In this talk, I will discuss recent advancements in calculating integrals of cosmological correlators in the de Sitter universe. I will begin by examining the case of massless scalars and how they have been recently addressed using twisted cohomology. The main focus of this talk will be on relative twisted cohomology, presenting our new results for correlators with internally massive states by...
Recently, we initiated a positive semi-definite numerical bootstrap program for multi-point correlators. Considering six-point functions of operators on a line we reformulated the crossing symmetry equation for a pair of comb-channel expansions as a semi-definite programming problem. Through a combination of analytical and numerical techniques we obtained rigorous bounds on CFT data in the...
Geometric formulations of EFTs formulate fields as coordinates on a field space manifold, which provides an alternative method of studying theories by relating physical quantities emerging from the two derivative term to geometric tensors.
Jet Bundles provide us with the tools to express any scalar Lagrangian of any derivative order in terms of a (pseudo-)Riemannian metric, thus allowing us...
Understanding the infrared dynamics of the massless, minimally coupled, real scalar field in de Sitter space remains an important open problem. When computed in perturbation theory, the in-in correlation functions are plagued by infrared divergences and secularly growing terms. The Soft de Sitter Effective Theory (SdSET) was developed as a framework in which these issues can be addressed. In...
Using twistor methods for determinant operators, we compute
integrands for correlators of external half-BPS operators of
arbitrary charges and polarizations at one and two loops and at
five and six points, in the planar limit. Collecting integrands
for all charges in a generating function, that generating
functions displays poles at ten-dimensional null limits which
effectively produce...
There is a surprising connection between Feyman integrals and geometry: often families of Feynman integrals are related to geometric quantities of Calabi-Yau or other manifolds. This relation makes it possible to use geometric techniques to compute the Feyman integrals, and reveals some interesting structures, both in Feynman integrals and the associated geometries. Intirguingly, it is...
The study of line defects in conformal field theories (CFTs) is a crucial area of research, as they describe a wide range of physical phenomena from magnetic impurities in condensed-matter systems to the radiation of moving quarks in high-energy physics. A notable class of defects, called conformal defects, breaks the conformal symmetry in a controlled way, with the residual symmetry...
We consider the 4d $\mathcal{N}=2$ superconformal quiver gauge theory obtained by a $\mathbb{Z}_2$ orbifold of $\mathcal{N}=4$ super Yang-Mills (SYM). By exploiting supersymmetric localization, we study the integrated correlator of two Coulomb branch and two moment map operators and the integrated correlator of four moment map operators, determining exact expressions valid for any value of the...
The landscape of 6d SCFTs with minimal supersymmetry constitutes the perfect playground to learn about interesting aspects of SCFTs due to the many constraints that symmetries enforce. Therefore, I will discuss an intriguing class of minimal supersymmetric conformal field theories in six dimensions that under Higgs branch RG flow presents supersymmetry enhancement to the 6d $(2,0)$ SCFTs of...
By rearranging its terms, the Quantum Focusing Conjecture (QFC) can be viewed as a quantum energy condition, and we can consider various limits. I will review the status of energy conditions in general relativity and the QFC. Of specific interest is a restricted version where the quantum focusing vanishes Θ → 0, which has been proven for Braneworld scenario.
As a result, I derive an improved...
