Tropical branes

A bstract We investigate canonically quantized open string solutions associated to the analytically continued action for the recently proposed tropical limit of topological A-type models, tropological sigma models , with various tropical versions of boundary conditions. These solutions naturally give rise to a non-relativistic counterpart of branes, which we name tropical branes . We provide a worldsheet description of these tropical branes. We find that instead of the usual string spectrum of infinitely many coupled harmonic oscillators, the Hamiltonian for tropical branes describes an infinite tower of increasingly massive asymptotic string states. This results supports the claim that a tropicalization of the worldsheet formulation of string theory gives a viable description for the asymptotic behavior of string amplitudes and their non-equilibrium extensions.