A Note on the CFT Origin of the Strong Constraint of DFT

Abstract

In double field theory, motivated by its field theoretic consistency, the level matching condition is generalized to the so-called strong constraint. In this note, it is investigated what the two-dimensional conformal field theory origin of this constraint is. Initially treating the left- and right-movers as independent, we compute the torus partition function as well as a generalized Virasoro-Shapiro amplitude. In non-compact directions the strong constraint arises from the factorization of the Virasoro-Shapiro amplitude over physical states as determined by the modular invariant partition function. From the same argument, along internal toroidal directions, no analogous constraint arises.

arXiv comment14 + 5 pages

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• Lobotomy of Flux Compactifications
• T-duality, Quotients and Currents for Non-Geometric Closed Strings
• Star products on graded manifolds and ${\alpha }^{\prime }$-corrections to Courant algebroids from string theory
• Equivalence of open/closed strings
• Solution-generating transformations in duality-invariant theories and the fluid/gravity correspondence
• Duality Covariant Solutions in Extended Field Theories
• Cosmological constant as quantum error correction from generalised gauge invariance in double field theory
• More Stringy Effects in Target Space from Double Field Theory