1992/06/23 by Barton Zwiebach, W. Siegel
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1016/0550-3213(93)90388-6
published as Nucl.Phys.B390:33-152,1993 · 115 pages, 5 figures (not included). IASSNS-HEP-92/41
arxiv created 1992/06/23 · arxiv updated 2010/11/01
The complete quantum theory of covariant closed strings is constructed in detail. The action is defined by elementary vertices satisfying recursion relations that give rise to Jacobi-like identities for an infinite chain of string field products. The genus zero string field algebra is the homotopy Lie algebra L_∞, and the higher genus algebraic structure implies the Batalin-Vilkovisky (BV) master equation. From these structures on the off-shell state space, we show how to derive the L_∞ algebra, and the BV equation on physical states, recently constructed in d=2 string theory. The string diagrams are surfaces with minimal area metrics, foliated by closed geodesics of length 2π. These metrics generalize quadratic differentials in that foliation bands can cross. The string vertices are succinctly characterized; they include the surfaces whose foliation bands are all of height smaller than 2π. --While this is not a review paper, an effort was made to give a fairly complete and accessible account of the quantum closed string field theory.--