Abstract
We study simple models of the world-sheet CFTs describing non-geometric backgrounds based on the topological interfaces, the ‘gluing condition’ of which imposes T-duality- or analogous twists. To be more specific, we start with the torus partition function on a target space S1[base] × (S1 × S1)[fiber] with rather general values of radii. The fiber CFT is defined by inserting the twist operators consisting of the topological interfaces which lie along the cycles of the world-sheet torus according to the winding numbers of the base circle. We construct the partition functions involving such duality twists. The modular invariance is achieved straightforwardly, whereas ‘unitarization’ is generically necessary to maintain the unitarity. We demonstrate it in the case of the equal fiber radii. The resultant models are closely related to the CFTs with the discrete torsion. The unitarization is also physically interpreted as multiple insertions of the twist/interface operators along various directions.
Highlights
Important class, where the left- and right-movers of the string feel different geometries
The fiber CFT is defined by inserting the twist operators consisting of the topological interfaces which lie along the cycles of the world-sheet torus according to the winding numbers of the base circle
The conformal interfaces are regarded as a generalization of the conformal boundaries, which describe the D-branes in string theory
Summary
Before presenting our main analysis, we first set up the necessary notation. Through this paper we shall use the α = 1 convention. We set Λ ≡ Zτ + Z, where τ ∈ H (upper half plane) is the modulus of the world-sheet torus parametrized as τ = τ1+iτ (τ1 ∈ R, τ2 > 0). 2.1 Partition functions of compact bosons The partition function of a free boson compactified on the circle with radius R should be ZR(τ ) = ZR(τ | ν), ν∈Λ. Where ZR(τ | ν) represents a contribution from the winding sector specified by ν. Its modular property is expressed as ZR(τ + 1 | ν) = ZR(τ | ν), 1ν. √ When the radius R can be written as R = k, (k ∈ Z>0), the partition function ZR(τ ) is rewritten in terms of theta functions,
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