Related papers: Descending into the Modular Bootstrap
We present two complementary approaches to calculating the 2-point function of stress tensors in the presence of a 1/2 BPS surface defect of the 6d $\mathcal{N} = (2,0)$ theories. First, we use analytical bootstrap techniques at large $N$…
We discuss the structure of 2D conformal field theories (CFT) at central charge c=0 describing critical disordered systems, polymers and percolation. We construct a novel extension of the c=0 Virasoro algebra, characterized by a number b…
We explore the space of extremal functionals in the conformal bootstrap. By recasting the bootstrap problem as a set of non-linear equations parameterized by the CFT data, we find an efficient algorithm for converging to the extremal…
We describe examples of drastic truncations of conformal bootstrap equations encoding much more information than that obtained by a direct numerical approach. A three-term truncation of the four point function of a free scalar in any space…
The connection problem for isomonodromic tau functions on the one-punctured torus concerns the ratio between the tau function and its modular transform, associated to dual pants decompositions of the torus. In this paper, we study the…
Scattering amplitudes in $d+2$ dimensions can be recast as correlators of conformal primary operators in a putative holographic CFT$_d$ by working in a basis of boost eigenstates instead of momentum eigenstates. It has been shown previously…
Constrained density functional theory (cDFT) is a versatile electronic structure method that enables ground-state calculations to be performed subject to physical constraints. It thereby broadens their applicability and utility. Automated…
The most widely used methods for toolpath planning in fused deposition 3D printing slice the input model into successive 2D layers in order to construct the toolpath. Unfortunately slicing-based methods can incur a substantial amount of…
We study a general class of functionals providing an analytic handle on the conformal bootstrap equations in one dimension. We explicitly identify the extremal functionals, corresponding to theories saturating conformal bootstrap bounds, in…
We study scalar conformal field theories whose large $N$ spectrum is fixed by the operator dimensions of either Ising model or Lee-Yang edge singularity. Using numerical bootstrap to study CFTs with $S_N\otimes Z_2$ symmetry, we find a…
We propose a novel method for reconstructing floor plans from noisy 3D point clouds. Our main contribution is a principled approach that relies on the Monte Carlo Tree Search (MCTS) algorithm to maximize a suitable objective function…
The method of large spin perturbation theory allows to analyse conformal field theories (CFT) by turning the crossing equations into an algebraic problem. We apply this method to a generic CFT with weakly broken higher spin (HS) symmetry,…
We study the 2D vertex operator algebra (VOA) construction in 4D $\mathcal{N}=2$ superconformal field theories (SCFT) on $S^3 \times S^1$, focusing both on old puzzles as well as new observations. The VOA lives on a two-torus…
In recent work we computed the path integral of three-dimensional gravity with negative cosmological constant on spaces which are topologically a torus times an interval. Here we employ a modular bootstrap to show that the amplitude is…
We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…
We present an analytic study of conformal field theories on the real projective space $\mathbb{RP}^d$, focusing on the two-point functions of scalar operators. Due to the partially broken conformal symmetry, these are non-trivial functions…
We consider rigorous consequences of modular invariance for two-dimensional unitary non-rational CFTs with $c > 1$. Simple estimates for the torus partition function can lead to remarkably strong results. We show in particular that the…
Decision trees are popular machine learning models that are simple to build and easy to interpret. Even though algorithms to learn decision trees date back to almost 50 years, key properties affecting their generalization error are still…
Motivated by sine-square deformation (SSD) for quantum critical systems in 1+1-dimension, we discuss a Mobius quantization approach to the two-dimensional conformal field theory (CFT), which bridges the conventional radial quantization and…
For expansions in one-dimensional conformal blocks, we provide a rigorous link between the asymptotics of the spectral density of exchanged primaries and the leading singularity in the crossed channel. Our result has a direct application to…