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Register a new userParallelisable Heterotic Backgrounds
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Authors
Jose Figueroa-OFarrill
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We classify the simply-connected supersymmetric parallelisable backgrounds of heterotic supergravity. They are all given by parallelised Lie groups admitting a bi-invariant lorentzian metric. We find examples preserving 4, 8, 10, 12, 14 and 16 of the 16 supersymmetries.
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We classify the geometries of the most general warped, flux AdS backgrounds of heterotic supergravity up to two loop order in sigma model perturbation theory. We show under some mild assumptions that there are no $AdS_n$ backgrounds with $n ot=3$. Moreover the warp factor of AdS$_3$ backgrounds is constant, the geometry is a product $AdS_3times M^7$ and such solutions preserve, 2, 4, 6 and 8 supersymmetries. The geometry of $M^7$ has been specified in all cases. For 2 supersymmetries, it has been found that $M^7$ admits a suitably restricted $G_2$ structure. For 4 supersymmetries, $M^7$ has an $SU(3)$ structure and can be described locally as a circle fibration over a 6-dimensional KT manifold. For 6 and 8 supersymmetries, $M^7$ has an $SU(2)$ structure and can be described locally as a $S^3$ fibration over a 4-dimensional manifold which either has an anti-self dual Weyl tensor or a hyper-Kahler structure, respectively. We also demonstrate a new Lichnerowicz type theorem in the presence of $alpha$ corrections.
Compactification of M- / string theory on manifolds with $G_2$ structure yields a wide variety of 4D and 3D physical theories. We analyze the local geometry of such compactifications as captured by a gauge theory obtained from a three-manifold of ADE singularities. Generic gauge theory solutions include a non-trivial gauge field flux as well as normal deformations to the three-manifold captured by non-commuting matrix coordinates, a signal of T-brane phenomena. Solutions of the 3D gauge theory on a three-manifold are given by a deformation of the Hitchin system on a marked Riemann surface which is fibered over an interval. We present explicit examples of such backgrounds as well as the profile of the corresponding zero modes for localized chiral matter. We also provide a purely algebraic prescription for characterizing localized matter for such T-brane configurations. The geometric interpretation of this gauge theory description provides a generalization of twisted connected sums with codimension seven singularities at localized regions of the geometry. It also indicates that geometric codimension six singularities can sometimes support 4D chiral matter due to physical structure hidden in T-branes.
We summarize the foliation approach to ${cal N}=1$ compactifications of eleven-dimensional supergravity on eight-manifolds $M$ down to $mathrm{AdS}_3$ spaces for the case when the internal part $xi$ of the supersymmetry generator is chiral on some proper subset ${cal W}$ of $M$. In this case, a topological no-go theorem implies that the complement $Msetminus {cal W}$ must be a dense open subset, while $M$ admits a singular foliation ${bar {cal F}}$ (in the sense of Haefliger) which is defined by a closed one-form $boldsymbol{omega}$ and is endowed with a longitudinal $G_2$ structure. The geometry of this foliation is determined by the supersymmetry conditions. We also describe the topology of ${bar {cal F}}$ in the case when $boldsymbol{omega}$ is a Morse form.
The superspace geometry relevant to the heterotic string is reviewed from the point of view of the off-shell supermultiplet structure of $N=1,d=10$ supergravity. The anomaly-modified seven-form Bianchi identity is analysed at order $a^3$ and shown to admit a complete solution. The corresponding $a^3$ deformation of the dimension-zero torsion tensor is derived and shown to obey the appropriate cohomological constraint.
We present a class of smooth supersymmetric heterotic solutions with a non-compact Eguchi-Hanson space. The non-compact geometry is embedded as the base of a six-dimensional non-Kahler manifold with a non-trivial torus fiber. We solve the non-linear anomaly equation in this background exactly. We also define a new charge that detects the non-Kahlerity of our solutions.
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