Exact Tachyon Potential from the Wilsonian Renormalization Group

The derivative expansion of the Wilsonian renormalization group generates additional terms in the effective β-functions not present in the perturbative approach. Applied to the nonlinear σ model, to lowest order the vanishing of the β-function for the tachyon field generates an equation analogous to that found in open string field theory. Although the nonlinear term depends on the cut-off function, this arbitrariness can be removed by a rescaling of the tachyon field.