Topology and metastability in the lattice Skyrme model

Abstract

We offer the Skyrme model on a lattice as an effective field theory - fully quantized - of baryon-meson interactions at temperatures below the chiral phase transition. We define a local topological density that involves the volumes of tetrahedra in the target space S^3 and we make use of Coxeter's formula for the Schlafli function to implement it. This permits us to calculate the mean-square radius of a skyrmion in the three-dimensional lattice Skyrme model, which may be viewed as a Ginzburg-Landau effective theory for the full quantum theory at finite temperature. We find that, contrary to expectations, the skyrmion shrinks as quantum and thermal fluctuations are enhanced. We ascribe this to a large number of metastable states that become accessible as the temperature is raised.