Conformal bootstrap signatures of the tricritical Ising universality class

Gowdigere, Chethan N.; Santara, Jagannath; Sumedha,

doi:10.1103/physrevd.101.116020

Cited by 7 publications

(8 citation statements)

References 45 publications

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“…For example, it played an essential role in the recent high-precision determination of CFT data in the 3d Ising model [8,10]. It has also been used for exploring theories in 2 dimensions [29,42,48,49,82], 3 dimensions [8-10, 22, 23, 25, 26, 31, 33, 36, 44, 52, 53, 56, 60, 63-66, 69, 71, 76, 80, 86], 4 dimensions [27, 28, 34, 35, 45-47, 62, 68, 77, 84], 5 dimensions [39,61], and 6 dimensions [24,54], as well as theories in fractional dimensions [30,41,51,74,75], defect theories [67,85], and nonlocal theories [50,70], and for studying the modular bootstrap [40,43,55,58,59,72,78,81], and the S-matrix bootstrap [37,38,57,83,87].…”

Section: Introductionmentioning

confidence: 99%

Scaling the semidefinite program solver SDPB

Landry¹,

Simmons-Duffin²

2019

Preprint

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We present enhancements to SDPB, an open source, parallelized, arbitrary precision semidefinite program solver designed for the conformal bootstrap. The main enhancement is significantly improved performance and scalability using the Elemental library and MPI. The result is a new version of SDPB that runs on multiple nodes with hundreds of cores with excellent scaling, making it practical to solve larger problems. We demonstrate performance on a moderate-size problem in the 3d Ising CFT and a much larger problem in the O(2) Model.

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Section: Introductionmentioning

confidence: 99%

Scaling the semidefinite program solver SDPB

Landry¹,

Simmons-Duffin²

2019

Preprint

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“…The restriction then arises since we don't want to gap spin 2 operators above the unitarity bound 16. The first 2D bound appeared in[20], and a wider plot where the second kink at (1,4) is visible has appeared recently in[21]. However, the existence of this kink was communicated to us by S. El-Showk a long time ago, who seems to have been the first to notice it.…”

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confidence: 98%

A functional approach to the numerical conformal bootstrap

Paulos

Zan

2020

J. High Energ. Phys.

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We apply recently constructed functional bases to the numerical conformal bootstrap for 1D CFTs. We argue and show that numerical results in this basis converge much faster than the traditional derivative basis. In particular, truncations of the crossing equation with even a handful of components can lead to extremely accurate results, in opposition to hundreds of components in the usual approach. We explain how this is a consequence of the functional basis correctly capturing the asymptotics of boundsaturating extremal solutions to crossing. We discuss how these methods can and should be implemented in higher dimensional applications.

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“…See for instance[43][44][45][46][47][48][49][50][51] or for supersymmetric studies. Other analysis can also be found in[75][76][77][78][79][80][81].…”

mentioning

confidence: 99%

Carving out OPE space and precise O(2) model critical exponents

Chester

Landry

Liu

et al. 2020

J. High Energ. Phys.

147

217

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We develop new tools for isolating CFTs using the numerical bootstrap. A "cutting surface" algorithm for scanning OPE coefficients makes it possible to find islands in high-dimensional spaces. Together with recent progress in large-scale semidefinite programming, this enables bootstrap studies of much larger systems of correlation functions than was previously practical. We apply these methods to correlation functions of charge-0, 1, and 2 scalars in the 3d O(2) model, computing new precise values for scaling dimensions and OPE coefficients in this theory. Our new determinations of scaling dimensions are consistent with and improve upon existing Monte Carlo simulations, sharpening the existing decades-old 8σ discrepancy between theory and experiment.

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Conformal bootstrap signatures of the tricritical Ising universality class

Cited by 7 publications

References 45 publications

Scaling the semidefinite program solver SDPB

Scaling the semidefinite program solver SDPB

A functional approach to the numerical conformal bootstrap

Carving out OPE space and precise O(2) model critical exponents

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