Publicising Lattice Field Theory through Visualisation
James Biddle, Josh Charvetto, Waseem Kamleh, Derek Leinweber, Helen Piercy, Ethan Puckridge, Finn Stokes, Ross D. Young, James Zanotti
PPublicising Lattice Field Theory throughVisualisation
James Biddle, Josh Charvetto, Waseem Kamleh, Derek Leinweber ∗ , Helen Piercy,Ethan Puckridge, Finn Stokes, Ross D. Young ∗ , James Zanotti † Centre for the Subatomic Structure of Matter, Department of Physics,The University of Adelaide, SA 5005, AustraliaE-mail: [email protected]
The gluon field configurations that form the foundation of every lattice QCD calculation con-tain a rich diversity of emergent nonperturbative structure. Visualisations of these phenom-ena not only serve to explain the concept of a nontrivial vacuum but also entertain a diverseaudience from research funding panels to the next generation of science enthusiasts. In thisbrief review, a collection of QCD-vacuum visualisations is presented including the structure ofchromo-electromagnetic fields, centre-cluster evolution at finite temperature, the structure of pro-jected centre vortices, and novel correlations between the electromagnetic fields of QED and thechromo-electromagnetic fields of QCD in QED+QCD dynamical-fermion simulations from theQCDSF collaboration.
The 36th Annual International Symposium on Lattice Field Theory - LATTICE201822-28 July, 2018Michigan State University, East Lansing, Michigan, USA. ∗ Speaker. † This research is supported with supercomputing resources provided by the Phoenix HPC service at the Universityof Adelaide and the National Computational Infrastructure (NCI) supported by the Australian Government. This researchis supported by the Australian Research Council through Grants No. DP140103067, DP150103164, and LE160100051. c (cid:13) Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/ a r X i v : . [ h e p - l a t ] M a r attice Field Theory Visualisation Derek Leinweber
1. Understanding Complexity through Visualisation
Deep insight into the mechanisms giving rise to quantum phenomena can be obtained throughthe visualisation of the complex scientific data sets considered in theoretical computational-physicscalculations. These are insights that would otherwise remain hidden in the typical gigabyte datasets of modern quantum field theory. If one can see what’s going on, it is easy to share this newunderstanding with a broad audience. In this sense, a picture is worth a thousand equations.For 20 years, the Centre for the Subatomic Structure of Matter (CSSM) has aimed to reveal thequantum phenomena of the nontrivial vacuum that underpins every calculation in lattice QCD. Thefocus is on displaying the results of genuine calculations and creating new insights into the funda-mental mechanisms that give rise to the observed phenomena. Visualisations of these phenomenanot only serve to explain the novel concept of a nontrivial vacuum but also inform and entertain adiverse audience from researchers in the field to the next generation of science enthusiasts.These data sets contain a rich diversity of emergent structure and a variety of approaches torevealing this structure has been explored. In this presentation, four approaches to understandingQCD vacuum structure are presented. Each approach is illustrated by animations which are avail-able via YouTube, enabling easy dissemination through social media. The original HD-streamingformat videos have also been placed on line. In the following, references contain active URL’s tothese animations.
