Relevant deformations in open string field theory: a simple solution for lumps

Abstract

We propose a remarkably simple solution of cubic open string field theory which describes inhomogeneous tachyon condensation. The solution is in one-to-one correspondence with the IR fixed point of the RG-flow generated in the two-dimensional worldsheet theory by integrating a relevant operator with mild enough OPE on the boundary. It is shown how the closed string overlap correctly captures the shift in the closed string one point function between the UV and the IR limits of the flow. Examples of lumps in non-compact and compact transverse directions are given.

Comments on lump solutions in SFT

“…The corresponding Q and K will be called Q ND , K ND , and Q DN , K DN , respectively. With these new entries it seems to be more appropriate to rewrite (15) as…”

“…In [15] a general method has been proposed to obtain new exact analytic solutions in open string field theory, and in particular solutions that describe inhomogeneous tachyon condensation. The method consists in translating an exact renormalization group (RG) flow generated in a two-dimensional world-sheet theory by a relevant operator, into the language of OSFT.…”

“…analytic solutions interpretable as lower dimensional branes (meant to complete the analytic proof of the three conjectures by Sen [14]), is instead poorer. There have been essentially two attempts to find such analytic solutions: the first is the so-called BMT proposal [15][16][17], the second is the most recent one formulated in [18], which we will refer to as EM. They are both modeled on the Erler-Schnabl (ES) solution [5], an alternative simpler formulation of the original tachyon vacuum (TV) solution (for recent reviews on the whole subject, see [19][20][21][22]).…”

“…By the latter we mean that one can derive a variety of backgrounds as solutions of the SFT equation of motion, although such an equation of motion is formulated in a specific background (the D25-brane). The only way to clarify these issues is to implement the EM approach in an explicit 2D field theory formulation similar to the one in [5,12,15], consistent with the original one in which the SFT is formulated. The first part of our paper is an attempt in this direction.…”

Open superstring field theory I: gauge fixing, ghost structure, and propagator

“…Classical solutions that represent changes of the open string background are of particular interest, and considerable progress was made in this subject in the last few years (see, for example, [1,2,3,4,5]). …”