means that the gauge constraint is not independent and there are additional constraints that affect the degrees of freedom of the theory as ignoring the reducibility would lead to over fixing of the degrees of freedom of the theory. So the standard process of gauge fixing and introducing ghosts to reduce the degrees of freedom is followed, but we have to introduce another ghost system. The statistics of these ghosts are the same as those of the matter fields (in this case bosonic) and can be thought of as the reintroduction of those degrees of freedom that have been over fixed. However, in the case of this theory, it doesn't stop there. There is another reducibility constraint that shows that all of the degrees of freedom in the previous reducibility constraint aren't independent either necessitating the introduction of another system of ghosts.

The goal of this thesis is to produce the BRST charge for the Bosonic Ambitwistor string represented in the Ambitwistor variables shown in [1] for future study. The procedure for doing this is outlined in [13] and is followed through the insertion of the constraints of the string theory. Once this has been done the nilpotency of the BRST charge is tested on several fields and constraints are obtained that fix the BRST charge to be nilpotent. After that following a similar procedure to Ohmori [11] A simple gauge fixed action for a free topological theory is produced.

School of Mathematics and Physics, The University of Hull
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