On the domain of string perturbation theory
- 1 December 1989
- journal article
- Published by IOP Publishing in Classical and Quantum Gravity
- Vol. 6 (12) , 1791-1803
- https://doi.org/10.1088/0264-9381/6/12/008
Abstract
For a large class of effectively closed surfaces, it is shown that the only divergences in string scattering amplitudes at each order in perturbation theory are those associated with the coincidence of vertex operators and the boundary of moduli space. This class includes all closed surfaces of finite genus, and infinite-genus surfaces which can be uniformised by a group of Schottky type. While the computation is done explicitly for bosonic strings in their ground state, it can also be extended to excited states and to superstrings. The properties of these amplitudes lead to a definition of the domain of perturbation theory as the set of effectively closed surfaces. The implications of the restriction to effectively closed surfaces on the behaviour of the perturbation series are discussed.Keywords
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