Lattice QCD and String Theory

Abstract

Bosonic string formation in gauge theories is reviewed with particular attention to the confining flux in lattice QCD and its string theory description. Recent results on the Casimir energy of the ground state and the string excitation spectrum are analyzed in the Dirichlet string limit of large separation between static sources. The closed string-soliton (torelon) with electric flux winding around a compact dimension and the three-string with a Y-junction created by three static sources are also reviewed. It is shown that string spectra from lattice simulations are consistent with universal predictions of the leading operators from the derivative expansion of a Poincare invariant effective string Lagrangian with reparameterization symmetry. Important characterisitics of the confining flux, like stiffness and the related massive breather modes, are coded in operators with higher derivatives and their determination remains a difficult challenge for lattice gauge theory.

Figures (15)

• Figure 1: Strings and quark confinement
• Figure 2: Monte Carlo simulation of the first massless Goldstone excitation (upper two wavefunctions) and the second massive breather mode (lower two wavefunctions) in three-dimensional Z(2) lattice gauge theory are shown. The length of the string grows from$R / a=10$ to $R / a=100$ in lattice spacing units which on a physical scale, set by the string tension, corresponds to $R$ changing from 0.675 fm to 6.75 fm . Real time animations are constructed from the wavefunctions and energy eigenvalues of Euclidean simulations. Using Adobe Acrobat 6.0, a click within the black frame will start the animation including the $\mathrm{N}=3$ Goldstone excitation.
• Figure 3: Chart summarizing important properties of the three-dimensional Z(2) lattice gauge model and its dual transformation to the Ising model.
• Figure 4: Classical string solutions in the dual field variable$\phi$.
• Figure 5: The massive$\eta$ propagator with derivative interaction vertices leads to the effective local derivative expansion of the string Lagrangian for $\xi(\sigma, \tau)$.