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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider the finite part of the leading local interactions in the lowenergy expansion of the four graviton amplitude from the ladder skeletondiagrams in maximal supergravity on T^2, at three and four loops. At threeloops, we express the D^8 R^4 and D^{10} R^4 amplitudes as integrals over themoduli space of an underlying auxiliary geometry. These amplitudes areevaluated exactly for special values of the the moduli of the auxiliarygeometry, where the integrand simplifies. We also perform a similar analysisfor the D^8 R^4 amplitude at four loops that arise from the ladder skeletondiagrams for a special value of a parameter in the moduli space of theauxiliary geometry. While the dependence of the amplitudes on the volume of theT^2 is very simple, the dependence on the complex structure of the T^2 is quiteintricate. In some of the cases, the amplitude consists of terms each of whichfactorizes into a product of two SL(2,Z) invariant modular forms. While one ofthe factors is a non--holomorphic Eisenstein series, the other factor splitsinto a sum of modular forms each of which satisfies a Poisson equation onmoduli space with source terms that are bilinear in the Eisenstein series. Thisleads to several possible perturbative contributions unto genus 5 in type IIstring theory on S^1. Unlike the one and two loop supergravity analysis, theseamplitudes also receive non--perturbative contributions from bound states ofthree D--(anti)instantons in the IIB theory.

Some finite terms from ladder diagrams in three and four loop maximal supergravity