dc.contributor.advisor | McLoughlin, Tristan | en |
dc.contributor.author | HÄHNEL, PHILIPP | en |
dc.date.accessioned | 2018-08-21T13:43:54Z | |
dc.date.available | 2018-08-21T13:43:54Z | |
dc.date.issued | 2018 | en |
dc.date.submitted | 2018 | en |
dc.identifier.citation | HÄHNEL, PHILIPP, Higher Spin Theories in Twistor Space, Trinity College Dublin.School of Mathematics.MATHEMATICS, 2018 | en |
dc.identifier.other | Y | en |
dc.identifier.uri | http://hdl.handle.net/2262/83839 | |
dc.description | APPROVED | en |
dc.description.abstract | In this thesis we formulate an action principle for conformal higher spin theory on twistor space. For this theory, and for a unitary sub-sector that we identify, we construct an MHV amplitude expansion by considering anti-self-dual fluctuations moving in a self-dual background.
We begin by reviewing some elements of gauge theory, including gravity as a gauge theory and its higher spin generalisations. We start with Yang-Mills theory, introducing the Chalmers-Siegel action and the spinor-helicity formalism, before turning to the structure of Einstein-Cartan theory, conformal gravity, and its classical truncation to Einstein gravity. We continue with an outline of linearised massless higher spin theory and the higher-derivative conformal theory. Finally, we give a short introduction to twistor theory, which leads to a discussion of twistor space actions for Yang-Mills theory and gravity.
In the second half of the thesis we consider the twistor description of conformal higher spin theories and give twistor space actions for the self-dual sector of theories with spin greater than two that produce the correct flat space-time spectrum. Upon identifying a ghost-free, unitary sub-sector, analogous to the embedding of Einstein gravity with cosmological constant in Weyl gravity, we can generate the unique three- point anti-MHV amplitude for arbitrary spin consistent with Poincaré invariance and helicity constraints. By including interactions between the infinite tower of higher-spin fields, we give a geometric interpretation to the twistor equations of motion as the integrability condition for a holomorphic structure on an infinite jet bundle, and introduce anti-self-dual interaction terms to define a twistor action for the full conformal higher spin theory.
This leads to finding expressions for all three-point anti-MHV amplitudes and all MHV amplitudes, involving positive helicity conformal gravity particles and two negative helicity higher spins, which provides the on-shell analogue for the covariant coupling of conformal higher-spin fields to a conformal gravity background. We study the flat-space limit and show that the restricted amplitudes vanish, supporting the conjecture that in the unitary sector the S-matrix of conformal higher spin theories is trivial. However, by appropriately rescaling the amplitudes we find non-vanishing results which we compare with chiral flat-space higher spin theories. | en |
dc.publisher | Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics | en |
dc.rights | Y | en |
dc.subject | action principles | en |
dc.subject | twistor theory | en |
dc.subject | higher spin theory | en |
dc.subject | conformal higher spin theory | en |
dc.subject | MHV amplitudes | en |
dc.title | Higher Spin Theories in Twistor Space | en |
dc.type | Thesis | en |
dc.type.supercollection | thesis_dissertations | en |
dc.type.supercollection | refereed_publications | en |
dc.type.qualificationlevel | Postgraduate Doctor | en |
dc.identifier.peoplefinderurl | http://people.tcd.ie/hahnelp | en |
dc.identifier.rssinternalid | 191234 | en |
dc.rights.ecaccessrights | openAccess | |
dc.contributor.sponsor | Marie Curie | en |
dc.contributor.sponsor | SFI stipend | en |