Precision Bootstrap for the $\mathcal{N}=1$ Super-Ising Model

Atanasov, Alexander; Hillman, Aaron; Poland, David; Rong, Junchen; Su, Ning

doi:10.48550/arxiv.2201.02206

Cited by 3 publications

(9 citation statements)

References 51 publications

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“…When applying the hybrid bootstrap to other CFTs, one may start with the most reliable analytics that one has. Quick applications could be super-Ising and the O(N) CFTs, where some analytics were worked out in [16,28] 29 .…”

Section: Discussionmentioning

confidence: 99%

“…But one contributing factor might be, as the dimension of the external operator gets larger, the leading twist family usually also has a larger twist that is further away from the unitary bound, so the unitary bound we put in each channel may not be sufficient. A relevant hint is that the EFM spectrum of the super-Ising CFT [28] also suffers from the sharing effect, i.e. it has fake operators on the unitary bound.…”

Section: Discussionmentioning

confidence: 99%

“…We then derive an improved version for [σσ] 0, , which will be used later. Our goal is actually slightly different from [27,13,16,28]. For the purpose of hybrid bootstrap, the analytics has to simultaneously meet (1), computational efficiency; (2), accuracy at large spin; (3), dependence only on a few parameters (at most {∆ σ , ∆ , f , f σσ , f T }).…”

Section: Analytical Bootstrapmentioning

confidence: 99%

“…11 Similar procedure has been used in [13,28]. 12 When implemented in Mathematica, on a computer with 64 AMD EPYC 7532 32-Core Processor, computations for [σσ] 0, =4,...,52 takes about 7 seconds.…”

Section: Analytical Bootstrapmentioning

confidence: 99%

“…The validity and robustness of this method is subject to future studies in other scenarios and models. It would also be interesting to find other methods to balance out multiple analytics 28 .…”

Section: Balance Out Multiple Analytics With Different Accuracymentioning

confidence: 99%

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The Hybrid Bootstrap

Su¹

2022

Preprint

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Finding a method to combine the numerical bootstrap with the analytic lightcone bootstrap is an important goal to advance the conformal bootstrap program. We propose a hybrid bootstrap method to do just that. The numerical and analytic bootstrap approaches are sensitive to different regions of the spectrum and complement each other. When they are effectively combined, the hybrid bootstrap enjoys the best of both worlds and the prediction for the actual CFT can be significantly improved. In this work, we discuss the general strategy to perform such a hybrid bootstrap, and we make a partial implementation of the strategy for 3D Ising CFT {σ, } system. Even at relatively low derivative order Λ = 19, the hybrid bootstrap predicts very precise values for the scaling dimension ∆ σ , ∆ that are within the previous Λ = 43 rigorous error bars.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Analytical Bootstrapmentioning

confidence: 99%

Section: Analytical Bootstrapmentioning

confidence: 99%

Section: Balance Out Multiple Analytics With Different Accuracymentioning

confidence: 99%

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The Hybrid Bootstrap

Su¹

2022

Preprint

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Celestial Blocks and Transverse Spin in the Three-Point Energy Correlator

Chen¹,

Moult²,

Sandor³

et al. 2022

Preprint

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Quantitative theoretical techniques for understanding the substructure of jets at the LHC enable new insights into the dynamics of QCD, and novel approaches to search for new physics. Recently, there has been a program to reformulate jet substructure in terms of correlation functions, E( n 1 )E( n 2 ) • • • E( n k ) , of light-ray operators, E( n), allowing the application of techniques developed in the study of Conformal Field Theories (CFTs). In this paper we further develop these techniques in the particular context of the three-point correlator E( n 1 )E( n 2 )E( n 3 ) , using recently computed perturbative data in both QCD and N = 4 sYM. We derive the celestial blocks appearing in the light-ray operator product expansion (OPE) of the three-point correlator, and use the Lorentzian inversion formula to extract the spectrum of light-ray operators appearing in the expansion, showing, in particular, that the OPE data is analytic in transverse spin. Throughout our presentation, we highlight the relation between the OPE approach, and more standard splitting function based approaches of perturbative QCD, emphasizing the utility of the OPE approach for incorporating symmetries in jet substructure calculations. We hope that our presentation introduces a number of new techniques to the jet substructure community, and also illustrates the phenomenological relevance of the study of light-ray operators in the OPE limit to the CFT community.

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Navigating through the O(N) archipelago

Sirois¹

2022

Preprint

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A novel method for finding allowed regions in the space of CFT-data, coined navigator method, was recently proposed in [1]. Its efficacy was demonstrated in the simplest example possible, i.e. that of the mixed-correlator study of the 3D Ising Model. In this paper, we would like to show that the navigator method may also be applied to the study of the family of d-dimensional O(N ) models. We will aim to follow these models in the (d, N ) plane. We will see that the "sailing" from island to island can be understood in the context of the navigator as a parametric optimization problem, and we will exploit this fact to implement a simple and effective path-following algorithm. By sailing with the navigator through the (d, N ) plane, we will provide estimates of the scaling dimensions (∆ φ , ∆ s , ∆ t ) in the entire range (d, N ) ∈ [3, 4] × [1, 3]. We will show that to our level of precision, we cannot see the non-unitary nature of the O(N ) models due to the fractional values of d [2] or N [3] in this range. We will also study the limit N − → 1, and see that we cannot find any solution to the unitary mixed-correlator crossing equations below N = 1.

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Precision Bootstrap for the $\mathcal{N}=1$ Super-Ising Model

Cited by 3 publications

References 51 publications

The Hybrid Bootstrap

The Hybrid Bootstrap

Celestial Blocks and Transverse Spin in the Three-Point Energy Correlator

Navigating through the O(N) archipelago

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