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A Metric for Heterotic Moduli

Candelas, Philip, de la Ossa, Xenia and McOrist, Jock (2017) A Metric for Heterotic Moduli Communications in Mathematical Physics, 356 (2). pp. 567-612.

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Heterotic vacua of string theory are realised, at large radius, by a compact threefold with vanishing first Chern class together with a choice of stable holomorphic vector bundle. These form a wide class of potentially realistic four-dimensional vacua of string theory. Despite all their phenomenological promise, there is little understanding of the metric on the moduli space of these. What is sought is the analogue of special geometry for these vacua. The metric on the moduli space is important in phenomenology as it normalises D-terms and Yukawa couplings. It is also of interest in mathematics, since it generalises the metric, first found by Kobayashi, on the space of gauge field connections, to a more general context. Here we construct this metric, correct to first order in α‵ , in two ways: first by postulating a metric that is invariant under background gauge transformations of the gauge field, and also by dimensionally reducing heterotic supergravity. These methods agree and the resulting metric is Kähler, as is required by supersymmetry. Checking the metric is Kähler is intricate and the anomaly cancellation equation for the H field plays an essential role. The Kähler potential nevertheless takes a remarkably simple form: it is the Kähler potential of special geometry with the Kähler form replaced by the α‵ -corrected hermitian form.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Date : 8 September 2017
Identification Number : 10.1007/s00220-017-2978-7
Copyright Disclaimer : © Springer-Verlag GmbH Germany 2017
Depositing User : Clive Harris
Date Deposited : 08 Mar 2018 08:58
Last Modified : 13 Mar 2018 15:48

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