arXiv subjects

Facundo Rost

Publications and source records attributed to Facundo Rost.

4 recordsLinked to original sources

arXiv2026

Positive Geometry of Yang-Mills Correlators

We develop a positive-geometric formulation of tree-level Yang-Mills correlators in de Sitter space at three and four points through their helicity-stripped representatives on the cosmological Grassmannian. In its Pfaffian (or spinor) embedding, physical singularities become natural geometric boundaries. At three points, the Yang-Mills correlator is the canonical form of the non-negative orthant in the Grassmannian. At four points, the Mandelstam divisors partition the Pfaffian-positive domain of the Grassmannian into four positive geometries. Requiring factorization into three-point forms, together with the correct flat-space limit, uniquely selects an oriented union of two of these regions, whose canonical form reproduces the reduced color-ordered Yang-Mills correlator. The full color-ordered correlator, on the other hand, arises from a uniquely fixed signed linear combination of homology cycles. Thus, the broader homological formulation of positive geometry is essential for capturing the complete four-point result. Our construction provides a concrete starting point for a geometric description of higher-point cosmological correlators.

hep-th↗

arXiv2026

The Cosmological Grassmannian

We introduce the orthogonal Grassmannian as a novel kinematic space for describing correlators of massless spinning fields in de Sitter space. By automatically encoding the constraints of conformal symmetry and current conservation, the formalism drastically simplifies these correlators. We show that three-point functions are fixed by little group covariance and take the same form as the corresponding Schwinger-parameterized correlators in twistor space. The power of the Grassmannian approach is especially evident for four-point functions, which require dynamical input beyond kinematics. We demonstrate that unitarity enforces the same factorization properties as for scattering amplitudes and use these to bootstrap the four-point functions in several non-trivial examples, including Yang-Mills theory and gravity. We find expressions that are astonishingly simple and reveal a close connection to the corresponding scattering amplitudes. Our results suggest that the Grassmannian provides the natural language for spinning correlators in de Sitter space and illuminates their geometric origin.

hep-th↗

arXiv2025

Quasinormal Modes and the Switchback Effect in Schwarzschild-de Sitter

We study the causal structure of Schwarzschild-de Sitter (SdS), including shock wave perturbations, in $D>3$ using reflected null ray trajectories, either through the interior black hole or the exterior de Sitter region. Specifically, we compute the quasinormal mode frequencies in the eikonal, high-frequency, limit, by identifying the `critical time', for arbitrary values of the black hole mass. We emphasize the important role of the static sphere proper time normalization and related boundary conditions. The computed critical times indicate the presence of singularities in the late-time, large mass, scalar field correlator in SdS, which should be resolved by introducing complex geodesics consistent with interior black hole and exterior de Sitter effective thermofield double states. In addition we relate the critical time to a diverging holographic complexity observable and compute the `switchback' delay by adding a pair of shock wave perturbations for arbitrary values of the mass of the black hole.

hep-th↗

arXiv2024

A New Twist on Spinning (A)dS Correlators

Massless spinning correlators in cosmology are extremely complicated. In contrast, the scattering amplitudes of massless particles with spin are very simple. We propose that the reason for the unreasonable complexity of these correlators lies in the use of inconvenient kinematic variables. For example, in de Sitter space, consistency with unitarity and the background isometries imply that the correlators must be conformally covariant and also conserved. However, the commonly used kinematic variables for correlators do not make all of these properties manifest. In this paper, we introduce twistor space as a powerful way to satisfy all kinematic constraints. We show that conformal correlators of conserved currents can be written as twistor integrals, where the conservation condition translates into holomorphicity of the integrand. The functional form of the twistor-space correlators is very simple and easily bootstrapped. For the case of three-point functions, we verify explicitly that this reproduces known results in embedding space. We also perform a half-Fourier transform of the twistor-space correlators to obtain their counterparts in momentum space. We conclude that twistors provide a promising new avenue to study conformal correlation functions that exposes their hidden simplicity.

hep-th↗