We present a large class of new backgrounds that are solutions of type IIB supergravity with a warped AdS5 factor, non-trivial axion-dilaton, B-field and three-form Ramond-Ramond flux but yet have no five-form flux. We obtain these solutions and many of their variations by judiciously applying non-Abelian and Abelian T-dualities, as well as coordinate shifts to AdS5 × X
 5 IIB supergravity solutions with X
 5 = S
 5
 , T
 1,1
 , Y
 p,q
 . We address a number of issues pertaining to charge quantization in the context of non-Abelian T-duality. We comment on some properties of the expected dual super conformal field theories by studying their CFT central charge holographically. We also use the structure of the supergravity Page charges, central charges and some probe branes to infer aspects of the dual super conformal field theories.

https://link.springer.com/content/pdf/10.1007%2FJHEP02%282015%29040.pdf

Type IIB supergravity solutions with AdS5 from Abelian and non-Abelian T dualities

We study the effect of T-duality on supersymmetry in the context of type II supergravity. For both U(1) Abelian and SU(2) non-Abelian T-duality, we demonstrate that the supersymmetry variations after T-duality are related to the variations before T-duality through the Kosmann spinorial Lie derivative, which vanishes when the Killing spinors are independent of the T-duality directions. As a byproduct of our analysis, we present closed expressions for SU(2) T-duality in a class of spacetimes with diagonal Bianchi IX symmetry and comment on specific examples of T-dual geometries, including a novel AdS3 geometry with large superconformal symmetry.

http://iopscience.iop.org/article/10.1088/0264-9381/32/3/035014/pdf

Supersymmetry and non-Abelian T-duality in type II supergravity

For a general class of SO(4) symmetric backgrounds in type II-supergravity, we show that the action of non-Abelian T-duality can be described via consistent truncation to seven dimensional theories with seemingly massive modes. As such, any solution to these theories uplifts to both massive type IIA and IIB supergravities presenting an invertible map between the two. For supersymmetric backgrounds, we show that for spinors transforming under SO(4) the non-Abelian T-duality transformation breaks the original supersymmetry by half. We use these mappings to generate the non-Abelian T-duals of the maximally supersymmetric pp-wave, the Lin, Lunin, Maldacena geometries and spacetimes with Lifshitz symmetry.

Non-Abelian T-duality and consistent truncations in type-II supergravity

There is a rich theory of so-called (strict) nearly Kaehler manifolds, almost-Hermitian manifolds generalising the famous almost complex structure on the 6-sphere induced by octonionic multiplication. Nearly Kaehler 6-manifolds play a distinguished role both in the general structure theory and also because of their connection with singular spaces with holonomy group the compact exceptional Lie group G2: the metric cone over a Riemannian 6-manifold M has holonomy contained in G2 if and only if M is a nearly Kaehler 6-manifold. 
A central problem in the field has been the absence of any complete inhomogeneous examples. We prove the existence of the first complete inhomogeneous nearly Kaehler 6-manifolds by proving the existence of at least one cohomogeneity one nearly Kaehler structure on the 6-sphere and on the product of a pair of 3-spheres. We conjecture that these are the only simply connected (inhomogeneous) cohomogeneity one nearly Kaehler structures in six dimensions.

New G2 holonomy cones and exotic nearly Kaehler structures on the 6-sphere and the product of a pair of 3-spheres

We investigate instantons on manifolds with Killing spinors and their cones. Examples of manifolds with Killing spinors include nearly Kahler 6-manifolds, nearly parallel G
 2-manifolds in dimension 7, Sasaki-Einstein manifolds, and 3-Sasakian manifolds. We construct a connection on the tangent bundle over these manifolds which solves the instanton equation, and also show that the instanton equation implies the Yang-Mills equation, despite the presence of torsion. We then construct instantons on the cones over these manifolds, and lift them to solutions of heterotic supergravity. Amongst our solutions are new instantons on even-dimensional Euclidean spaces, as well as the well-known BPST, quaternionic and octonionic instantons.

/pdf/instantons-and-killing-spinors-5d13x5qho8.pdf

Instantons and Killing spinors

In [9], Boyer and Galicki introduced a contact reduction method in the context of Sasakian manifolds, which produces 5-dimentional Sasaki-Einstein manifolds from a 7-sphere. In this paper, we compute very explicitly the metric obtained from the above mentioned reduction via a projection, $S^3 \times S^3 \to S^2 \times S^3$, and show that this metric is the homogeneous Kobayashi-Tanno metric.

/pdf/sasaki-einstein-metrics-on-s-2-times-s-3-pv7lov49yp.pdf

Sasaki-Einstein Metrics on $S^2 \times S^3$

Kobayashi [13] introduced complex contact manifolds as a variant of real contact manifolds. Later, Ishihara and Konishi [11] defined normality of complex contact manifolds as for Sasakian manifolds in real contact geometry. In this paper, we construct normal complex contact manifolds via reduction from hyperk\"{a}hler manifolds, and give a new example of normal complex contact manifolds. To check the normality for the new examples, we give a useful identity about sectional curvatures of normal complex contact manifolds. We also give an explicit example of a non-normal complex almost contact metric structure on $S^{4m+3} \times S^{4n+3}$.

/pdf/construction-of-complex-contact-manifolds-via-reduction-rm7wbmz71t.pdf

Mitsuhiro Imada

Papers

Sasaki-Einstein Metrics on $S^2 \times S^3$

Construction of Complex Contact Manifolds via Reduction