T-duality twists and asymmetric orbifolds

Abstract

Abstract:We study some aspects of asymmetric orbifolds of tori, with the orbifold group being some Z N subgroup of the T-duality group and, in particular, provide a concrete understanding of certain phase factors that may accompany the T-duality operation on the stringy Hilbert space in toroidal compactification. We discuss how these T-duality twist phase factors are related to the symmetry and locality properties of the closed string vertex operator algebra, and clarify the role that they enact in the modular covariance of the orbifold theory, mainly using asymmetric orbifolds of tori which are root lattices as working examples.

Non-supersymmetric asymmetric orbifolds with vanishing cosmological constant

“…These types of string vacua have been studied based on the world-sheet CFT e.g. in [9][10][11][12][13][14][15][16]. 1 In this paper, we study type II string vacua defined by torus compactifications twisted by T-duality transformations in the above sense.…”

“…The explicit forms of the relevant building blocks are summarized in appendix B. The case with phases for T 4 [SO (8)] can be similarly discussed following [10,16], although we do not work on it in this paper.…”

“…In this subsection, we would like to comment on the relation to the construction of Tfolds in [10,16]. In these works, the T-duality twists are accompanied by extra phases, so that the full operator product expansion (OPE), not only the chiral one, respects the invariance under the twist: supposed that two vertex operators including both the left and right movers are invariant, their OPE yields invariant operators.…”

More on non-supersymmetric asymmetric orbifolds with vanishing cosmological constant

“…These types of non-geometric backgrounds have been studied by the approach of world-sheet CFT e.g. in [25][26][27][28][29][30][31][32]. Now, in this paper, we would like to explore a variety of non-SUSY string vacua of this type.…”

Not doomed to fail

“…Sarmadi and C. Vafa [28,29], and in a slightly different context by J. Lepowsky [30,31]. Hai Siong Tan used a similar approach in [32] to determine consistent asymmetric orbifold group actions. The condition can be traced back to the properties of involutions on the charge lattice which fix the parameter point: whenever there exists a charge vector which has an odd scalar product with its image under such an involution, the lift is "doomed to fail", i.e.…”