Related papers: A constructive solution to the cosmological bootst…
In this paper, we study the asymptotics of the $6j$-symbols for the principal series of the modular double of $\mathrm U_q\mathfrak{sl}(2;\mathbb R)$, and of their analytic extension -- what we call the $b$-$6j$ symbols, relating them in…
A key insight of the bootstrap approach to cosmological correlations is the fact that all correlators of slow-roll inflation can be reduced to a unique building block---the four-point function of conformally coupled scalars, arising from…
This paper studies the critical behavior of the 3d classical $\mathrm{O}(N)$ model with a boundary. Recently, one of us established that upon treating $N$ as a continuous variable, there exists a critical value $N_c > 2$ such that for $2…
We establish the geometry behind the quantum $6j$-symbols under only the admissibility conditions as in the definition of the Turaev-Viro invariants of $3$-manifolds. As a classification, we show that the $6$-tuples in the quantum…
It has long been clear that the conformal bootstrap is associated with a rich geometry. In this paper we undertake a systematic exploration of this geometric structure as an object of study in its own right. We study conformal blocks for…
We study the asymptotic expansion of the 6j-symbol using the Schulten-Gordon recursion relations. We focus on the particular case of the isosceles tetrahedron and we provide explicit formulas for up to the third order corrections beyond the…
We show that cosmological wavefunction coefficients associated with $n$-site chain and loop graphs for a cubic scalar theory in de Sitter spacetime have symbol alphabets given by subsets of $A_{2n{-}2}$ and $B_{2n{-}1}$ cluster variables,…
The cosmological polytope and bootstrap programs have revealed interesting connections between positive geometries, modern on-shell methods and bootstrap principles studied in the amplitudes community with the wavefunction of the Universe…
We apply recently constructed functional bases to the numerical conformal bootstrap for 1D CFTs. We argue and show that numerical results in this basis converge much faster than the traditional derivative basis. In particular, truncations…
We work out all of the details required for implementation of the conformal bootstrap program applied to the four-point function of two scalars and two vectors in an abstract conformal field theory in arbitrary dimension. This includes a…
We split the program of explicit descent of elliptic curves into two parts. For $n=3$ and $n=5,$ we first display a model for the universal elliptic curve $E$ with full level $n$ structure and describe the map of rational points of $E$ to…
We construct a symplectic realization and a bi-hamiltonian formulation of a 3-dimensional system whose solution are the Jacobi elliptic functions. We generalize this system and the related Poisson brackets to higher dimensions. These more…
We generalize the colored Alexander invariant of knots to an invariant of graphs, and we construct a face model for this invariant by using the corresponding 6j-symbol, which comes from the non-integral representations of the quantum group…
General positivity constraints linking various powers of observables in energy eigenstates can be used to sharply locate acceptable regions for the energy eigenvalues, provided that efficient recursive methods are available to calculate the…
We will attach a scalar invariant to a tetrahedron whose edges are labelled by irreducible representations of a ternary orthogonal group $\mathrm{SO}_3$ over a local field. This generalizes the $6j$ symbol whose theory was developed by…
We recently proposed a chameleonic solution to the cosmological constant problem - Phys. Rev. D82 (2010) 044006. One of the results of that paper is a non-equivalence of different conformal frames at the quantum level. In this letter we…
We develop a bootstrap approach to Euclidean two-point correlators, in the thermal or ground state of quantum mechanical systems. We formulate the problem of bounding the two-point correlator as a semidefinite programming problem, subject…
We derive linear scalar perturbation equations for Einstein-Cartan field equations of Weyssenhoff fluid, as well as for the corresponding perturbations of Bianchi identity and geodesic equations. The equations are given in both conformal…
We begin the process of unitarizing the Pomeron at large 't Hooft coupling. We do so first in the conformal regime, which applies to good accuracy to a number of real and toy problems in QCD. We rewrite the conformal Pomeron in the…
The redshift $z_t$ and the jerk parameter $j_t$ of the transition epoch are constrained by using two model-independent approaches involving the direct expansion of the Hubble rate and the expansion of the deceleration parameter around…