Ambitwistor strings: worldsheet approaches to perturbative quantum field theories

Thesis

Tree-level scattering amplitudes in massless theories not only exhibit a simplicity entirely unexpected from Feynman diagrams, but also an underlying structure remarkably reminiscent of worldsheet theory correlators, yet essentially algebraic. These features can be explained by ambitwistor strings - two-dimensional chiral conformal field theories in an auxiliary target space, the complexified phase space of null geodesics, known as ambitwistor space. The aim of this thesis is to explore the ambitwistor string approach to understand these structures in amplitudes, and thereby provide a new angle on quantum field theories.

In the first part of this thesis, the wide-ranging impact of ambitwistor strings on the study of tree-level amplitudes is highlighted in three developments: an extension of ambitwistor string worldsheet models to an extensive family of massless theories, emphasising the universality of ambitwistor strings for massless theories; a beautiful proof of the duality between asymptotic symmetries and the low energy behaviour of a theory, relying on the contact geometry of the ambitwistor target space; and finally a twistorial representation of ambitwistor strings in four dimensions, leading to remarkably simple formulae for scattering amplitudes in Yang-Mills and gravity with any degree of supersymmetry.

The second part of this thesis focusses on proving a conjectured ambitwistor string formula for loop amplitudes, and extending the formalism to more general theories. Remarkably, residue theorems reduce the computationally challenging ambitwistor higher-genus expressions to simple formulae on nodal Riemann spheres. This idea is developed into a widely applicable framework for loop integrands, that is shown to be applicable to both supersymmetric and non-supersymmetric theories. In the case of supergravity, this provides strong evidence for the validity of the ambitwistor string at loop level, and explicit proofs are given for non-supersymmetric theories. Notably, this leads to a proposal for an all-loop integrand for gravity and Yang-Mills.

Authors: Geyer, Y

• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Keywords: Ambitwistor Strings; Quantum Field Theory
• Subjects: Mathematical physics