18 research outputs found
N=2 Topological Yang-Mills Theory on Compact K\"{a}hler Surfaces
We study a topological Yang-Mills theory with fermionic symmetry. Our
formalism is a field theoretical interpretation of the Donaldson polynomial
invariants on compact K\"{a}hler surfaces. We also study an analogous theory on
compact oriented Riemann surfaces and briefly discuss a possible application of
the Witten's non-Abelian localization formula to the problems in the case of
compact K\"{a}hler surfaces.Comment: ESENAT-93-01 & YUMS-93-10, 34pages: [Final Version] to appear in
Comm. Math. Phy
Instantons and Yang-Mills Flows on Coset Spaces
We consider the Yang-Mills flow equations on a reductive coset space G/H and
the Yang-Mills equations on the manifold R x G/H. On nonsymmetric coset spaces
G/H one can introduce geometric fluxes identified with the torsion of the spin
connection. The condition of G-equivariance imposed on the gauge fields reduces
the Yang-Mills equations to phi^4-kink equations on R. Depending on the
boundary conditions and torsion, we obtain solutions to the Yang-Mills
equations describing instantons, chains of instanton-anti-instanton pairs or
modifications of gauge bundles. For Lorentzian signature on R x G/H, dyon-type
configurations are constructed as well. We also present explicit solutions to
the Yang-Mills flow equations and compare them with the Yang-Mills solutions on
R x G/H.Comment: 1+12 page
Reducible connections and non-local symmetries of the self-dual Yang-Mills equations
We construct the most general reducible connection that satisfies the
self-dual Yang-Mills equations on a simply connected, open subset of flat
. We show how all such connections lie in the orbit of the flat
connection on under the action of non-local symmetries of the
self-dual Yang-Mills equations. Such connections fit naturally inside a larger
class of solutions to the self-dual Yang-Mills equations that are analogous to
harmonic maps of finite type.Comment: AMSLatex, 15 pages, no figures. Corrected in line with the referee's
comments. In particular, restriction to simply-connected open sets now
explicitly stated. Version to appear in Communications in Mathematical
Physic
Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces
Higgs bundles and non-abelian Hodge theory provide holomorphic methods with
which to study the moduli spaces of surface group representations in a
reductive Lie group G. In this paper we survey the case in which G is the
isometry group of a classical Hermitian symmetric space of non-compact type.
Using Morse theory on the moduli spaces of Higgs bundles, we compute the number
of connected components of the moduli space of representations with maximal
Toledo invariant.Comment: v2: added due credits to the work of Burger, Iozzi and Wienhard. v3:
corrected count of connected components for G=SU(p,q) (p \neq q); added due
credits to the work of Xia and Markman-Xia; minor corrections and
clarifications. 31 page
Extremal Bundles on Calabi-Yau Threefolds
We study constructions of stable holomorphic vector bundles on Calabi–Yau threefolds, especially those with exact anomaly cancellation which we call extremal. By going through the known databases we find that such examples are rare in general and can be ruled out for the spectral cover construction for all elliptic threefolds. We then introduce a general Hartshorne–Serre construction and use it to find extremal bundles of general ranks and study their stability, as well as computing their Chern numbers. Based on both existing and our new constructions, we revisit the DRY conjecture for the existence of stable sheaves on Calabi–threefolds, and provide theoretical and numerical evidence for its correctness. Our construction can be easily generalized to bundles with no extremal conditions imposed
Sequences of stable bundles over compact complex surfaces
When identified with sequences of irreducible Hermitian-Einstein connections, sequences of stable holomorphic bundles of fixed topological type and bounded degree on a compact complex surface equipped with a Gauduchon metric are shown to have strongly convergent subsequences after blowing-up and pulling-back sufficiently many times.Nicholas P. Buchdah