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Related papers: Finite-$N$ Bootstrap Constraints in Matrix and Ten…

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In this paper we analyze the multi-matrix model arising from the intermediate field representation of the tensor model with all quartic melonic interactions. We derive the saddle point equation and the Schwinger-Dyson constraints. We then…

Mathematical Physics · Physics 2015-06-22 Viet Anh Nguyen , Stephane Dartois , Bertrand Eynard

We consider the properties of the bootstrap as a tool for inference concerning the eigenvalues of a sample covariance matrix computed from an $n\times p$ data matrix $X$. We focus on the modern framework where $p/n$ is not close to 0 but…

Methodology · Statistics 2016-08-03 Noureddine El Karoui , Elizabeth Purdom

We implement the conformal bootstrap for N=4 superconformal field theories in four dimensions. Consistency of the four-point function of the stress-energy tensor multiplet imposes significant upper bounds for the scaling dimensions of…

High Energy Physics - Theory · Physics 2022-08-22 Christopher Beem , Leonardo Rastelli , Balt C. van Rees

We present a complete study of boundary bound states and related boundary S-matrices for the sine-Gordon model with Dirichlet boundary conditions. Our approach is based partly on the bootstrap procedure, and partly on the explicit solution…

High Energy Physics - Theory · Physics 2016-09-06 S. Skorik , H. Saleur

The technique of $Q$-polinomials are used to derive the $w$- constraints in the two-matrix and Kontsevich-like model at finite $N$. These constraints are closed and form Lie algebra. They are associated with the matrices, $\lambda…

High Energy Physics - Theory · Physics 2007-05-23 N. L. Khviengia

We discuss the q-state Potts models for q<=4, in the scaling regimes close to their critical or tricritical points. Starting from the kink S-matrix elements proposed by Chim and Zamolodchikov, the bootstrap is closed for the scaling regions…

High Energy Physics - Theory · Physics 2010-04-05 Patrick Dorey , Andrew Pocklington , Roberto Tateo

We develop new tools for an in-depth study of our recent proposal for Matrix Theory. We construct the anomaly-free and finite planar continuum limit of the ground state with SO(2^{13}) symmetry matching with the tadpole and tachyon free IR…

High Energy Physics - Theory · Physics 2007-05-23 Shyamoli Chaudhuri

Representation theory provides a suitable framework to count and classify invariants in tensor models. We show that there are two natural ways of counting invariants, one for arbitrary rank of the gauge group and a second, which is only…

High Energy Physics - Theory · Physics 2018-04-04 Pablo Diaz , Soo-Jong Rey

A survey of the interrelationships between matrix models and field theories on the noncommutative torus is presented. The discretization of noncommutative gauge theory by twisted reduced models is described along with a rigorous definition…

High Energy Physics - Theory · Physics 2008-11-26 Richard J. Szabo

We summarize some aspects of matrix models from the approaches directly based on their properties at finite N.

High Energy Physics - Theory · Physics 2007-05-23 H. Itoyama

We write down and solve a closed set of Schwinger-Dyson equations for the two-matrix model in the large $N$ limit. Our elementary method yields exact solutions for correlation functions involving angular degrees of freedom whose calculation…

High Energy Physics - Theory · Physics 2009-10-22 Matthias Staudacher

The S-matrix bootstrap maps out the space of S-matrices allowed by analyticity, crossing, unitarity, and other constraints. For the $2\rightarrow 2$ scattering matrix $S_{2\rightarrow 2}$ such space is an infinite dimensional convex space…

High Energy Physics - Theory · Physics 2021-09-15 Yifei He , Martin Kruczenski

The paper contributes to an ongoing effort to extend the conformal bootstrap beyond its traditional focus on systems of four-point correlation functions. Recently, it was demonstrated that semidefinite programming can be used to formulate a…

High Energy Physics - Theory · Physics 2025-12-10 Sebastian Harris

The modern S-Matrix Bootstrap provides non-perturbative bounds on low-energy aspects of scattering amplitudes, leveraging the constraints of unitarity, analyticity and crossing. Typically, the solutions saturating such bounds also saturate…

High Energy Physics - Theory · Physics 2023-10-12 António Antunes , Miguel S. Costa , José Pereira

We study the numerical bounds obtained using a conformal-bootstrap method - advocated in ref. [1] but never implemented so far - where different points in the plane of conformal cross ratios $z$ and $\bar z$ are sampled. In contrast to the…

High Energy Physics - Theory · Physics 2016-11-04 Alejandro Castedo Echeverri , Benedict von Harling , Marco Serone

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…

High Energy Physics - Theory · Physics 2021-04-28 Martin Kruczenski , Harish Murali

We study the spectrum of the large $N$ quantum field theory of bosonic rank-$3$ tensors, whose quartic interactions are such that the perturbative expansion is dominated by the melonic diagrams. We use the Schwinger-Dyson equations to…

High Energy Physics - Theory · Physics 2017-11-29 Simone Giombi , Igor R. Klebanov , Grigory Tarnopolsky

We define a new large $N$ limit for general $\text{O}(N)^{R}$ or $\text{U}(N)^{R}$ invariant tensor models, based on an enhanced large $N$ scaling of the coupling constants. The resulting large $N$ expansion is organized in terms of a…

High Energy Physics - Theory · Physics 2019-04-23 Frank Ferrari , Vincent Rivasseau , Guillaume Valette

We study two-dimensional conformal field theories (CFTs) with boundaries via the conformal bootstrap. We derive a positive semi-definite program from crossing symmetry of three observables: the annulus partition function, the two-point…

High Energy Physics - Theory · Physics 2025-06-24 Marco Meineri , Bharathkumar Radhakrishnan

We introduce a method based on semidefinite programming that produces rigorous two-sided bounds on ground state energy densities and correlation functions of translation-invariant classical spin models on infinite lattices. In this method,…

Statistical Mechanics · Physics 2026-05-11 Nisarga Paul , Gil Refael