The fixed points of RG flow with a tachyon

We examine the fixed points to first-order RG flow of a non-linear sigmamodel with background metric, dilaton and tachyon fields. We show that oncompact target spaces, the existence of fixed points with non-zero tachyon islinked to the sign of the second derivative of the tachyon potential $V''(T)$(this is the analogue of a result of Bourguignon for the zero-tachyon case).For a tachyon potential with only the leading term, such fixed points arepossible. On non-compact target spaces, we introduce a small non-zero tachyonand compute the correction to the Euclidean 2d black hole (cigar) solution atsecond order in perturbation theory with a tachyon potential containing a cubicterm as well. The corrections to the metric, tachyon and dilaton arewell-behaved at this order and tachyon `hair' persists. We also briefly discusssolutions to the RG flow equations in the presence of a tachyon that suggest acomparison to dynamical fixed point solutions obtained by Yang and Zwiebach.Comment: 15 pages, 1 figure, journal versio