2. Structure of the QCD Vacuum
Among the earliest of CSSM visualisations are animations of the Euclidean action density andthe topological charge density of gluon field configurations [1]. Calculations were based on pureSU(3) gluon dynamics with the standard Wilson action at β = . ×
36 lattice. The firstcoordinate was used for the time axis creating a 24 ×
36 spatial volume with a lattice spacing of 0.1fm. It is these calculations that captured the attention of Prof Frank Wilczek as he prepared his 2004Nobel Prize lecture. Ref. [2] provides a link to the
QCD Lava Lamp animation that appeared in hisNobel Lecture [3]. In support of the Nobel Lecture a web page incorporating the best algorithmsand visualisation techniques of the time was created to engage the public’s interest [4]. Since thenthese images and animations have appeared in popular-science publications, YouTube channels[5, 6], public talks and lectures, conference presentations, journal articles, annual reports, grantapplications, school visits [7] and newspaper articles.In this report, a new animation [8] is presented drawing on the legacy calculations of theNobel Lecture and providing new insights into the structure of the eight chromo-electric and eightchromo-magnetic fields. Correlations between the energy density, topological charge density andthe 16 vector fields are explored. The HD-streaming version is available via the link in Ref. [9].Calculations of the chromo-electromagnetic fields proceed via the O ( a ) -five-loop improvedfield-strength tensor, F µν , designed to ensure the most local 1 × × O ( a ) -three-loop improved action [11], ensuring the lattice operators are accurate whilepreserving topological structure within the gauge fields. After assigning the electric and magnetic1 attice Field Theory Visualisation Derek Leinweber
Figure 1:
Frames from the animation of Refs. [8, 9] illustrating the energy density (left) and one of thechromo-magnetic fields composing the nontrivial QCD vacuum. fields in the Euclidean field-strength tensor for the case with the first coordinate playing the role oftime, the eight fields are extracted via a trace with the Gell-Mann matrices.The associated animation [8, 9], illustrates the reduction of the energy density of the gluonfield in the first 25 frames of the animation and then displays the time dependence over the 24frames of the periodic lattice. Areas of high energy density are rendered in red and regions ofmoderate energy density are rendered in blue. Low-energy regions are not rendered so we can seeinto the volume. Subsequently, the eight chromo-electric and eight chromo-magnetic gluon fieldsgiving rise to the energy density are illustrated in Landau gauge [12]. Here the colour and lengthof the arrows describe the magnitude of the vector fields. Figure 1 displays two frames from theanimation. Finally, the animation presents correlations with the topological charge density withregions of positive density rendered in red through yellow and regions of negative density renderedblue through cyan.
3. Visualisation of Centre Clusters in Local Polyakov Loops
In Ref. [13] an anisotropic gauge action was used to explore the evolution of coherent centredomains in the gluon field under both temperature and the Hybrid Monte Carlo (HMC) updatealgorithm. Centre clusters are defined in terms of the complex-valued local Polyakov loop whoseexpectation value acts as an order parameter for the finite temperature phase transition in QCD.It has an expectation value of zero in the confined phase and a nonzero expectation value in thedeconfined phase [14]. The local Polyakov loop is defined as L ( (cid:126) x ) : = Tr (cid:18) P exp (cid:20) ig (cid:90) d x A ( x ) (cid:21)(cid:19) = Tr N t ∏ t = U ( t ,(cid:126) x ) = ρ ( (cid:126) x ) e i φ ( (cid:126) x ) , where it is decomposed into a phase, φ ( (cid:126) x ) and a magnitude, ρ ( (cid:126) x ) in the final expression. Boththe proximity of the phase to one of the cube-roots of one and the magnitude are considered invisualising the structure of the centre domains of the gluon field. In either case, the most proximalcube root of one to the phase is indicated by the use of colour.To investigate the larger-scale behaviour of the clusters, small scale noise is removed from thevisualisation by performing four sweeps of stout-link smearing prior to calculating the Polyakovloops. Fig. 2 illustrates two different ways of defining the clusters. In Fig. 2b, clusters are renderedwhere the phase φ ( (cid:126) x ) is within some small window around each centre phase, and the rest ofthe volume is rendered transparent. The evolution of these clusters with HMC simulation time is2 attice Field Theory Visualisation Derek Leinweber (a) Defined by phase (b) Defined by magnitude
Figure 2:
Centre clusters on a gauge field configuration at T = . ( ) T C . Similar structure is revealed forcentre clusters defined as regions proximal to a single centre phase, and as regions with a larger magnitude.Four sweeps of stout-link smearing are applied to the gauge links prior to calculating the Polyakov loops.The length of each side of the cubic volume is 2.4 fm. presented in Refs. [15, 16], showing how centre clusters are slowly moving. The animation [15, 16]reveals correlations in the centre clusters persisting for approximately 5 seconds corresponding to25 HMC trajectories. The temperature dependence of the centre-cluster structure is also exploredin these animations where a single phase eventually dominates above the critical temperature. InFig. 2b, and the animation of Ref. [17, 18], the clusters are rendered where the magnitude ρ ( (cid:126) x ) isabove some threshold.These fundamental structures support the concept of hadrons being described as a quark coredressed by a meson cloud. Within these coherent centre domains, colour-singlet quark-antiquarkpairs or three-quark triplets have a finite energy and are spatially correlated. Thus, these fundamen-tal domains govern the size of the quark cores of hadrons. As one domain dominates the vacuumabove the critical temperature, the correlation length diverges and quarks become deconfined.
