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We consider critical points of a class of functionals on compact four-dimensional manifolds arising from Regularized Determinants for conformally covariant operators, whose explicit form was derived in [10], extending Polyakov's formula.…

Analysis of PDEs · Mathematics 2019-06-20 Pierpaolo Esposito , Andrea Malchiodi

We study 3d CFTs with an $O(N)$ global symmetry using the conformal bootstrap for a system of mixed correlators. Specifically, we consider all nonvanishing scalar four-point functions containing the lowest dimension $O(N)$ vector $\phi_i$…

High Energy Physics - Theory · Physics 2015-11-30 Filip Kos , David Poland , David Simmons-Duffin , Alessandro Vichi

It was demonstrated in recent work that $d=4$ unitary CFT's satisfy a special property: if a scalar operator with conformal dimension $\Delta$ exists in the operator spectrum, then the conformal bootstrap demands that large spin primary…

High Energy Physics - Theory · Physics 2015-08-12 Gideon Vos

Implications of inserting a conformal, monodromy line defect in three dimensional O($N$) models are studied. We consider then the WF O($N$) model, and study the two-point Green's function for bulk-local fields found from both the…

High Energy Physics - Theory · Physics 2018-03-15 Alexander Söderberg

We describe how to implement the conformal bootstrap program in the context of the embedding space OPE formalism introduced in previous work. To take maximal advantage of the known properties of the scalar conformal blocks for…

High Energy Physics - Theory · Physics 2025-04-14 Jean-François Fortin , Wen-Jie Ma , Valentina Prilepina , Witold Skiba

We consider the supersymmetric approach to gaussian disordered systems like the random bond Ising model and Dirac model with random mass and random potential. These models appeared in particular in the study of the integer quantum Hall…

High Energy Physics - Theory · Physics 2009-10-30 Z. Maassarani , D. Serban

This paper explores the numerical conformal bootstrap in general spacetime dimensions through the lens of a distinct category of analytic functionals, previously employed in two-dimensional studies. We extend the application of these…

High Energy Physics - Theory · Physics 2024-08-30 Kausik Ghosh , Zechuan Zheng

The establishment of the Wilson-Fisher fixed point (WFP) for $O(n)$ spin models in $d=4-\epsilon$ dimensions stands as a cornerstone of the renormalization group (RG) theory for critical phenomena. However, when long-range (LR)…

Statistical Mechanics · Physics 2026-03-20 Zhiyi Li , Kun Chen , Youjin Deng

In this paper, we investigate the (in)-consistency of different bootstrap methods for constructing confidence intervals in the class of estimators that converge at rate $n^{1/3}$. The Grenander estimator, the nonparametric maximum…

Statistics Theory · Mathematics 2010-10-20 Bodhisattva Sen , Moulinath Banerjee , Michael Woodroofe

A proof of critical conformal invariance of Green's functions for a quite wide class of models possessing critical scale invariance is given. A simple method for establishing critical conformal invariance of a composite operator, which has…

High Energy Physics - Theory · Physics 2008-02-03 S. E. Derkachov , N. A. Kivel , A. S. Stepanenko , A. N. Vasiliev

We compute the large $N$ critical exponents $\eta$, $\eta_\phi$ and $1/\nu$ in $d$-dimensions in the chiral Heisenberg Gross-Neveu model to several orders in powers of $1/N$. For instance, the large $N$ conformal bootstrap method is used to…

High Energy Physics - Theory · Physics 2018-05-23 J. A. Gracey

We implement the conformal bootstrap program for three-dimensional CFTs with $\mathcal{N}=2$ supersymmetry and find universal constraints on the spectrum of operator dimensions in these theories. By studying the bounds on the dimension of…

High Energy Physics - Theory · Physics 2015-08-11 Nikolay Bobev , Sheer El-Showk , Dalimil Mazac , Miguel F. Paulos

We revisit the classic $O(N)$ symmetric scalar field theories in $d$ dimensions with interaction $(\phi^i \phi^i)^2$. For $2<d<4$ these theories flow to the Wilson-Fisher fixed points for any $N$. A standard large $N$ Hubbard-Stratonovich…

High Energy Physics - Theory · Physics 2014-08-13 Lin Fei , Simone Giombi , Igor R. Klebanov

Statistical systems near a classical critical point have been intensively studied both from theoretical and experimental points of view. In particular, correlation functions are of relevance in comparing theoretical models with the…

High Energy Physics - Theory · Physics 2018-05-25 Andrea Amoretti , Nicodemo Magnoli

Let $\hat\Sigma=\frac{1}{n}\sum_{i=1}^n X_i\otimes X_i$ denote the sample covariance operator of centered i.i.d.~observations $X_1,\dots,X_n$ in a real separable Hilbert space, and let $\Sigma=\mathbb{E}(X_1\otimes X_1)$. The focus of this…

Statistics Theory · Mathematics 2024-01-25 Miles E. Lopes

A fully stochastic second-order adaptive-regularization method for unconstrained nonconvex optimization is presented which never computes the objective-function value, but yet achieves the optimal $\mathcal{O}(\epsilon^{-3/2})$ complexity…

Optimization and Control · Mathematics 2025-01-22 Serge Gratton , Sadok Jerad , Philippe L. Toint

In this work, we compute the anomalous dimensions of the $\phi^Q$ operator in six-dimensional cubic scalar theory. The renormalization analysis is carried out within the framework of the Operator Product Expansion method, while the…

High Energy Physics - Theory · Physics 2025-12-22 Rijun Huang , Qingjun Jin , Yi Li

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

Non-abelian Chern-Simons theories coupled to fermions are known to provide an interesting class of non-supersymmetric conformal fixed points \cite{Giombi:2011kc}. These theories, particularly those based on bifundamental matter, are…

High Energy Physics - Theory · Physics 2017-10-30 V. Gurucharan , Shiroman Prakash

Turning the divergent epsilon-expansion into a numerically sensible algorithm, relies on the knowledge of the behaviour of the large order contributions. Two different pictures are known to compete there. The first one was based on…

High Energy Physics - Theory · Physics 2023-01-04 Edouard Brezin