Celestial amplitudes on electromagnetic backgrounds: T-duality from S-duality

TL;DR

This paper investigates the holographic dual of S-duality in flat-space gauge theories using celestial amplitudes, revealing that S-duality corresponds to T-duality in the boundary theory, with implications for gauge invariance and scattering processes.

Contribution

It demonstrates that S-duality in four-dimensional Abelian gauge theories corresponds to T-duality in the two-dimensional holographic boundary, supported by celestial amplitude analysis and low-energy boundary actions.

Findings

Celestial amplitudes relate soft modes to CFT correlators.

Evidence links S-duality to T-duality via celestial amplitude comparisons.

Gauge invariance is maintained through Dirac quantization in scattering scenarios.

Abstract

What is the boundary holographic dual of S-duality for gauge theories in asymptotically flat space-times? Celestial amplitudes, by virtue of exhibiting holographic properties of the S-matrix, appear well-suited for studying this question. We scatter electrically and magnetically charged massless scalars off non-trivial electromagnetic potentials such as shockwaves, spin-one conformal primary waves, conformally soft modes and their magnetic duals which we construct. This reveals an intricate relation between conformally soft solutions, descendant CFT three-point functions and, by means of the two-dimensional shadow transform, CFT two-point functions. By comparing celestial amplitudes on electric and magnetic dual backgrounds, we provide evidence that the four-dimensional flat-space holographic dual of S-duality in Abelian gauge theory is two-dimensional T-duality. Moreover, we demonstrate that for two-dimensional boundary actions describing low-energy sectors of the bulk gauge theory, S-duality can be explicitly implemented as a T-duality transformation. We show that the Dirac quantisation condition guarantees gauge invariance in the eikonal re-summation for scattering from potentials which for magnetic scalars can be expressed in terms of 't Hooft loops.