Non-geometric orbifolds and wrapping rules

Abstract

Abstract:We show that the number of half-supersymmetric p-branes in the Type II theories compactified on orbifolds is determined by the wrapping rules recently introduced, provided that one accounts correctly for both geometric and non-geometric T-dual configurations. Starting from the Type II theories compactified on K3, we analyze their toroidal dimensional reductions, showing how the resulting half-supersymmetric p-branes satisfy the wrapping rules only by taking into account all the possible higher-dimensional origins. We then consider Type II theories compactified on the orbifold T 6 /(Z 2 × Z 2 ), whose massless four-dimensional theory is an N = 2 supergravity. Again, the wrapping rules are obeyed only if one includes the complete orbit of the T-duality group, namely either Type IIA or Type IIB theories compactified on either the geometric or the non-geometric T-dual orbifold. Finally, we comment on the interpretation of our results in the framework of the duality between the Heterotic string compactified on K3 × T 2 and the Type II string compactified on a Calabi-Yau threefold.

Weaving the exotic web

“…This prediction is based on the analysis of roots and weights of the U-duality group at any dimension [25][26][27][28][29][30]. Lately, the so-called wrapping rules were formulated [11,17,[31][32][33]. This set of rules allows one to construct a set of mixed-symmetry potentials, depending on the type of T -and S-duality transformations that one performs.…”

Wrapping rules (in) string theory

“…3 Wrapping rules for IIA/IIB on (T 4 /Z 2 ) × T n In [27,28] it was shown that the wrapping rules satisfied by the branes of the maximal theory are still valid if one compactifies the Type IIA and Type IIB string theories to the six dimensional N = (1, 1) and N = (2, 0) theories on the orbifold T 4 /Z 2 , provided that only even cycles are taken into account. In [26] it was then shown that if the six-dimensional theory is further reduced on a torus, the resulting branes with α = 0, −1, −2, −3 are obtained starting from the six-dimensional ones by applying the standard wrapping rules. The aim of this section is to first review how the branes of the six-dimensional theories result from applying the wrapping rules of the maximal theory with only even cycles taken…”

“…into account, and then move to the lower-dimensional case showing that the analysis of [26] can be extended so that all the branes of the (T 4 /Z 2 ) × T n theory result from generalised wrapping rules, where as explained in the previous section additional multiplicity factors given by the mixed-symmetry indices of the potentials involved have to be taken into account.…”

“…After discussing the maximal case, we proceed to apply the wrapping rules to the halfmaximal supersymmetric theory corresponding to the compactification of Type IIA/IIB string theory on (T 4 /Z 2 ) × T n . The number of single-brane states of this theory in any dimension was determined in [26]. In this reference it was shown that the wrapping rules in eqs.…”

P fluxes and exotic branes

“…In a series of papers, the full classification of 1/2-BPS branes in type-II string theory compactified on a torus was achieved by analysing the supersymmetry of the corresponding brane effective action [39][40][41]44], while the connection of this analysis with specific group theory properties of such branes was shown in [42,43]. This classification was also extended to theories with less supersymmetry in [64][65][66][67]. In the following, we will first review the basic results of this classification and we will then derive a universal T-duality transformation rule for any brane in string theory, which will give in particular the IIA branes that are related by duality to the S-dual of the D7-brane in our model, together with additional branes in IIB that must be included for consistency.…”