Ambitwistor Strings: Worldsheet Approaches to perturbative Quantum Field Theories

Abstract

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. 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. 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. The first part of the thesis provides a user-friendly introduction to ambitwistor strings, as well as a condensed overview over the literature and some novel results. Emphasising the study of tree-level amplitudes, we then explore the wide-ranging impact of ambitwistor strings for an extensive family of massless theories, and discuss the duality between asymptotic symmetries and the low energy behaviour of a theory from the point of view of the worldsheet CFT. 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. This leads to a proposal for an all-loop integrand for gravity and Yang-Mills.

arXiv comment205 pages, D.Phil thesis, references accounted for until 02/16 (submission date)

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Cited by in corpus (11)

• Celestial operator products from the worldsheet
• Celestial $w_{1+\infty }$ Symmetries from Twistor Space
• The polarized scattering equations for 6d superamplitudes
• Gluon scattering on self-dual radiative gauge fields
• Supersymmetric celestial OPEs and soft algebras from the ambitwistor string worldsheet
• Four dimensional ambitwistor strings and form factors of local and Wilson line operators
• Supersymmetric S-matrices from the worldsheet in 10 and 11d
• Chiral Splitting and $\mathcal{N}=4$ Einstein--Yang--Mills Tree Amplitudes in 4d
• The Algebraic Structure of the KLT Relations for Gauge and Gravity Tree Amplitudes
• Ambitwistor strings and reggeon amplitudes in N=4 SYM
• Spectrum, Scattering Amplitudes, and String Field Theory of 4 Dimensional Twistor String