English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In the first part of this thesis, we study form factors of generalgauge-invariant local composite operators in $\mathcal{N}=4$ super Yang-Millstheory at various loop orders and for various numbers of external legs. We showhow to use on-shell methods for their calculation and in particular extract thedilatation operator from the result. We also investigate the properties of thecorresponding remainder functions. Moreover, we extend on-shell diagrams, aGra{\ss}mannian integral formulation and an integrability-based constructionvia R-operators to form factors, focussing on the chiral part of thestress-tensor supermultiplet as an example. In the second part, we study the$\beta$- and the $\gamma_i$-deformation, which were respectively shown to bethe most general supersymmetric and non-supersymmetric field-theorydeformations of $\mathcal{N}=4$ super Yang-Mills theory that are integrable atthe level of the asymptotic Bethe ansatz. For these theories, a new kind offinite-size effect occurs, which we call prewrapping and which emerges fromdouble-trace structures that are required in the deformed Lagrangians. Whilethe $\beta$-deformation is conformal when the double-trace couplings are attheir non-trivial IR fixed points, the $\gamma_i$-deformation has runningdouble-trace couplings without fixed points, which break conformal invarianceeven in the planar theory. Nevertheless, the $\gamma_i$-deformation allows forhighly non-trivial field-theoretic tests of integrability at arbitrarily highloop orders.

Form factors and the dilatation operator in $\mathcal{N}=4$ super Yang-Mills theory and its deformations