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A novel approach for computing glueball masses and matrix elements in Yang-Mills theories on the lattice
High Energy Physics - Lattice · Submitted 12 Dec 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We make use of the global symmetries of the Yang-Mills theory on the lattice to design a new computational strategy for extracting glueball masses and matrix elements which achieves an exponential reduction of the statistical error with respect to standard techniques.
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The abstract, sentence by sentence
We make use of the global symmetries of the Yang-Mills theory on the lattice to design a new computational strategy for extracting glueball masses and matrix elements which achieves an exponential reduction of the statistical error with respect to standard techniques. By generalizing our previous work on the parity symmetry, the partition function of the theory is decomposed into a sum of path integrals each giving the contribution from multiplets of states with fixed quantum numbers associated to parity, charge conjugation, translations, rotations and central conjugations Z_N^3. Ratios of path integrals and correlation functions can then be computed with a multi-level Monte Carlo integration scheme whose numerical cost, at a fixed statistical precision and at asymptotically large times, increases power-like with the time extent of the lattice. The strategy is implemented for the SU(3) Yang--Mills theory, and a full-fledged computation of the mass and multiplicity of the lightest glueball with vacuum quantum numbers is carried out at a lattice spacing of 0.17 fm.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We make use of the global symmetries of the Yang-Mills theory on the lattice to design a new computational strategy for extracting glueball masses and matrix elements which achieves an exponential reduction of the statistical error with respect to standard techniques. | contribution 0.93 | 0.95 | 0.81 | asserted 1.00 |
| s1 | By generalizing our previous work on the parity symmetry, the partition function of the theory is decomposed into a sum of path integrals each giving the contribution from multiplets of states with fixed quantum numbers associated to parity, charge conjugation, translations, rotations and central conjugations Z_N^3. | method 0.98 | 0.81 | 0.07 | asserted 1.00 |
| s2 | Ratios of path integrals and correlation functions can then be computed with a multi-level Monte Carlo integration scheme whose numerical cost, at a fixed statistical precision and at asymptotically large times, increases power-like with the time extent of the lattice. | method 1.00 | 0.76 | 0.16 | asserted 0.99 |
| s3 | The strategy is implemented for the SU(3) Yang--Mills theory, and a full-fledged computation of the mass and multiplicity of the lightest glueball with vacuum quantum numbers is carried out at a lattice spacing of 0.17 fm. | result 0.63 | 0.96 | 0.21 | asserted 1.00 |
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The paper
Original abstract
We make use of the global symmetries of the Yang-Mills theory on the lattice to design a new computational strategy for extracting glueball masses and matrix elements which achieves an exponential reduction of the statistical error with respect to standard techniques. By generalizing our previous work on the parity symmetry, the partition function of the theory is decomposed into a sum of path integrals each giving the contribution from multiplets of states with fixed quantum numbers associated to parity, charge conjugation, translations, rotations and central conjugations Z_N^3. Ratios of path integrals and correlation functions can then be computed with a multi-level Monte Carlo integration scheme whose numerical cost, at a fixed statistical precision and at asymptotically large times, increases power-like with the time extent of the lattice. The strategy is implemented for the SU(3) Yang--Mills theory, and a full-fledged computation of the mass and multiplicity of the lightest glueball with vacuum quantum numbers is carried out at a lattice spacing of 0.17 fm.
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References
How the literature uses it
16 arXiv papers cite this in 24 sentences
Papers citing it · 18 sentences without a confident label
Uses its method or tool 2 papers
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By following the standard line of argumentation in multi-level integration technique [ref] , it follows that ⟨{ γ_5 D^-1_Γ_0(x,x) } { γ_5 D^-1_Γ^*_0(y,y) } ⟩ = ⟨[{ γ_5 D^-1_Γ_0(x,x) } ] [{ γ_5 D^-1_Γ^*_0(y,y) } ] ⟩.
Domain decomposition, multi-level integration and exponential noise reduction in lattice QCD · Two-level integration · 0.94
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In the future we may adopt the algorithm in [ref] to overcome the problem.
A non-perturbative study of massive gauge theories · Numerical Results · 0.93
Cites it as support 1 paper
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The variances of projectors have appealing features including the non-appearance of states with different quantum numbers than the signal squared (e.g. three-pion states in nucleon variances) [ref] ; the finiteness of the variance of $|n > < n |$ is already sufficient to ensure the variance of $λ_n^(m)$ approaches a finite $m$-independent value.
Lanczos, the transfer matrix, and the signal-to-noise problem · Introduction · 0.96
Cites it as background 3 papers
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In the cases in which the dynamics is described by a local action, and one is interested in local observables, multilevel Monte Carlo integration algorithms [ref] are known to result in an impressive acceleration of the computation.
Domain decomposition and multilevel integration for fermions · Multilevel algoritms · 0.85
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To confront these difficulties, various strategies for the reduction of variance in the Monte Carlo procedure have been pursued [ref] .
Correlation function distributions for O(N) lattice field theories in the disordered phase · Introduction · 0.80
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Recent works have focused on characterising the nature of statistical fluctuations [ref] and on proposing strategies for noise reduction [ref] .
Large-time correlation functions in bosonic lattice field theories · Introduction · 0.91
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