Abstract
The quantum Batalian-Vilkovisky master action for closed string field theory consists of kinetic term and infinite number of interaction terms. The interaction strengths (coupling constants) are given by integrating the off-shell string measure over the distinct string diagrams describing the elementary interactions of the closed strings. In the first paper of this series, it was shown that the string diagrams describing the elementary interactions can be characterized using the Riemann surfaces endowed with the hyperbolic metric with constant curvature −1. In this paper, we construct the off-shell bosonic-string measure as a function of the Fenchel-Nielsen coordinates of the Teichmüller space of hyperbolic Riemann surfaces. We also describe an explicit procedure for integrating the off-shell string measure over the region inside the moduli space corresponding to the elementary interactions of the closed strings.
Highlights
We dedicate this paper to the memory of Maryam Mirzakhani who tragically passed away recently, and whose seminal ideas about the space of hyperbolic Riemann surfaces form some of the basic tools that we use in this work
The interaction strengths in closed string field theory are obtained by integrating the off-shell string measure, which is an mapping class group (MCG)-invariant object, over the region in the moduli space that corresponds to the Riemann surfaces describing the elementary interactions of the closed strings
The moduli space is the quotient of the Teichmuller space with the action of the mapping class group (MCG)
Summary
The quantum BV master action for closed string field theory is a functional of the fields and the antifields in the theory. The Riemann surfaces that belong to the string vertices must be equipped with a specific choice of local coordinates around each of its punctures. ∆ denotes the operation of taking a pair of punctures on a Riemann surface that belongs to the string vertex Vg−1,n+2 and gluing them via the special plumbing fixture relation (2.8). The geometric condition (2.7) demands that the set of Riemann surfaces that belong to the boundary of a string vertex having dimension, say d, must agree with the set of union of surfaces having dimension d obtained by applying the special plumbing fixture construction (2.8) to the surfaces belong to the lower dimensional string vertices only once, both in their moduli parameters and in their local coordinates around the punctures. Consider the tangent vectors of Pg,n that are the tangent vectors of the moduli space of Riemann surfaces equipped with the choice local coordinates that defines the section. Im(x) is the action for matter fields and Igh(b, c) is the actions for ghost fields. z is the global coordinate on R
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