N = 2 heterotic-type II duality and bundle moduli

Abstract

Heterotic string compactifications on a K3 surface S depend on a choice of hyperkähler metric, anti-self-dual gauge connection and Kalb-Ramond flux, parametrized by hypermultiplet scalars. The metric on hypermultiplet moduli space is in principle computable within the (0, 2) superconformal field theory on the heterotic string worldsheet, although little is known about it in practice. Using duality with type II strings compactified on a Calabi-Yau threefold, we predict the form of the quaternion-Kähler metric on hypermultiplet moduli space when S is elliptically fibered, in the limit of a large fiber and even larger base. The result is in general agreement with expectations from KaluzaKlein reduction, in particular the metric has a two-stage fibration structure, where the B-field moduli are fibered over bundle and metric moduli, while bundle moduli are themselves fibered over metric moduli. A more precise match must await a detailed analysis of R 2 -corrected ten-dimensional supergravity.

Moduli spaces of non-geometric type II/heterotic dual pairs

“…For a different class of models, non-geometric heterotic/type II dual pairs have been considered previously in[16]. For a general recent review about non-geometric compactifications, see[17].2 See[21] for a review about corrections to the hypermultiplets moduli space and more specifically[22] for recent advances in understanding heterotic/type II duality in the hypermultiplets sector.…”

Non-Geometric F-Theory-Heterotic Duality

“…Analyzing the heterotic theory in four dimensions in the heterotic Sen limit, we observed that α ′ -corrections modified the semi-classical two-staged fibrational structure derived by Alexandrov, Louis, Pioline and Valandro [26]. While such alterations to the hypermultiplet sector are expected on general grounds [42], we believe that the analysis of non-geometric heterotic compactifications in the quantum regime -in particular at special loci in the moduli space such as the heterotic Sen limitmay shed light on conceptual questions concerning the quantum hypermultiplet moduli space.…”

“…In particular, for non-geometric heterotic compactifications to six and four space-time dimensions, we connect the heterotic Sen limit to the structure of the hypermultiplet moduli space, as recently discussed in the semi-classical approximation in refs. [25,26]. By comparing with the heterotic Sen limit, we give evidence that their proposed hierarchical fibrational structure in the hypermultiplet moduli space is a property of the semi-classical approximation in the absence of quantum corrections.…”

“…In ref. [26] Alexandrov, Louis, Pioline and Valandro study the heterotic hypermultiplet sector in a similar context. They utilize the duality between the heterotic string on K3 × T 2 and the type IIB string on the mirror Y of the dual elliptically fibered Calabi-Yau threefold X.…”

Non-geometric orbifolds and wrapping rules

“…Dual Type II models, in this case, require at least h 11 ≥ 3 on the Type IIA side and h 12 ≥ 3 on the Type IIB side. The gauge bundle does contribute both to the vector multiplet moduli space, a special Kähler manifold, and to the hypermultiplet moduli space, whose generic structure is actually more difficult to characterize [33]. Moreover, the duality is no longer an S-duality.…”