Related papers: Bootstrap Method in Theoretical Physics
Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…
We review and systematize two (analytic) bootstrap techniques in two-dimensional conformal field theories using the S-modular transformation. The first one gives universal results in asymptotic regimes by relating extreme temperatures.…
We combine supersymmetric localization results with numerical bootstrap techniques to compute upper bounds on the low-lying CFT data of ${\cal N} = 4$ super-Yang-Mills theory as a function of the complexified gauge coupling $\tau$. In…
Finding a method to combine the numerical bootstrap with the analytic lightcone bootstrap is an important goal to advance the conformal bootstrap program. We propose a hybrid bootstrap method to do just that. The numerical and analytic…
We use the conformal bootstrap to perform a precision study of 3d maximally supersymmetric ($\mathcal{N}=8$) SCFTs that describe the IR physics on $N$ coincident M2-branes placed either in flat space or at a $\C^4/\Z_2$ singularity. First,…
The bootstrap is a popular data-driven method to quantify statistical uncertainty, but for modern high-dimensional problems, it could suffer from huge computational costs due to the need to repeatedly generate resamples and refit models. We…
An algorithm is described that enables efficient deterministic approximate computation of the bootstrap distribution for any linear bootstrap method $T_n^*$, alleviating the need for repeated resampling from observations (resp.…
We consider constraints on the S-matrix of any gapped, Lorentz invariant quantum field theory in 1 + 1 dimensions due to crossing symmetry and unitarity. In this way we establish rigorous bounds on the cubic couplings of a given theory with…
Bootstrap techniques (also called resampling computation techniques) have introduced new advances in modeling and model evaluation. Using resampling methods to construct a series of new samples which are based on the original data set,…
Structural equation models are commonly used to capture the relationship between sets of observed and unobservable variables. Traditionally these models are fitted using frequentist approaches but recently researchers and practitioners have…
The S-matrix bootstrap is extended to a 1+1d theory with $O(N)$ symmetry and a boundary in what we call the R-matrix bootstrap since the quantity of interest is the reflection matrix (R-matrix). Given a bulk S-matrix, the space of allowed…
Reliable forward uncertainty quantification in engineering requires methods that account for aleatory and epistemic uncertainties. In many applications, epistemic effects arising from uncertain parameters and model form dominate prediction…
This paper deals with the Gaussian and bootstrap approximations to the distribution of the max statistic in high dimensions. This statistic takes the form of the maximum over components of the sum of independent random vectors and its…
We describe the formalism to compute gravitational-wave observables for compact binaries via the effective field theory framework in combination with modern tools from collider physics. We put particular emphasis on solving the "multi-loop"…
We revisit analytical methods for constraining the nonperturbative $S$-matrix of unitary, relativistic, gapped theories in $d \geq 3$ spacetime dimensions. We assume extended analyticity of the two-to-two scattering amplitude and use it…
Many of the exciting features of the Standard Model of the elementary particles are inherently non-perturbative. A theoretical understanding of many physics aspects beyond the Standard Model of elementary particles also requires a…
1+1 dimensional integrable quantum field theories correspond to a sparse subset of quantum field theories where the calculation of physically interesting observables can be brought to explicit, closed and manageable expressions thanks to…
The numerical conformal bootstrap is used to study mixed correlators in $\mathcal{N}=1$ superconformal field theories (SCFTs) in $d=4$ spacetime dimensions. Systems of four-point functions involving scalar chiral and real operators are…
In this work, we develop machine learning techniques to study nonperturbative scattering amplitudes. We focus on the two-to-two scattering amplitude of identical scalar particles, setting the double discontinuity to zero as a simplifying…
We study the conformal bootstrap constraints for 3D conformal field theories with a $\mathbb{Z}_2$ or parity symmetry, assuming a single relevant scalar operator $\epsilon$ that is invariant under the symmetry. When there is additionally a…