Solving Conformal Field Theories with Artificial Intelligence

Kántor, Gergely; Niarchos, Vasilis; Papageorgakis, Constantinos

doi:10.48550/arxiv.2108.08859

Cited by 3 publications

(4 citation statements)

References 20 publications

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“…It would be interesting to see how our numerical method performs with respect to Gliozzi's method [33,34] and its subsequent versions [35,36]. The aim of this work is very similar to that of [14,15], where approximate solutions to crossing have been achieved using a similar logic but a different technique (reinforcement learning instead of MC techniques). It would be interesting to systematically compare the two approaches.…”

Section: Discussionmentioning

confidence: 99%

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A Monte Carlo approach to the conformal bootstrap

Laio,

Valenzuela,

Serone

2022

Preprint

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We introduce an approach to find approximate numerical solutions of truncated bootstrap equations for Conformal Field Theories (CFTs) in arbitrary dimensions. The method is based on a stochastic search via a Metropolis algorithm guided by an action S which is the logarithm of the truncated bootstrap equations for a single scalar field correlator. While numerical conformal bootstrap methods based on semidefinite programming put rigorous exclusion bounds on CFTs, this method looks for approximate solutions, which correspond to local minima of S and can be even far from the extremality region. By this protocol we find minima of S associated to known theories, including the 2d and 3d Ising theories, the 2d Yang-Lee model, as well as new ones. Imposing a conserved stress-tensor, a Z 2 symmetry and one relevant scalar, we identify two regions where local minima of S are present. When projected in the (∆ σ , ∆ )-plane, σ and being the external and the lightest exchanged operators, one of these regions essentially coincides with the extremality line found in previous bootstrap studies. The other region is along the generalized free theories in d = 2 and below that in both d = 3 and d = 4.

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Section: Discussionmentioning

confidence: 99%

“…Very recently numerical methods based on reinforcement learning have been used to find approximate solutions to the bootstrap equations[14,15]. Though this is an interesting line of research to pursue, it is not clear to us if and how such techniques can alleviate the problem of fake local minima 4.…”

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confidence: 99%

A Monte Carlo approach to the conformal bootstrap

Laio,

Valenzuela,

Serone

2022

Preprint

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“…In addition, the only reliable source for initial conditions is finding an extremal functional using traditional bootstrap methods, which are limited to unitary regions of the parameter space. It would be interesting if reinforcement-learning techniques utilized in [62,63] can be leveraged to produce initial conditions for deformations.…”

Section: Discussion and Outlookmentioning

confidence: 99%

Conformal Bootstrap Deformations

Afkhami-Jeddi¹

2021

Preprint

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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 solution corresponding to the boundary of allowed regions in the parameter space of CFTs. Furthermore, by deforming these solutions, we demonstrate that certain solutions corresponding to known theories are continuously connected. Employing these methods, we will explore the space of non-unitary CFTs in the context of modular as well as correlation function bootstrap. In two dimensions, we show that the extremal solution corresponding to the Ising model is connected to that of the Yang-Lee minimal model. By deforming this solution to three dimensions, we provide evidence that the CFT data obtained in this way is compatible with the -expansion for a non-unitary theory.

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“…As the Gaussian CFTs with higher derivatives are nonunitary, we expect that the interacting CFTs violate unitarity as well. To perform the nonperturbative study, we need to use the bootstrap methods that do not rely on positivity constraints [85][86][87][88][89][90][91][92][93][94].…”

Section: Discussionmentioning

confidence: 99%

The Intellectual Legacy of Sun Yat-sen

Guo

2020

Freedom of the Press in China

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This chapter discusses Sun Yat-sen’s thoughts on ‘liberty’ and their later development along anti-liberal lines. The near-deification of Sun Yat-sen in the late 1920s following his death ensured that his views and theories became the dominant discourse and that his intellectual legacy exerted significant influence on discussions of press freedom in China over the first half of the twentieth century. Sun Yat-sen’s anti-liberal thoughts became integrated into the area of national news policy and journalism theory. The ‘San-min Doctrine of Journalism’ was formulated and came to dominate the official discourse. This later became the theoretical foundation that legitimized the policy of press censorship carried out by the Nationalist government.

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Solving Conformal Field Theories with Artificial Intelligence

Cited by 3 publications

References 20 publications

A Monte Carlo approach to the conformal bootstrap

A Monte Carlo approach to the conformal bootstrap

Conformal Bootstrap Deformations

The Intellectual Legacy of Sun Yat-sen

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