Instantons at work

Abstract

The aim of this review is to demonstrate that there exists a coherent picture of strong interactions, based on instantons. Starting from the first principles of QCD - via the microscopic mechanism of spontaneous chiral symmetry breaking - one arrives to a quantitative description of light hadron properties, with no fitting parameters. The discussion of the importance of instanton-induced interactions in soft high-energy scattering is new.

Figures (13)

• Figure 1: The lattice-simulated potential between static quarks in pure glue theory BSW exceeds $m_\pi$ at the separation of $0.26\,{\rm fm}$ (left). The screening of the linear potential by dynamical quarks is clearly seen in simulations at high temperatures but below the phase transition KLP (right). As one lowers the pion mass the string breaking happens at smaller distances; the scale is $\sqrt{\sigma}\simeq 425\,{\rm MeV}\simeq (0.47\,{\rm fm})^{-1}$.
• Figure 2: Potential energy of the gluon field is periodic in one direction and oscillator-like in all other directions in functional space.
• Figure 3: "Cooling" the normal zero-point oscillations reveals large fluctuations of the gluon field, which were identified with instantons and anti-instantons with random positions and sizes CGHN. The left column shows the action density and the right column shows the topological charge density for the same snapshot.
• Figure 4: An illustration of how dyons can induce the confinement-deconfinement phase transition. We plot the sum of the perturbative (\ref{['Tpot']}) and dyon-induced (\ref{['Vdyon']}) potentials as function of $\phi/2\pi T$. We choose the constants $\Lambda=280\,{\rm MeV}$, $c=2$. The curves corresponds to temperatures $T=250\,{\rm MeV}$ (solid), $T=280\,{\rm MeV}$ (long-dashed) and $T=400\,{\rm MeV}$ (short-dashed). In this example, the phase transition is at $T_c=280\,{\rm MeV}$.
• Figure 5: Schematic eigenvalue distribution of the Dirac operator. The solid lines are the zero mode and free contributions, the dashed line an estimate of the full spectrum.