Superstrings with intrinsic torsion

Abstract

We systematically analyse the necessary and sufficient conditions for the preservation of supersymmetry for bosonic geometries of the form Ê 1,9−d × M d , in the common NS-NS sector of type II string theory and also type I/heterotic string theory. The results are phrased in terms of the intrinsic torsion of G-structures and provide a comprehensive classification of static supersymmetric backgrounds in these theories. Generalised calibrations naturally appear since the geometries always admit NS or type I/heterotic fivebranes wrapping calibrated cycles.Some new solutions are presented. In particular we find d = 6 examples with a fibred structure which preserve N = 1, 2, 3 supersymmetry in type II and include compact type I/heterotic geometries.

BPS action and superpotential for heterotic string compactifications with fluxes

“…In all the known examples of IIB compactifications the resulting effective four-dimensional models were of no-scale type [8,19,23,25,31,35,38] and the overall size modulus remained free even after the introduction of fluxes. This cannot happen in the heterotic compactifications because of the modified Bianchi identity for the three-form [55,46]. As we will now show, the various terms appearing in equation (2.14) generically scale differently with respect to this parameter and therefore it needs to be fixed in order to obtain a consistent solution.…”

“…An interesting subclass of solutions of the geometrical constraints (2.8)-(2.10) is given by manifolds which are products of tori and twisted tori (included in the class of the nilmanifolds in [37]) or by torus fibration of Calabi-Yau two-folds, where the fiber is twisted [33,37,42,45,46,52]. A simple instance of such spaces is given by a metric of the form…”

“…This then implies that solutions to the equations of motion can be found by setting these BPS-like squares to zero. An interesting outcome of this rewriting is that the conditions appearing in the squares are precisely the geometric conditions discussed in [1,37,46]. Therefore, the heterotic equations of motion (which have contributions from higher curvature terms) do not impose additional constraints on the solutions constructed by solving the supersymmetry equations of [1] and the Bianchi identities for the various fields.…”

Global symmetries and 't Hooft anomalies in brane tilings

“…Global symmetries which do not act on the supercharge are called flavor symmetries, and they are divided into two groups, mesonic and baryonic symmetries. 2 These global symmetries should be realized as gauge symmetries in string theory. The purpose of this section is to identify the gauge symmetries corresponding to the global symmetries in gauge theories.…”

“…This duality has been generalized to more complicated ones. The recent discovery of the explicit metrics of classes of Sasaki-Einstein manifolds [2,3,4] provides us many examples of dualities we can explicitly check the validity. For example, it has been confirmed that the volumes of the SasakiEinstein manifolds and some supersymmetric cycles in them correctly reproduce the central charges and conformal dimensions of baryonic operators in superconformal gauge theories, which can be determined on the field theory side with the help of the a-maximization technique [5].…”