Tachyon condensates, carrollian contraction of Lorentz group, and fundamental strings

We study the rolling tachyon condensate in the presence of a gauge field. The generic vacuum admits both a rolling tachyon, (T) over dot, and a uniform electric field, (E) over right arrow, which together affect the effective metric governing the fluctuations of open string modes. If one suppresses the gauge field altogether, the light-cone collapses completely. This is the carrollian limit, with vanishing speed of light and no possible propagation of signals. In the presence of a gauge field, however, the lightcone is squeezed to the shape of a fan, allowing propagation of signals along the direction of +/-(E) over right arrow at speed |(E) over right arrow| less than or equal to 1. This shows that there are perturbative degrees of freedom propagating along electric flux lines. Such causal behavior appears to be a very general feature of tachyon effective lagrangian with runway potentials. We speculate on how this may be connected to appearance of fundamental strings.