arXiv subjects

Carolina Figueiredo

Publications and source records attributed to Carolina Figueiredo.

21 records · Page 2Linked to original sources

arXiv2024

Circles and Triangles, the NLSM and Tr($Φ^3$)

A surprising connection has recently been made between the amplitudes for Tr($Φ^3$) theory and the non-linear sigma model (NLSM). A simple shift of kinematic variables naturally suggested by the associahedron/stringy representation of Tr$(Φ^3$) theory yields pion amplitudes at all loops. In this note we provide an elementary motivation and proof for this link going in the opposite direction, starting from the non-linear sigma model and discovering its formulation as a sum over triangulations of surfaces with simple numerator factors. This uses an ancient connection between "circles" and "triangles", interpreting the equation $y = \sqrt{1 - x^2}$ both as parametrizing points on a circle as well as generating the number of triangulations of polygons. A further simplification of the numerator factors exposes them as arising from the kinematically shifted Tr($Φ^3$) theory, and gives rise to novel tropical representations of NLSM amplitudes. The connection to Tr$(Φ^3)$ theory defines a natural notion of "surface-soft limit" intrinsic to curves on surfaces. Remarkably, with this definition, the soft limit of pion amplitudes vanishes directly at the level of the integrand, via obvious pairwise cancellations. We also give simple, explicit expressions for the multi-soft factors for tree and loop-level integrands in the limit as any number of pions are taken "surface-soft".

hep-th↗

arXiv2024

Tropical Amplitudes For Colored Lagrangians

Recently a new formulation for scattering amplitudes in Tr($Φ^3$) theory has been given based on simple combinatorial ideas in the space of kinematic data. This allows all-loop integrated amplitudes to be expressed as ''curve integrals'' defined using tropical building blocks - the ''headlight functions''. This paper shows how the formulation extends to the amplitudes of more general Lagrangians. We will present a number of different ways of introducing tropical ''numerator functions'' that allow us to describe general Lagrangian interactions. The simplest family of these ''tropical numerators'' computes the amplitudes of interesting Lagrangians with infinitely many interactions. We also describe methods for tropically formulating the amplitudes for general Lagrangians. One uses a variant of ''Wick contraction'' to glue together numerator factors for general interaction vertices. Another uses a natural characterization of polygons on surfaces to give a novel combinatorial description of all possible diagrams associated with arbitrary valence interactions.

hep-th↗

arXiv2020

Riemannian manifolds dual to static spacetimes

We establish a one-to-one correspondence between static spacetimes and Riemannian manifolds that maps causal geodesics to geodesics, as suggested by L. C. Epstein. We then explore constant curvature spacetimes - such as the de Sitter and the anti-de Sitter universes - and find that they map to constant curvature Riemannian manifolds, namely the Euclidean space, the sphere and the hyperbolic space. By imposing the conditions required to map to the sphere, we obtain the spherically symmetric metrics for which there is radial oscillatory motion with a period independent of the amplitude. We then consider the case of a perfect fluid and an Einstein cluster and determine the pressure and density profiles required to find this type of motion. Finally, we give examples of surfaces corresponding to certain types of motion for metrics that do not exhibit constant curvature, such as the Schwarzschild, Schwarzschild de Sitter and Schwarzschild anti-de Sitter solutions, and even for a simplified model of a wormhole.

gr-qc↗