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Fermionic T-duality in fermionic double space. (English) Zbl 1371.81263
Summary: In this article we offer the interpretation of the fermionic T-duality of the type II superstring theory in double space. We generalize the idea of double space doubling the fermionic sector of the superspace. In such doubled space fermionic T-duality is represented as permutation of the fermionic coordinates \(\theta^{\alpha}\) and \(\overline{\theta}^{\alpha}\) with the corresponding fermionic T-dual ones, \(\vartheta_{\alpha}\) and \(\overline{\vartheta}_{\alpha}\), respectively. Demanding that T-dual transformation law has the same form as initial one, we obtain the known form of the fermionic T-dual NS-R and R-R background fields. Fermionic T-dual NS-NS background fields are obtained under some assumptions. We conclude that only symmetric part of R-R field strength and symmetric part of its fermionic T-dual contribute to the fermionic T-duality transformation of dilaton field and analyze the dilaton field in fermionic double space. As a model we use the ghost free action of type II superstring in pure spinor formulation in approximation of constant background fields up to the quadratic terms.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
81S05 Commutation relations and statistics as related to quantum mechanics (general)
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