4. Structure of Projected Centre Vortices in the Nontrivial QCD Vacuum
Recent research is now exposing the centre-vortex structure of nonperturbative gluon-fieldconfigurations to be the most fundamental aspect of nonperturbative vacuum structure giving riseto both confinement and dynamical chiral-symmetry breaking. Removal of SU(3) centre vorticesremoves confinement, while consideration of the vortices alone provides confinement [19]. Sim-ilarly, removal of vortices suppresses the infrared enhancement of the gluon propagator, whileconsideration of the vortices alone provides the well-known infrared enhancement [20]. Studiesof the nonperturbative quark propagator provide evidence that centre vortices underpin dynamicalchiral symmetry breaking [21], and the removal of centre vortices from the gluon fields restoreschiral symmetry [22]. Centre vortices are the seeds of dynamical chiral symmetry breaking.In light of the importance of these most fundamental aspects of QCD vacuum structure, visu-alisations of the complex structures formed by the projected centre vortices in SU(3) gauge theoryhave been presented in Ref. [23]. Here we explore their correlation with the topological charge den-sity of the gluon fields and present a new animation [24, 25] showcasing a prevalence of branchingpoints in the flow of centre charge that look like monopole or anti-monopole contributions. De-tails of the identification of projected centre vortices and the techniques used to render them are3 attice Field Theory Visualisation
Derek Leinweber
Figure 3: The projected centre-vortex structure of the gluon field.
The flow of centre charge is illustratedby the red and blue jets. The motion of the jets through time-oriented plaquettes is indicated by the orangeand cyan arrows. The correlation of the vortex lines with the topological charge density is examined byvolume-rendering the topological charge density in a translucent manner. Additional details are available inRef. [23]. (Click on the image to activate it in Adobe Reader. Click and drag to rotate, Ctrl-click to translate,Shift-click or mouse wheel to zoom. Right click to access the “Views” menu.) described in Ref. [23] of these proceedings. The topological charge is determined using the tech-niques of Sec. 2 with eight sweeps of O ( a ) -three-loop improved cooling [11].The structure of projected centre vortices and their correlation with the topological charge den-sity is illustrated in Fig. 3. Inspection of the vortices reveals the flow of centre charge, intersectionpoints and a prevalence of branching points that look like monopole or anti-monopole contribu-tions. An engaging presentation suitable for outreach activities is presented in the animation ofRef. [24] with the original HD-streaming animation available via Ref. [25].
5. Interplay of QED and QCD in the Nontrivial Vacuum
The QCDSF collaboration have generated gauge field configurations incorporating the dynam-ical effects of both QCD and QED [26, 27]. As the dynamics of the QCD fields include the creationof quark-antiquark pairs, their electric charge – enhanced by a factor of 10 in the simulations – par-ticipates in a dynamical manner through QED interactions. Here we consider the 24 ×
48 lattice To interact with Fig. 3, open this pdf document in Adobe Reader 9 or later. Linux users should install Adobeacroread version 9.4.1, the last edition to have full 3D support. From the “Edit” menu, select “Preferences...” and ensure“3D & Multimedia” is enabled and “Enable double-sided rendering” is selected. attice Field Theory Visualisation Derek Leinweber
Figure 4:
Frames from the animation of Refs. [28, 29] illustrating the topological charge density of QCDand the electric charge density of QED (left) with the QED magnetic field superposed (right). Regions ofsignificant topological charge density are rendered in red through yellow (blue through cyan) for positive(negative) values of the density. Regions of large electric charge density are rendered in red (purple) forpositive (negative) charge and the associated magnetic field is illustrated by the vector field. at the flavor-symmetric point with a lattice spacing of 0.068 fm [26]. The calculations of the fieldsproceed in a manner analogous to that presented in Sec. 2.There is an interesting relationship between the electric charge density, obtained through thedivergence of the electric field, and the topological charge density of QCD. As the electric chargemoves, magnetic fields are created in the vacuum. The movement of electric charge relative tothe magnetic field, particularly when that charge is influenced by the topological charge density ofQCD is of particular interest. Figure 4 presents two frames from the animation of Refs. [28, 29].In this animation the topological charge density is compared with the electric charge density ofquark-antiquark pairs and the magnetic field they create.
