A semidefinite program solver for the conformal bootstrap

By David Simmons-Duffin. Journal of High Energy Physics, 2015

425 citations recorded by the source corpus.

We introduce SDPB: an open-source, parallelized, arbitrary-precision semidefinite program solver, designed for the conformal bootstrap. SDPB significantly outperforms less specialized solvers and should enable many new computations. As an example application, we compute a new rigorous high-precision bound on operator dimensions in the 3d Ising CFT, Δσ = 0.518151(6), Δϵ = 1.41264(6).

Subfields: Nuclear and High Energy Physics, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/09b0d28de58f8fb3b5180b5c69897601d46aaf62

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Nuclear and High Energy Physics

1. David Simmons-Duffin
2. David Poland
3. S. Rychkov
4. A. Vichi
5. M. Paulos
6. L. Rastelli
7. Filip Kos
8. B. C. Rees

In Numerical Analysis

1. S. Rychkov
2. David Simmons-Duffin
3. B. C. Rees
4. David Poland
5. A. Vichi
6. L. Rastelli
7. M. Paulos
8. Bernardo Zan

In Statistics and Probability

1. David Simmons-Duffin
2. S. Rychkov
3. David Poland
4. B. C. Rees
5. L. Rastelli
6. A. Vichi
7. M. Paulos
8. Filip Kos

Citations in the corpus

• Weight shifting operators and conformal blocks (2017, neutral): “In numerical conformal bootstrap one usually requires simple rational approximations to conformal blocks [8, 22, 30], which are hard to construct from these expressions.”
• Conformal invariance in the long-range Ising model (2015, methodology): “2 In 3d, an exact solution is not yet known, but the conformal bootstrap has recently been used to get the world’s most precise numerical determinations of the SRI critical exponents [13].”
• Carving out OPE space and precise O(2) model critical exponents (2019, methodology): “One tool that will facilitate going beyond previous studies is a new version of the semidefinite program solver SDPB [82], which can now run on hundreds of cores across multiple machines [83].”
• TASI Lectures on the Conformal Bootstrap (2016, methodology): “qqWe use the SDPB parameters listed in the appendix of [61].”
• Bootstrapping 3D fermions (2015, methodology): “We search for functionals satisfying these constraints by approximating the search as a semidefinite program and implementing it in the solver SDPB [8].”
• EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions (2016, methodology): “This happens for the 3d Ising model [46, 47] and for the O(N) models [48].”
• The (2, 0) superconformal bootstrap (2015, methodology): “We are especially indebted to David Simmons-Duffin for many useful insights and for help with his SDPB software, and to Sheer El-Showk for sharing his CPLEX interface.”
• The lightcone bootstrap and the spectrum of the 3d Ising CFT (2016, methodology): “A.3 Several operators in the 3d Ising CFT In this section, we list dimensions and OPE coefficients of 112 stable operators obtained from the calculation described in section A.1 (and plotted in figures 1 and 2).”
• The ϵ ?> -expansion from conformal field theory (2015, background): “A flagship result of this line of research is the world’s most precise determination of the operator dimensions in the critical 3d Ising model [12].”
• The conformal bootstrap: Theory, numerical techniques, and applications (2018, methodology): “A Mathematica notebook by Simmons-Duffin (2015b) can be used for general scalar conformal blocks; at step (i) it implements the recursion relation from analytic structure discussed in Sec.”
• The S-matrix bootstrap. Part I: QFT in AdS (2016, methodology): “Current state-of-the-art methods have been encoded in specialized software packages like JuliBootS [28] and SDPB [29], both of which were used to obtain the results discussed below.”
• A proof of the conformal collider bounds (2016, background): “[2–5, 61–72]).”