8 research outputs found
A Note on Mirror Symmetry for Manifolds with Spin(7) Holonomy
Starting from the superconformal algebras associated with manifolds, I
extend the algebra to the manifolds with spin(7) holonomy. I show how the
mirror symmetry in manifolds with spin(7) holonomy arises as the automorphism
in the extended sperconformal algebra. The automorphism is realized as 14 kinds
of T-dualities on the supersymmetric toroidal fibrations. One class of
Joyce's orbifolds are pairwise identified under the symmetry.Comment: 12 pages, harvmac bi
G2 Hitchin functionals at one loop
We consider the quantization of the effective target space description of
topological M-theory in terms of the Hitchin functional whose critical points
describe seven-manifolds with G2 structure. The one-loop partition function for
this theory is calculated and an extended version of it, that is related to
generalized G2 geometry, is compared with the topological G2 string. We relate
the reduction of the effective action for the extended G2 theory to the Hitchin
functional description of the topological string in six dimensions. The
dependence of the partition functions on the choice of background G2 metric is
also determined.Comment: 58 pages, LaTeX; v2: Acknowledgments adde
Killing-Yano equations and G-structures
We solve the Killing-Yano equation on manifolds with a -structure for
and . Solutions
include nearly-K\"ahler, weak holonomy , balanced SU(n) and holonomy
manifolds. As an application, we find that particle probes on
compactifications of type IIA and 11-dimensional supergravity admit a -type of symmetry generated by the fundamental forms. We also explore the
-symmetries of string and particle actions in heterotic and common
sector supersymmetric backgrounds. In the heterotic case, the generators of the
-symmetries completely characterize the solutions of the gravitino
Killing spinor equation, and the structure constants of the -symmetry
algebra depend on the solution of the dilatino Killing spinor equation.Comment: 10 pages, minor change
The topological G(2) string
We construct new topological theories related to sigma models whose target space is a seven-dimensional manifold of G(2) holonomy. We define a new type of topological twist and identify the BRST operator and the physical states. Unlike the more familiar six-dimensional case, our topological model is defined in terms of conformal blocks and not in terms of local operators of the original theory. We also present evidence that one can extend this definition to all genera and construct a seven-dimensional topological string theory. We compute genus zero correlation functions and relate these to Hitchin’s functional for three-forms in seven dimensions. Along the way we develop the analogue of special geometry for G(2) manifolds. When the seven-dimensional topological twist is applied to the product of a Calabi-Yau manifold and a circle, the result is an interesting combination of the six-dimensional A and B models
Killing–Yano equations with torsion, worldline actions and G
We determine the geometry of the target spaces of supersymmetric
non-relativistic particles with torsion and magnetic couplings, and with
symmetries generated by the fundamental forms of G-structures for and . We find that the
Killing-Yano equation, which arises as a condition for the invariance of the
worldline action, does not always determine the torsion coupling uniquely in
terms of the metric and fundamental forms. We show that there are several
connections with skew-symmetric torsion for and that
solve the invariance conditions. We describe all these compatible connections
for each of the -structures and explain the geometric nature of the
couplings.Comment: 17 page