48 research outputs found
Spin Cohomology
We explore differential and algebraic operations on the exterior product of
spinor representations and their twists that give rise to cohomology, the spin
cohomology. A linear differential operator is introduced which is
associated to a connection and a parallel spinor ,
, and the algebraic operators are constructed from
skew-products of gamma matrices. We exhibit a large number of spin
cohomology operators and we investigate the spin cohomologies associated with
connections whose holonomy is a subgroup of , , and
. In the case, we findthat the spin cohomology of complex spin
and spin manifolds is related to a twisted Dolbeault cohomology. On
Calabi-Yau type of manifolds of dimension , a spin cohomology can be
defined on a twisted complex with operator which is the sum of a
differential and algebraic one. We compute this cohomology on six-dimensional
Calabi-Yau manifolds using a spectral sequence. In the and
cases, the spin cohomology is related to the de Rham cohomology.Comment: 30 pages, late
The super-correlator/super-amplitude duality: Part I
We extend the recently discovered duality between MHV amplitudes and the
light-cone limit of correlation functions of a particular type of local scalar
operators to generic non-MHV amplitudes in planar N=4 SYM theory. We consider
the natural generalization of the bosonic correlators to super-correlators of
stress-tensor multiplets and show, in a number of examples, that their
light-cone limit exactly reproduces the square of the matching
super-amplitudes. Our correlators are computed at Born level. If all of their
points form a light-like polygon, the correlator is dual to the tree-level
amplitude. If a subset of points are not on the polygon but are integrated
over, they become Lagrangian insertions generating the loop corrections to the
correlator. In this case the duality with amplitudes holds at the level of the
integrand. We build up the superspace formalism needed to formulate the duality
and present the explicit example of the n-point NMHV tree amplitude as the dual
of the lowest nilpotent level in the correlator.Comment: 56 page