Timelike boundary Liouville theory

Abstract

The timelike boundary Liouville (TBL) conformal field theory consisting of a negative norm boson with an exponential boundary interaction is considered. TBL and its close cousin, a positive norm boson with a non-hermitian boundary interaction, arise in the description of the c = 1 accumulation point of c < 1 minimal models, as the worldsheet description of open string tachyon condensation in string theory and in scaling limits of superconductors with line defects. Bulk correlators are shown to be exactly soluble. In contrast, due to OPE singularities near the boundary interaction, the computation of boundary correlators is a challenging problem which we address but do not fully solve. Analytic continuation from the known correlators of spatial boundary Liouville to TBL encounters an infinite accumulation of poles and zeros. A particular contour prescription is proposed which cancels the poles against the zeros in the boundary correlator d(ω) of two operators of weight ω 2 and yields a finite result. A general relation is proposed between two-point CFT correlators and stringy Bogolubov coefficients, according to which the magnitude of d(ω) determines the rate of open string pair creation during tachyon condensation. The rate so obtained agrees at large ω with a minisuperspace analysis of previous work. It is suggested that the mathematical ambiguity arising in the prescription for analytic continuation of the correlators corresponds to the physical ambiguity in the choice of open string modes and vacua in a time dependent background. *

Bosonic D-brane Effective Action in Linear Dilaton Background

“…As was shown in [31] the time-like part of the worldsheet CFT is the Timelike Boundary Liouville theory [33] − 1 2π…”

“…We mean that it would be very interesting to perform the same analysis in the supersymmetric case as well. In order to do this we should firstly understand the time-like form of the N = 1 super Liouville theory [43,44,45], following [33]. We hope to return to this problem in future.…”

The tachyon at the end of the universe

“…As explained for example in [41], the two-point function of two negative frequency modes in the bulk is…”

“…In [20,41,22] subtleties were encountered in a prescription for analytically continuing higher point amplitudes from spacelike Liouville theory. It will be interesting to study these issues in more detail in our case, keeping careful track of the vacuum in which the computations are being done in the various prescriptions for continuing the amplitudes.…”

Closed string tachyon condensation and worldsheet inflation

“…In this regard, note also that the two signs of open string tachyon condensate also have very different physics [36,37], with an interpretation similar to the closed string dynamics above. Some aspects of the worldsheet physics of the µ < 0 boundary cosmological term in the bosonic string were explored in [38] (for a particular inhomogeneous condensate, see [37] and section 3 below). One may be able to ascribe some of the pathologies of their results to the fact that the open string condensate is heading in the bottomless direction of the spacetime effective potential.…”