Nuclear Physics B361 (1991) 519-538 North-Holland TWIST SYMMETRY AND OPEN-STRING WILSON LINES Massimo BIANCHI and August0 SAGNOTTI Dipartimento di Fisica, Universitd di Roma “Tor Vergata”, INFN- Sezione di Roma “Tar Vergata”, via E. Carnevale, 00173 Rome, Italy Received 28 December 1990 The Mobius amplitude plays an important role in open-string theories, since it determines which sectors of a given model consist of unoriented open strings. It also fixes the Chan-Paton representations of all their states, according to the behavior under the interchange of the ends of open strings (“twist”). In this paper we discuss the role played by conventional Wilson lines in Chan-Paton symmetry breaking, and we show that the presence of an extended symmetry algebra allows, in general, a number of choices for the behavior of massive states under twist. This freedom may be ascribed to additional discrete Wilson lines, and yields consistent modifications of the group assignments, that are illustrated in a number of examples. 1. Introduction In a recent paper [l], Cardy pointed out the dual role of boundaries and characters in the annulus amplitude of (rational) conformal field theory. He also stressed that the fusion-rule coefficients Nir of the chiral algebra encode the operator content flowing through the annulus with prescribed boundary condi- tions. These are important clues to the general structure of (rational) open-string theories [2], since the annulus contribution to the partition function counts the particles in the open-string spectrum, with relative signs fixed by the spin-statistics relation, as demanded by higher-genus modular invariance [3]. In addition, the sum is weighted by the product multiplicity of the charges carried by the ends of open strings, reflecting the presence of a Chan-Paton symmetry group [4] acting on the open-string states. One is therefore linking the internal symmetry group to the string spectrum. As a result, the proposal of ref. [5] may be turned into an algorithm to derive the open-string descendants of left-right symmetric closed strings. The basic step consists in formulating the “parent” closed-string theory in terms of a (quasi)diagonal modular invariant. This requires the introduction of a suitable basis of generalized characters, whose fusion rules determine the group assignments. The number of independent factors in the Chan-Paton group is related to the number of terms in the diagonal modular invariant. It will be shown 0550-3213/91/$03.50 0 1991 - Elsevier Science Publishers B.V. (North-Holland)