The Fixed Points of RG Flow with a Tachyon

Abstract

We examine the fixed points to first-order RG flow of a non-linear sigma model with background metric, dilaton and tachyon fields. We show that on compact target spaces, the existence of fixed points with non-zero tachyon is linked to the sign of the second derivative of the tachyon potential $V^{\prime \prime }(T)$ (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 are possible. On non-compact target spaces, we introduce a small non-zero tachyon and compute the correction to the Euclidean 2d black hole (cigar) solution at second order in perturbation theory with a tachyon potential containing a cubic term as well. The corrections to the metric, tachyon and dilaton are well-behaved at this order and tachyon `hair' persists. We also briefly discuss solutions to the RG flow equations in the presence of a tachyon that suggest a comparison to dynamical fixed point solutions obtained by Yang and Zwiebach.

15 pages, 1 figure, journal version

References in corpus (1)

• Singularities and Closed String Tachyons

Cited by in corpus (3)

• Cosmologies with Null Singularities and their Gauge Theory Duals
• Ricci flows, wormholes and critical phenomena
• A note on tachyon actions in string theory