Heterotic-Type II duality and wrapping rules

Abstract

We show how the brane wrapping rules, recently discovered in closed oriented string theories compactified on tori, are extended to the case of the Type IIA string compactified on K3. To this aim, a crucial role is played by the duality between this theory and the Heterotic string compactified on a four-dimensional torus T 4 . We first show how the wrapping rules are applied to the T 4 /Z N orbifold limits of K3 by relating the D0 branes, obtained as D2 branes wrapping two-cycles, to the perturbative BPS states of the Heterotic theory on T 4 . The wrapping rules are then extended to the solitonic branes of the Type IIA string, finding agreement with the analogous Heterotic states. Finally, the geometric Type IIA orbifolds are mapped, via T-duality, to non-geometric Type IIB orbifolds, where the wrapping rules are also at work and consistent with string dualities.

Towards a classification of branes in theories with eight supercharges

“…These wrapping rules were shown to apply also to the branes of the heterotic theory compactified on tori, as well as to the IIA theory compactified on K3 [25,28]. Considering the six-dimensional models with eight supercharges as resulting from the heterotic theory compactified on K3, we will show that our classification in any dimension is consistent with the wrapping rules.…”

“…A similar phenomenon occurs in the half-maximal case, where an additional halving takes place for the unwrapped NS5-branes, as discussed in [28]. In that case the halving was interpreted in the orbifold limit T 4 /Z 2 of K3 as an additional action of Z 2 on the charges, leading to a self-duality condition.…”

“…In [25,28] the duality between the Type-IIA theory compactified on K3 and the heterotic theory on T 4 was used to determine how the wrapping rules can be applied in K3 compactifications. More specifically, one identifies a basis of six homology 2-cycles, and allowing the IIA branes to either wrap these 2-cycles, the whole of K3 or remain unwrapped, and using the same wrapping rules as derived for the torus reduction, one reproduces the branes of the heterotic side, in agreement with the duality.…”

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.…”

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.…”