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

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• Quantum Fluctuations and Geometry: From Graph Counting to Ricci Flow
• A note on tachyon actions in string theory
• Closed String Tachyon Driving $f(R)$ Cosmology
• A proposal for studying off-shell stability of vacuum geometries in string theory
• The Wasserstein geometry of non-linear sigma models and the Hamilton-Perelman Ricci flow