Physics Letters B 311 (1993) 433-440 North-Holland PHYSICS LETTERS B Semiclassical tunneling in 1 + 1 dimensional string theory Juhan Lee i and Paul F Mende 2 Department of Phystcs, Brown Umverstty, Provtdence, RI 02912, USA Received 1 November 1992 Editor M Dine We describe time-dependent Iunnehng of massless particles in 1+ 1 dimensional string field theory PolchInski'sdescription of the classical soluUons in terms of the Fermi sea is used to identify the leading instanton contribution connecting the two half- lines The field theory Lagrangianis proportional to l/g2, where g ~sthe string coupling constant, but the S-matrix for tunneling from one half-line to the other behaves as exp(-C/g) We note the constant C involves curious boundary contributions and observe that a prescription connecting the two half-hnes unifies treatments of the Fermi level above and belowthe barrier 1. Introduction String theory promises to provide a consistent the- ory of gravitational and quantum physics Two-di- mensional string theories (for a review see ref [ 1 ] ) provide solvable models in which many of the essen- tial properties can be explored Among them are non- perturbatlve effects, spacetlme singularities and ho- rizons, time-dependent backgrounds, background in- dependence, string symmetries, and string symmetry breaking Other effects, such as the full role of non- locality, are probably not among them since in two dimensions, where the string has no transverse oscil- lations, it resembles local point-particle field theory as much as it can This is unfortunate since the ex- tended nature of strings is likely the key to a quantum theory of gravitation )n higher dimensions Never- theless there is a great deal to be learned and, as em- phasized by Shenker [2] reason to believe that non- perturbatIve effects such as tunneling may indeed share the behavior characteristic of higher dimen- sional theories In this paper we examine one of the intriguing as- pects of one of the richer such theories yet to be Research supported in part by the U S Department of Energy under contract DE-AC02-76-ER03130 E-mail address lee@het brown edu 2 E-malladdress mende@het brown edu solved, the string field theory for c= 1 This theory perturbatlvely describes a massless scalar excitation (possibly augmented by discrete contributions) hv- ing on one of two half-hnes We shall consider these to be weakly coupled through the repulsive potential barrier which defines the theory and compute the amplitude for excitations to tunnel from one half-line to the other This is done for the semiclasslcal limit of the collective field Lagrangian by the standard method of solving the Euclidean time field equations with the boundary conditions appropriate to tunnel- ing This is all the more straightforward since Pol- chlnskl has given a general solution for real-time evo- lution of the classical fields We show that tunneling amplitudes behave as exp(-C/g), where C is a constant, even though the LagrangIan IS proportional to 1/g2 The reason for this is found to be a simple vestige of the underlying fermlons which have all but disappeared in the pas- sage to the collective field We give an expression for C in terms of an arbitrary initial field configuration Curiously C has both a local contribution, largely in- dependent of the details of the initial field, and a non- local contribution The latter piece arises from boundary terms in the LagrangIan which mix left- and right-movers These terms are absent in the Hamll- tonian We also give examples of algebraic solutions to the field equations, which might be explicit enough to help unravel the role of the boundary effects, al- Elsevier SciencePubhshers B V 433