A KK-theoretic perspective on deformed Dirac operators

KK-Masses in Dipole Deformed Field Theories

We reconsider aspects of non-commutative dipole deformations of field theories. Among our findings there are hints to new phases with spontaneous breaking of translation invariance (stripe phases), similar to what happens in Moyal-deformed field theories. Furthermore, using zeta-function regularization, we calculate quantum corrections to KK-state masses. The corrections coming from non-planar ...

Dirac Operators on 4-manifolds

Dirac operators are important geometric operators on a manifold. The Dirac operator DA on the four dimensional Euclidean space M = R is the order one differential operator whose square DA ◦ DA is the Euclidean Laplacian − ∑4 i=1 ∂ψ ∂xi . However, this is not possible unless we allow coefficients for this linear operator to be matrix-valued. Let M = R be the four dimensional Euclidean space with...

Dirac operators on Lagrangian submanifolds

We study a natural Dirac operator on a Lagrangian submanifold of a Kähler manifold. We first show that its square coincides with the Hodge de Rham Laplacian provided the complex structure identifies the Spin structures of the tangent and normal bundles of the submanifold. We then give extrinsic estimates for the eigenvalues of that operator and discuss some examples. Mathematics Subject Classif...

Dirac Operator on a 7-Manifold with Deformed G2 Structure

In this work, we consider the deforming of a G2 structure by a vector field on a 7−manifold. To obtain the metric corresponding to deformed G2 structure, a new map is defined. By using this new map, the covariant derivatives on associated spinor bundles are compared. Then, the relation between Dirac operators on spinor bundles are investigated under some restrictions.

Dirac Operators