4-dimensional Lattice Gauge Theories Research Articles

Complex renormalization group flows for 2D nonlinearO(N)sigma models

Motivated by recent attempts to find nontrivial infrared fixed points in 4-dimensional lattice gauge theories, we discuss the extension of the renormalization group transformations to complex coupling spaces for $O(N)$ models on $L\ifmmode\times\else\texttimes\fi{}L$ lattices, in the large-$N$ limit. We explain the Riemann sheet structure and singular points of the finite $L$ mappings between the mass gap and the 't Hooft coupling. We argue that the Fisher's zeros appear on ``strings'' ending approximately near these singular points. We show that for the spherical model at finite $N$ and $L$, the density of states is stripwise polynomial in the complex energy plane. We compare finite volume complex flows obtained from the rescaling of the ultraviolet cutoff in the gap equation and from the two-lattice matching. In both cases, the flows are channelled through the singular points and end at the strong coupling fixed points, however strong scheme dependence appear when the Compton wavelength of the mass gap is larger than the linear size of the system. We argue that the Fisher's zeros control the global properties of the complex flows. We briefly discuss the implications for perturbation theory, proofs of confinement, and searches for nontrivial infrared fixed points in models beyond the standard model.

Independent Plaquette Trial Action for 4-Dimensional Lattice Gauge Theory

Based on the explicit expressions of the plaquette formulations, the independent plaquette trial action for 4-dimensional lattice gauge theory is introduced. As an example, the mean plaquette energy for the lattice gauge theory is calculated by using action variational approach with the independent trial action. The results are in good agreement with the Monte Carlo results in the strong coupling and the crossover region, and the curve is smooth in the whole region, which show that 4-dimensional theory has only a single, confining phase. The unwanted discontinuity of given by the single link trial action, which is used in the earlier variational calculations has been avoided.

Random surface Monte Carlo determination of the critical exponent ν in Z(5) and Z(8) lattice gauge theories

Abelian lattice gauge theories may be efficiently expanded into a sum over two-dimensional surfaces made up of plaquettes with weights that factorize over the plaquettes. We have performed a high-precision Monte Carlo simulation of this expansion for two discrete 4-dimensional lattice gauge theories, Z(5) and Z(8). Using a finite size scaling analysis we find the critical exponents to be ν z(5) = 0.328 (5) and ν z(8) = 0.335 (5). This supports the conjecture that these theories are in the same universality class as U(1).

Modified action glueballs

The mass of the 0 + glueball in 4-dimensional lattice gauge theory with a mixed SU(2)-SO(3) action is obtained via Monte Carlo. We work in a region far from the critical end point in the phase diagram, with an action partly motivated by renormalization group flows in the Migdal-Kadanoff approximation. A large- N resummation of perturbation theory is used to show that the mass gap scales as predicted by the perturbative renormalization group. Independent of this, our results show that the ratio of the glueball mass to the square root of the string tension, obtained from a previous Monte Carlo, is a renormalization group invariant.

Phase transitions and local minima of the action

We present evidence that non-trivial, non-degenerate local minima of the one-plaquette action in 4-dimensional lattice gauge theories with continuous gauge groups, give rise to a line of first-order “discreteness” phase transitions, persisting down to the region where the non-trivial minima become unstable. We illustrate this mechanism by analysing an extended model, involving the traces in the fundamental and six representation of SU(3), in which neither the topology, nor the group theoretic properties of the centre seem to play any role.