Topological susceptibility from the twisted mass Dirac operator spectrum

Elena Garcia-Ramos; Karl Jansen; Krzysztof Cichy

RECORD

Topological susceptibility from the twisted mass Dirac operator spectrum

Krzysztof Cichy, Elena Garcia-Ramos, Karl Jansen

High Energy Physics - Lattice · Submitted 18 Dec 2013

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We present results of our computation of the topological susceptibility with $N_f=2$ and $N_f=2+1+1$ flavours of maximally twisted mass fermions, using the method of spectral projectors.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

arXiv ID1312.5161 (version 2)

Pith IDCG3MYXJS, Pith's permanent record of this paper and its review

CitationElena Garcia-Ramos, Karl Jansen, Krzysztof Cichy. "Topological susceptibility from the twisted mass Dirac operator spectrum." arXiv:1312.5161 (2013). https://pith.science/paper/CG3MYXJS

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,890 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.81 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.94 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We present results of our computation of the topological susceptibility with $N_f=2$ and $N_f=2+1+1$ flavours of maximally twisted mass fermions, using the method of spectral projectors. We perform a detailed study of the quark mass dependence and discretization effects. We make an attempt to confront our data with chiral perturbation theory and extract the chiral condensate from the quark mass dependence of the topological susceptibility. We compare the value with the results of our direct computation from the slope of the mode number. We emphasize the role of autocorrelations and the necessity of long Monte Carlo runs to obtain results with good precision. We also show our results for the spectral projector computation of the ratio of renormalization constants $Z_P/Z_S$.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We present results of our computation of the topological susceptibility with $N_f=2$ and $N_f=2+1+1$ flavours of maximally twisted mass fermions, using the method of spectral projectors.	contribution 0.96	0.97	0.13	asserted 1.00
s1	We perform a detailed study of the quark mass dependence and discretization effects.	contribution 0.89	0.96	0.04	asserted 0.94
s2	We make an attempt to confront our data with chiral perturbation theory and extract the chiral condensate from the quark mass dependence of the topological susceptibility.	contribution 0.78	0.94	0.11	hedged possibility 0.67
s3	We compare the value with the results of our direct computation from the slope of the mode number.	contribution 0.41	0.93	0.10	asserted 0.98
s4	We emphasize the role of autocorrelations and the necessity of long Monte Carlo runs to obtain results with good precision.	limitation 0.60	0.66	0.07	asserted 1.00
s5	We also show our results for the spectral projector computation of the ratio of renormalization constants $Z_P/Z_S$.	result 0.76	0.97	0.05	asserted 1.00

What kind of paper the classifier reports this is: simulation study 1.00 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We present results of our computation of the topological susceptibility with $N_f=2$ and $N_f=2+1+1$ flavours of maximally twisted mass fermions, using the method of spectral projectors. We perform a detailed study of the quark mass dependence and discretization effects. We make an attempt to confront our data with chiral perturbation theory and extract the chiral condensate from the quark mass dependence of the topological susceptibility. We compare the value with the results of our direct computation from the slope of the mode number. We emphasize the role of autocorrelations and the necessity of long Monte Carlo runs to obtain results with good precision. We also show our results for the spectral projector computation of the ratio of renormalization constants $Z_P/Z_S$.

Human review

How Pith checks papers → · Full audit of this paper →

References

Forward citations

Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Axion phenomenology and $\theta$-dependence from $N_f = 2+1$ lattice QCD
hep-lat 2015-12 accept novelty 7.0 of 10

Continuum-extrapolated lattice QCD finds the topological susceptibility drops roughly as T to the minus three rather than the instanton-gas T to the minus eight, moving the axion dark matter window up by almost a fact...
Masses and decay constants of the $\eta$ and $\eta^\prime$ mesons from lattice QCD
hep-lat 2021-06 conditional novelty 6.0 of 10

Continuum-extrapolated lattice QCD in Nf=2+1 gives F8 = 115.0(2.8) MeV, theta8 = -25.8(2.3) deg, F0(2 GeV) = 100.1(3.0) MeV, theta0 = -8.1(1.8) deg, and gluonic matrix elements a_eta = 0.0170(10) GeV^3, a_eta' = 0.038...
Topology in full QCD at high temperature: a multicanonical approach
hep-lat 2018-07 conditional novelty 6.0 of 10

A bias-and-reweight lattice method samples rare topological sectors in hot QCD, yielding an assumption-free topological susceptibility consistent with prior work and direct support for dilute-instanton-gas volume scaling.
Chiral observables and topology in hot QCD with two families of quarks
hep-lat 2018-05 conditional novelty 6.0 of 10

Four-flavor lattice QCD simulations show the topological susceptibility falls as a power law above the chiral crossover, yielding an axion dark matter mass bound near 20 micro-electronvolts under standard cosmological...
Comparison of topological charge definitions in Lattice QCD
hep-lat 2017-08 accept novelty 5.0 of 10

Cooling, APE, stout and HYP smearing can each be rescaled to match gradient flow time, and all valid lattice topological charge definitions agree at 85 to 100 percent correlation.

