Generalised twisted partition functions

Abstract

We consider the set of partition functions that result from the insertion of twist operators compatible with conformal invariance in a given 2D Conformal Field Theory (CFT). A consistency equation, which gives a classification of twists, is written and solved in particular cases. This generalises old results on twisted torus boundary conditions, gives a physical interpretation of Ocneanu's algebraic construction, and might offer a new route to the study of properties of CFT.Comment: 12 pages, harvmac, 1 Table, 1 Figure . Minor typos corrected, the figure which had vanished reappears

Non-geometric backgrounds based on topological interfaces

“…In this paper, we studied simple models of non-geometric backgrounds based on the worldsheet CFT equipped with the topological interfaces [15,17]. The topological interfaces there composed the twist operators similar to those in orbifold CFTs, and we performed the twisted compactification of the Scherk-Schwarz type [28,29].…”

“…In particular, we discuss them based on the world-sheet conformal interfaces [14][15][16]. The conformal interfaces are defined as the one-dimensional defects which preserve the world-sheet conformal symmetry.…”

“…In this sense, the conformal interfaces are regarded as a generalization of the conformal boundaries, which describe the D-branes in string theory. In addition, when the left and right energy momentum tensors are separately continuous across the interfaces, they are called topological [15,17], since they can be deformed freely on the world-sheet.…”

The reflection coefficient for minimal model conformal defects from perturbation theory

“…The model has (p − 1)(q − 1)/2 primary fields corresponding to the Virasoro highest weight representations which are labelled by two integers (r, s) with (r, s) (p − r, q − s). We are going to be especially interested in the representation (1,3), and we will write h = h 13 = 2p/q − 1.…”

“…The boundary conditions and topological defects have been completely classified in [3] and further studied in [4]. The situation of more general conformal defects is much less clear.…”