Bootstrap for lattice Yang-Mills theory

Казаков, Владимир; Zheng, Zechuan

doi:10.1103/physrevd.107.l051501

Cited by 30 publications

(26 citation statements)

References 44 publications

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“…Our new method for calculating Feynman integrals is analogous to recent developments in bootstrapping quantum mechanics systems and lattice models [45][46][47][48][49][50][51]. For example, the role of IBP and dimensional-shifting identities in our work is analogous to the role of moment recursion relations in the quantum mechanics bootstrap.…”

Section: Discussionmentioning

confidence: 99%

“…Some of the predictions in the S-matrix and EFT contexts have been checked against explicit perturbative calculations involving Feynman integrals [42][43][44], so it is natural to explore positivity properties for Feynman integrals themselves. What directly inspired this paper, though, is recent applications of positivity constraints to bootstrapping simple quantum mechanical systems [45][46][47][48] and lattice models [49][50][51], which crucially use various linear identities that are reminiscent of integrationby-parts identities for Feynman integrals [52] as well as a numerical technique known as semidefinite programming [53] which will be adapted to our calculations. Semidefinite programming was introduced to theoretical physics by Ref.…”

Section: Contents 1 Introductionmentioning

confidence: 99%

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Feynman Integrals from Positivity Constraints

Zeng¹

2023

Preprint

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We explore inequality constraints as a new tool for numerically evaluating Feynman integrals. A convergent Feynman integral is non-negative if the integrand is nonnegative in either loop momentum space or Feynman parameter space. Applying various identities, all such integrals can be reduced to linear sums of a small set of master integrals, leading to infinitely many linear constraints on the values of the master integrals. The constraints can be solved as a semidefinite programming problem in mathematical optimization, producing rigorous two-sided bounds for the integrals which are observed to converge rapidly as more constraints are included, enabling high-precision determination of the integrals. Positivity constraints can also be formulated for the expansion terms in dimensional regularization and reveal hidden consistency relations between terms at different orders in . We introduce the main methods using one-loop bubble integrals, then present a nontrivial example of three-loop banana integrals with unequal masses, where 11 top-level master integrals are evaluated to high precision.

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Section: Discussionmentioning

confidence: 99%

Section: Contents 1 Introductionmentioning

confidence: 99%

Feynman Integrals from Positivity Constraints

Zeng¹

2023

Preprint

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“…as (7) should hold true for any vector α, the bootstrap matrix  must embody the positive semi definiteness i.e. 0   , which is essentially an eigenvalue problem…”

Section: Bootstrap Equations and Matricesmentioning

confidence: 99%

“…Bootstrap, a novel yet promising method which has recently been studied in quantum mechanics, is a way to utilize the very general self-consistency condition and solve the system numerically. Developed in the 1960s and 70s [1], the method was later applied in large N systems [2][3][4], lattice theory [5][6][7][8], conformal field theory [9][10][11][12][13], as well as matrix models [14,15]. This technique is also used to bootstrap the Dirac ensembles [16], some have integrated this method with artificial intelligence [17,18].…”

Section: Introductionmentioning

confidence: 99%

Microscopic ensemble bootstrap in phase space

Zhang

2024

Commun. Theor. Phys.

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The bootstrap method which has been studied under many quantum mechanical models turns out feasible in microcanonical ensemble as well. While the approach in [Y. Nakayama, Modern Physics Letters A 37, 10.1142/s0217732322500547 (2022)] produces a sector when energy is negative, in this paper we report a method that has stronger constraints and results in a smaller region. We also study other models to demonstrate the effectiveness of our method.

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“…In particular, the momentum loop equation was developed, similar to our momentum loop used below [6][7][8]. Recently, some numerical methods were found to solve loop equations beyond perturbation theory [9,10].…”

Section: Introductionmentioning

confidence: 99%

Decaying Turbulence as a Fractal Curve

Migdal¹

2023

Preprint

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We develop a quantitative microscopic theory of decaying Turbulence by studying the dimensional reduction of the Navier-Stokes loop equation for the velocity circulation. We have found an infinite dimensional manifold of solutions of the Navier-Stokes loop equation\cite{M93, M23PR} for the Wilson loop in decaying Turbulence in arbitrary dimension $d >2$. This family of solutions corresponds to a fractal curve in complex space $\mathbb C^d$, described by an algebraic equation between consecutive positions plus a nonlinear periodicity condition. We derive the constrained SDE for the evolution of the fractal curve at a fixed moment of physical time as a function of an auxiliary stochastic time. We expect this stochastic process to cover our fixed manifold of the solutions of the decaying Turbulence. The energy density of the fluid decays as $\mathcal E_0/t$, where $\mathcal E_0$ is an initial dissipation rate. Presumably, we have found a new phase of extreme Turbulence yet to be observed in real or numerical experiments.

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Bootstrap for lattice Yang-Mills theory

Cited by 30 publications

References 44 publications

Feynman Integrals from Positivity Constraints

Feynman Integrals from Positivity Constraints

Microscopic ensemble bootstrap in phase space

Decaying Turbulence as a Fractal Curve

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