Carrollian Amplitudes from Strings

In this work, we study the duality symmetry group of Carrollian (nonlinear) electrodynamics and propose a family of Carrollian ModMax theories, which are invariant under Carrollian SO(2) electromagnetic (EM) duality transformations and conformal transformation. We define the Carrollian SO(2) EM transformations, with the help of Hodge duality in Carrollian geometry, then we rederive the Gaillard-Zumino consistency condition for EM duality of Carrollian nonlinear electrodynamics. Together with the traceless condition for the energy-momentum tensor, we are able to determine the Lagrangian of the Carrollian ModMax theories among pure electrodynamics. We furthermore study their behaviors under the $$ \sqrt{T\overline{T}} $$ T T ¯ deformation flow, and show that these theories deform to each other and may reach two endpoints under the flow, with one of the endpoint being the Carrollian Maxwell theory. As a byproduct, we construct a family of two-dimensional Carrollian ModMax-like multiple scalar theories, which are closed under the $$ \sqrt{T\overline{T}} $$ T T ¯ flow and may flow to a BMS free multi-scalar model.

On self-dual Carrollian conformal nonlinear electrodynamics

Chen,

Hou,

Sun

2024

Differential equations for Carrollian amplitudes

Ruzziconi,

Stieberger,

Taylor

et al. 2024

Differential equations are powerful tools in the study of correlation functions in conformal field theories (CFTs). Carrollian amplitudes behave as correlation functions of Carrollian CFT that holographically describes asymptotically flat spacetime. We derive linear differential equations satisfied by Carrollian MHV gluon and graviton amplitudes. We obtain non-distributional solutions for both the gluon and graviton cases. We perform various consistency checks for these differential equations, including compatibility with conformal Carrollian symmetries.

Eikonal amplitudes on the celestial sphere

Adamo,

Bu,

Tourkine

et al. 2024

Celestial scattering amplitudes for massless particles are Mellin transforms of momentum-space scattering amplitudes with respect to the energies of the external particles, and behave as conformal correlators on the celestial sphere. However, there are few explicit cases of well-defined celestial amplitudes, particularly for gravitational theories: the mixing between low- and high-energy scales induced by the Mellin transform generically yields divergent integrals. In this paper, we argue that the most natural object to consider is the gravitational amplitude dressed by an oscillating phase arising from semi-classical effects known as eikonal exponentiation. This leads to gravitational celestial amplitudes which are analytic, apart from a set of poles at integer negative conformal dimensions, whose degree and residues we characterize. We also study the large conformal dimension limits, and provide an asymptotic series representation for these celestial eikonal amplitudes. Our investigation covers two different frameworks, related by eikonal exponentiation: 2 → 2 scattering of scalars in flat spacetime and 1 → 1 scattering of a probe scalar particle in a curved, stationary spacetime. These provide data which any putative celestial dual for Minkowski, shockwave or black hole spacetimes must reproduce. We also derive dispersion and monodromy relations for these celestial amplitudes and discuss Carrollian eikonal-probe amplitudes in curved spacetimes.