References [1] D. B. Leinweber,
Visual QCD Archive
QCD Lava Lamp
Visualizations of Quantum Chromodynamics
Empty Space is NOT Empty
Your Mass is NOT From the Higgs Boson
Origin of Mass
Structure of the QCD Vacuum , 2019.https://youtu.be/WZgZI5vymiM.[9] D. B. Leinweber and E. Puckridge,
Structure of the QCD Vacuum attice Field Theory Visualisation Derek Leinweber[10] S. O. Bilson-Thompson, D. B. Leinweber and A. G. Williams,
Highly improved lattice field strengthtensor , Annals Phys. (2003) 1 [ hep-lat/0203008 ].[11] S. O. Bilson-Thompson et al.,
Comparison of |Q| = 1 and |Q| = 2 gauge-field configurations on thelattice four-torus , Annals Phys. (2004) 267 [ hep-lat/0306010 ].[12] F. D. R. Bonnet, P. O. Bowman, D. B. Leinweber, A. G. Williams and D. G. Richards,
Discretizationerrors in Landau gauge on the lattice , Austral. J. Phys. (1999) 939 [ hep-lat/9905006 ].[13] F. M. Stokes, W. Kamleh and D. B. Leinweber, Visualizations of coherent center domains in localPolyakov loops , Annals Phys. (2014) 341 [ ].[14] C. Gattringer and A. Schmidt,
Center clusters in the Yang-Mills vacuum , JHEP (2011) 051[ ].[15] F. M. Stokes, W. Kamleh and D. B. Leinweber, Centre Domains in the QCD Vacuum - SmearedPhase , 2014. https://youtu.be/KkiOQOOb69k.[16] F. M. Stokes, W. Kamleh and D. B. Leinweber,
Centre Domains in the QCD Vacuum - SmearedPhase
Centre Domains in the QCD Vacuum - SmearedMagnitude , 2014. https://youtu.be/T4sRON6uOz0.[18] F. M. Stokes, W. Kamleh and D. B. Leinweber,
Centre Domains in the QCD Vacuum - SmearedMagnitude
Vortex structures in pure SU(3) lattice gauge theory , Phys. Rev.
D69 (2004) 014503[ hep-lat/0307030 ].[20] J. C. Biddle, W. Kamleh and D. B. Leinweber,
Gluon propagator on a center-vortex background , Phys. Rev.
D98 (2018) 094504 [ ].[21] D. Trewartha, W. Kamleh and D. Leinweber,
Evidence that centre vortices underpin dynamical chiralsymmetry breaking in SU(3) gauge theory , Phys. Lett.
B747 (2015) 373 [ ].[22] D. Trewartha, W. Kamleh and D. Leinweber,
Centre vortex removal restores chiral symmetry , J. Phys.
G44 (2017) 125002 [ ].[23] J. C. Biddle, W. Kamleh and D. B. Leinweber,
Visualizations of Centre Vortex Structure in LatticeSimulations , PoS
LATTICE2018 (2018) 256 [ ].[24] J. Biddle, W. Kamleh, D. Leinweber and H. Piercy,
Centre Vortices in the Gluon Field of the QCDVacuum , 2019. https://youtu.be/CDdmx989quA.[25] J. Biddle, W. Kamleh, D. Leinweber and H. Piercy,
Centre Vortices in the Gluon Field of the QCDVacuum
Isospin splittings of meson and baryon masses from three-flavor lattice QCD +QED , J. Phys.
G43 (2016) 10LT02 [ ].[27] R. Horsley et al.,
QED effects in the pseudoscalar meson sector , JHEP (2016) 093[ ].[28] J. Charvetto, W. Kamleh, D. Leinweber, R. Young and J. Zanotti, Interplay of QuantumElectrodynamics and Quantum Chromodynamics in the Nontrivial Vacuum , 2019.https://youtu.be/9TJe1Pr5c9Q.[29] J. Charvetto, W. Kamleh, D. Leinweber, R. Young and J. Zanotti,
Interplay of QuantumElectrodynamics and Quantum Chromodynamics in the Nontrivial Vacuum