Fermionic T-Duality, Dual Superconformal Symmetry, and the Amplitude/Wilson Loop Connection

TL;DR

The paper introduces fermionic T-duality in superstring theories, revealing a symmetry that relates scattering amplitudes to Wilson loops and explains dual superconformal invariance in N=4 super Yang-Mills theory.

Contribution

It demonstrates the existence of fermionic T-duality and its role in connecting scattering amplitudes with Wilson loops, providing insight into dual superconformal symmetry.

Findings

Fermionic T-duality maps supersymmetric backgrounds to new backgrounds with different RR fields.

A combination of bosonic and fermionic T-dualities maps AdS5×S5 to itself, relating gluon amplitudes to Wilson loops.

Dual superconformal symmetry in amplitudes corresponds to ordinary superconformal symmetry in the dual theory.

Abstract

We show that tree level superstring theories on certain supersymmetric backgrounds admit a symmetry which we call ``fermionic T-duality''. This is a non-local redefinition of the fermionic worldsheet fields similar to the redefinition we perform on bosonic variables when we do an ordinary T-duality. This duality maps a supersymmetric background to another supersymmetric background with different RR fields and a different dilaton. We show that a certain combination of bosonic and fermionic T-dualities maps the full superstring theory on $AdS_5 \times S^5$ back to itself in such a way that gluon scattering amplitudes in the original theory map to something very close to Wilson loops in the dual theory. This duality maps the ``dual superconformal symmetry'' of the original theory to the ordinary superconformal symmetry of the dual model. This explains the dual superconformal invariance of planar scattering amplitudes of N=4 super Yang Mills and also sheds some light on the connection between amplitudes and Wilson loops. In the appendix, we propose a simple prescription for open superstring MHV tree amplitudes in a flat background.