The QCD VacuumHere you'll find images and animations of the quantum fluctuations of the vacuum of QuantumChromodynamics (QCD). These images have been created via supercomputer simulations of QCD on a 24

^{3}× 36 space-time lattice using a 128-node Thinking Machines CM5.

Viewing the AnimationsThe half-size animations view well in your browser. To view the full size animations I recommend xanim on UNIX platforms and Paint Shop Pro's Animation Shop on Windows platforms.

Publications

The following animations are referenced in the e-print entitled "Visualizations of the QCD Vacuum." Further details are provided in the Images and Animations section below.

- End View Animation of Cooling - Action Density - 1755 kb or Half Size - 579 kb
- End View Animation of Cooling - Topological Charge Density - 1704 kb or Half Size - 611 kb
- End View Animation of the Action Density in 4 Dimensions - 1616 kb or Half Size - 488 kb
- End View Animation of the Topological Charge Density - 1364 kb or Half Size - 503 kb
- Comparison of 5-Loop Improved and 1-Loop Gauge Actions - 3440 kb or
- Half Size - 1136 kb
Acknowledgments

My thanks to John Ahern, Frederic Bonnet, Sundance Bilson-Thompson, Patrick Fitzhenry, Greg Kilcup, Mark Stanford and Tony Williams for their contributions to making these images possible. Additional thanks to Francis Vaughan of the SACPC for generous supercomputer support and the DHPC Group for support in the development of parallel algorithms.

## Images and Animations

- Untouched Action - 37 kb
- The QCD vacuum is not empty. Rather it contains quantum fluctuations in the gluon field at all scales.

- A few sweeps of cooling - 58 kb
- To eliminate the short range perturbative fluctuations and reveal the interesting long-distance non-perturbative phenomena, the fields are "cooled" by an algorithm which smoothes the fields locally by considering nearest neighbor interactions.

- A few more sweeps of cooling - 63 kb
- Animation of Cooling - 4284 kb
- Half Size - 2194 kb

- See how the nonperturbative structure of the QCD vacuum is revealed by cooling. Each frame of this animation follows one sweep of cooling.

- Persistent lumps - 68 kb
- Despite many sweeps of cooling, there are areas in which the gluon field has not been reduced to zero.

- Emergence of Topological Charge - 96 kb
- Topological charge is a measure of the winding in the gluon field configuration. After seven sweeps of cooling, lumps in the topological charge density appear. The topological charge density can be positive (red) or negative (blue).

- Lumps in the Action - 86 kb
- After seven sweeps of cooling, lumps in the action density appear. The persistent lumps coincide in position with the topological charge density structure.

- Topological Charge Density after 14 sweeps - 92 kb

- Action Density after 14 cooling sweeps - 82 kb

- Topological Charge Density after 25 sweeps - 87 kb

- Action Density after 25 cooling sweeps - 77 kb

- Action Density Animation of a Highly Cooled Field in 4 Dimensions - 880 kb
- Half Size - 424 kb

- Instantons are four dimensional objects. This animation illustrates the fourth dimension by stepping through the fourth dimension of the periodic lattice. This is a good animation for seeing and understanding the structure of these 4 dimensional objects.

- Topological Charge Density Animation of a Highly Cooled Field - 726 kb
- Half Size - 351 kb

- This animation illustrates the fourth dimension of instantons by stepping through the fourth dimension of the periodic lattice. This is also a good animation for seeing and understanding the topological structure of these 4 dimensional objects.

- Animation of the Action Density in 4 Dimensions - 1543 kb
- Half Size - 520 kb

- This is the QCD "Lava Lamp." It is an excellent animation of the 4 dimensional structure of the long-distance aspects of the QCD vacuum.

- Animation of the Topological Charge Density - 1346 kb
- Half Size - 510 kb

- The QCD "Lava Lamp" for topological charge. This too is an excellent animation of the 4 dimensional structure of the long-distance aspects of the QCD vacuum.

- End View Animation of the Action Density in 4 Dimensions - 1616 kb
- Half Size - 488 kb

- Another view of the QCD "Lava Lamp."

- End View Animation of the Topological Charge Density - 1364 kb
- Half Size - 503 kb

- Topological charge animation viewed from the end of the lattice.

- Topological Charge Density after 100 sweeps - 93 kb

- Action Density after 100 cooling sweeps - 88 kb

- Untouched Topological Charge Density - 112 kb
- Fluctuations are at the scale of the lattice spacing.

- Animation of Cooling - Action Density - 1853 kb
- Half Size - 628 kb

- This animation and the following feature instanton anti-instanton annihilation. Watch the upper-left corner of the lattice.

- Animation of Cooling - Topological Charge Density - 1665 kb
- Half Size - 610 kb

- Here, one can see that the objects annihilating in the upper-left corner of the lattice have opposite topological charge densities.

- End View Animation of Cooling - Action Density - 1755 kb
- Half Size - 579 kb

- This animation and the following feature another instanton anti-instanton annihilation. This time we are watching the same field configuration but at a different time slice. Watch the upper-centre of the lattice.

- End View Animation of Cooling - Topological Charge Density - 1704 kb
- Half Size - 611 kb

- Here one can see the instanton wrapping around the anti-instanton as they annihilate in the upper-centre of the lattice.

- Comparison of 5-Loop Improved and 1-Loop Gauge Actions - 3440 kb
- Half Size - 1136 kb

- The first 30 frames illustrate cooling with the 5-loop over-improved action of de Forcrand
et al.The 31st frame shows the result of 30 sweeps of cooling with the standard 1-loop action. The remainder of the animation shows 1-loop cooling in reverse. The gauge field is from an order-a^{2}improved action on a 16^{3}× 32 space-time lattice.

- 3-loop Improved Q from 5-Loop Improved Cooling - 6512 kb
- Half Size - 2416 kb

- This animation illustrates the behavior of the topological charge density obtained from a three-loop improved definition of the field strength tensor (which has smaller
O(a^{6}) errors than four or five loop improved operators). Cooling proceeds via a five-loop improved estimate of the action. Instanton anti-instanton interactions are featured in the lower right-hand corner of the animation.

- 3-loop Improved Q for Highly Cooled Configuration - 504 kb
- Half Size - 328 kb

- This animation illustrates the fourth dimension of a highly cooled configuration with Q=-2 and S/S
_{0}=3.7. The topological charge density is obtained from a three-loop improved definition of the field strength tensor (which has smallerO(a^{6}) errors than four or five loop improved operators). Cooling proceeds via a three-loop improved estimate of the action.

- Artist's Rendition of a Proton - jpeg 152 kb
- gzip-compressed postscript - 1144 kb

- Three quarks indicated by red, green and blue spheres (lower left) are localized by the gluon field.

- A quark-antiquark pair created from the gluon field is illustrated by the green-antigreen (magenta) quark pair on the right. These quark pairs give rise to a
mesoncloud around the proton.

- The masses of the quarks illustrated in this diagram account for only 3% of the proton mass. The gluon field is responsible for the remaining 97% of the proton's mass and is the origin of mass in most everything around us.

- Experimentalists probe the structure of the proton by scattering electrons (white line) off quarks which interact by exchanging a quantum of light (wavy line) known as a photon.