Show 2 more citing papers

Topological charge using cooling and the gradient flow
hep-lat 2015-09 accept novelty 5.0 of 10

The perturbative matching between cooling steps and gradient flow time generalizes to gauge actions with a rectangular term as tau approximately equals n_c divided by (3 minus 15 c_1), and numerical tests on Nf=2+1+1 ...
Topological susceptibility and the sampling of field space in $N_f=2$ lattice QCD simulations
hep-lat 2014-06 conditional novelty 4.0 of 10

The topological susceptibility of two-flavor QCD, measured with the Wilson-flow charge on three lattice spacings and extrapolated to the continuum, agrees with leading-order chiral perturbation theory within the quote...

How the literature uses it

16 arXiv papers cite this in 23 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 13 sentences without a confident label

Uses its method or tool 3 papers

This quantity can be computed from spectral methods using the eigenvectors obtained from the same eigenvalue problem in Eq. [ref] [ref] as follows:

Nonperturbative determination of the ${\cal N} = 1$ supersymmetric Yang-Mills gluino condensate at large $N$ · Spectral method (Banks–Casher) · 1.00
In order to compute $χ_∞$, we use the method of spectral projectors [ref] .

Testing the Witten-Veneziano Formula on the Lattice · Quenched $χ_∞$ · 1.00
We follow the strategy presented in Ref. [ref] to extract the value of $Z_P/Z_S$ for each ensemble, i.e. we take the central value to be the one corresponding to some large value of $r_0 M$, chosen as 1.5, in order to avoid contamination by non-perturbative effects appearing for small $r_0 M$.

Non-perturbative Test of the Witten-Veneziano Formula from Lattice QCD · Computation of ZP over ZS · 1.00

Uses its data or values 1 paper

The results that they have obtained in the $N_f=2+1+1$ theory is shown in the right plot of Figure [ref] as a function of the renormalized quark mass [ref] .

Recent progress on chiral symmetry breaking in QCD · Topological susceptibility in QCD · 0.92

Compares with it 2 papers

We also note that the scaling pattern we observe is quite comparable with those reported by the ETMC at zero temperature in their study of the topological susceptibility from the twisted mass Dirac operator spectrum [ref] .

Chiral observables and topology in hot QCD with two families of quarks · Details on lattice artifacts · 1.00
Our results are summarized in Fig. [ref] (see also Fig. [ref] for a comparison with Ref. [ref] and Ref. [ref] ).

Topological susceptibility of QCD with dynamical M\"obius domain wall fermions · Results at high beta · 1.00

Cites it as background 4 papers

Apart from the link to the chiral condensate, the Dirac spectrum is also related to the topological susceptibility [ref] and the quark mass anomalous dimension.

Quark mass anomalous dimension and $\Lambda_{\overline{\textrm{MS}}}$ from the twisted mass Dirac operator spectrum · Introduction · 0.89
Lattice QCD simulations have provided information on $θ$-dependence below [ref] and across the deconfinement temperature $T_c$ [ref] since long, and the interest related to axion physics has fostered renewed efforts from the lattice community in the recent past [ref] .

Topology in full QCD at high temperature: a multicanonical approach · Introduction · 0.96
It should be also noted that the spectral method has been extensively used in the QCD literature [ref] .

Nonperturbative determination of the ${\cal N} = 1$ supersymmetric Yang-Mills gluino condensate at large $N$ · Methods · 0.90

What it cites · 24 sentences without a confident label

Builds on 1 paper

This definition of the topological susceptibility was subject to numerical analysis in the quenched case [ref] and it is the aim of the present paper to analyze the results of its usage in the case with $N_f=2$ and $N_f=2+1+1$ active flavours of twisted mass fermions.

Universality of the topological susceptibility in the SU(3) gauge theory · Introduction · 0.96

Uses the method or tool of 2 papers

The method that we follow in this paper was introduced in Refs. [ref] and we refer to these papers for a comprehensive description.

Chiral symmetry breaking and the Banks--Casher relation in lattice QCD with Wilson quarks · Theoretical principles · 0.99
The method that we follow in this paper was introduced in Refs. [ref] and we refer to these papers for a comprehensive description.

Universality of the topological susceptibility in the SU(3) gauge theory · Theoretical principles · 0.99

Compares with 3 papers

Still, our result is in agreement with the direct determination from the mode number on the same set of gauge field ensembles – $r_0 Σ^1/3 = 0.680(20)(21)$ [ref] , indicating that LO$χ$PT describes the quark mass dependence of the topological susceptibility at least within the rather large errors of our results.

Chiral condensate from the twisted mass Dirac operator spectrum · $N_f=2+1+1$ results · 0.93
For all these ensembles, we can compare the values of $Z_P/Z_S$ with an alternative computation – in the framework of the RI-MOM renormalization scheme ($β=3.9, 4.05, 4.2$ [ref] ) or the X-space renormalization scheme ($β=4.35$ [ref] ).

Non-perturbative renormalization in coordinate space for $N_f=2$ maximally twisted mass fermions with tree-level Symanzik improved gauge action · $N_f=2$ · 0.97
For all these ensembles, we can compare the values of $Z_P/Z_S$ with an alternative computation – in the framework of the RI-MOM renormalization scheme ($β=3.9, 4.05, 4.2$ [ref] ) or the X-space renormalization scheme ($β=4.35$ [ref] ).

Renormalization constants of local operators for Wilson type improved fermions · $N_f=2$ · 0.97

Cites as background 1 paper

There exist many definitions of the topological charge on the lattice[For a short review and discussion of different definitions and for further references, we refer to Ref. [ref] .] and there has been a debate in the literature about the validity of different approaches.

Anomalies, gauge field topology, and the lattice · Introduction · 1.00

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.