33 research outputs found
Stable bundles on hypercomplex surfaces
A hypercomplex manifold is a manifold equipped with three complex structures
I, J, K satisfying the quaternionic relations. Let M be a 4-dimensional compact
smooth manifold equipped with a hypercomplex structure, and E be a vector
bundle on M. We show that the moduli space of anti-self-dual connections on E
is also hypercomplex, and admits a strong HKT metric. We also study manifolds
with (4,4)-supersymmetry, that is, Riemannian manifolds equipped with a pair of
strong HKT-structures that have opposite torsion. In the language of Hitchin's
and Gualtieri's generalized complex geometry, (4,4)-manifolds are called
``generalized hyperkaehler manifolds''. We show that the moduli space of
anti-self-dual connections on M is a (4,4)-manifold if M is equipped with a
(4,4)-structure.Comment: 17 pages. Version 3.0: reference adde
D0-D4 brane tachyon condensation to a BPS state and its excitation spectrum in noncommutative super Yang-Mills theory
We investigate the D0-D4-brane system for different B-field backgrounds
including the small instanton singularity in noncommutative SYM theory. We
discuss the excitation spectrum of the unstable state as well as for the BPS
D0-D4 bound state. We compute the tachyon potential which reproduces the
complete mass defect. The relevant degrees of freedom are the massless (4,4)
strings. Both results are in contrast with existing string field theory
calculations. The excitation spectrum of the small instanton is found to be
equal to the excitation spectrum of the fluxon solution on R^2_theta x R which
we trace back to T-duality. For the effective theory of the (0,0) string
excitations we obtain a BFSS matrix model. The number of states in the
instanton background changes significantly when the B-field becomes self-dual.
This leads us to the proposal of the existence of a phase transition or cross
over at self-dual B-field.Comment: a4 11pt Latex2e 40 pages; v2: typos fixed, refined comments on
renormalisation, refs added, v3: ref added, version publishe