Two-point string amplitudes

Harold Erbin,Juan Maldacena,Dimitri Skliros

doi:10.1007/jhep07(2019)139

Abstract

We show that the two-point tree level amplitude in string theory in flat space is given by the standard free particle expression.

Highlights

Open stringsIn order to derive a formal expression for the volume of the residual group, let us consider the three-point function
Where all operators are on the σ = 0 boundary and CD2 is the partition function of all worldsheet fields with an appropriate power of the string coupling determined by unitarity as in [1]
The partition function does not depend on x0, the zero mode of X0

Summary

Open strings

In order to derive a formal expression for the volume of the residual group, let us consider the three-point function. We integrate over the third point by inserting an integrated vertex operator, W2 = dτ V2(τ, 0), and after dividing by the volume of the residual group we get [1], A3 = go3CD2 V1(−∞)V2(0)V3(∞) D2 = go3CD2 dτ Vol(Res) V1(−∞)V2(τ )V3(∞) D2 (2.1). By noticing that the integrand is independent of τ we conclude that the volume of the residual conformal group (after fixing two points) is the formal expression. We can consider the following classical solution for X0, X0 = 2α′k0τ + x0 This can be viewed as the classical solution we expand around in order to compute the path integral.

Closed strings

Short review of the Fadeev Popov trick

Using the Fadeev Popov trick for the open string two-point amplitude

Discussion