arXiv subjects

Mattia Arundine

Publications and source records attributed to Mattia Arundine.

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.

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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.

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arXiv2026

Cosmological Collider in the Grassmannian

We revisit the computation of four-point wavefunction coefficients and correlators for external conformally coupled scalars exchanging a particle of generic mass and spin. Much of the phenomenology of cosmological collider physics in the near-de Sitter limit follows from these functions. Computing them in detail is a central challenge in the cosmological bootstrap. Using the cosmological Grassmannian, we write these objects in closed form using hypergeometric functions and Legendre polynomials. We achieve this by writing the standard bootstrap differential equation using the Plücker coordinates of the Grassmannian, and using the basis of Mandelstam invariants. The exchange in the s-channel can be written in terms of a hypergeometric function of the S Mandelstam, while the spin information appears as an overall Legendre polynomial factor that also depends on the other Mandelstams. We fix the boundary conditions by first demanding the absence of unphysical singularities, and, for correlators, by further matching to a kinematic limit in momentum space. Our formulae in Grassmannian space are much simpler than their counterparts in momentum space, demonstrating another useful application of the Grassmannian as a kinematic space for cosmology.

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arXiv2025

The DSSYK Model: Charge and Holography

The Anti-de Sitter/Conformal Field Theory correspondence (AdS/CFT) is one of the most significant findings in theoretical physics and forms the basis of this thesis. Although highly powerful, the main limitation of AdS/CFT is that AdS does not appear in the real world outside of very specific limits. This limitation justifies the attempt to generalize the holographic principle to other spacetimes. In this thesis, we will pursue this direction and seek spacetimes that have at least some connection to de Sitter (dS), whose cosmological interest is evident. dS is, in fact, not only the geometry that best represents our Universe on large scales in the present, but also during the inflationary epoch that followed the Big Bang, where our current description of Nature fails completely. First, we will present some basic facts about the AdS/CFT correspondence. Then, the gravitational path integral will be introduced. After presenting the Sachdev-Ye-Kitaev (SYK) model and dilaton-gravity models, a holographic link between the two will be established. Next, we will discuss the double-scaled limit of SYK, known as DSSYK. We will then consider a ``charged'' variation of SYK with Dirac fermions, for which we will determine the fermionic two-point function. After studying the thermodynamic properties of the gravitational dual of DSSYK and the quasinormal modes of massive real scalars propagating in this geometry, we will conjecture how to modify the duality when considering the Dirac version of the model, showing that several bounds constrain the space of possible dual theories. Finally, we will summarize our findings and present an outlook on possible future developments based on the results described here.

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