350 research outputs found
Normal bundles to Laufer rational curves in local Calabi-Yau threefolds
We prove a conjecture by F. Ferrari. Let X be the total space of a nonlinear
deformation of a rank 2 holomorphic vector bundle on a smooth rational curve,
such that X has trivial canonical bundle and has sections. Then the normal
bundle to such sections is computed in terms of the rank of the Hessian of a
suitably defined superpotential at its critical points
The K\ue4hler quotient resolution of C3/\u393 singularities, the McKay correspondence and D=3 N = 2 Chern-Simons gauge theories
We advocate that the generalized Kronheimer construction of the Ka \u308hler quotient crepant resolution M\u3b6 12\u2192 C3/\u393 of an orbifold singularity where \u393 82 SU(3) is a finite subgroup naturally defines the field content and the interaction structure of a superconformal Chern-Simons Gauge Theory. This latter is suppos- edlythedualofanM2-branesolutionofD=11supergravitywithC
7M\u3b6 astransversespace.Weillustrate and discuss many aspects of this type of constructions emphasizing that the equation p 27 p = 0 which provides the Ka \u308hler analogue of the holomorphic sector in the hyperKa \u308hler moment map equations canonically defines the structure of a universal superpotential in the CS theory. Furthermore the kernel D\u393 of the above equation can be described as the orbit with respect to a quiver Lie group G\u393 of a special locus L\u393 82 Hom\u393 (Q 97 R, R) that has also a universal definition. We provide an extensive discussion of the relation between the coset manifold G\u393/F\u393, the gauge group F\u393 being the maximal compact subgroup of the quiver group, the moment map equations and the first Chern classes of the so named tautological vector bundles that are in one-to-one correspondence with the nontrivial irreps of \u393. These first Chern classes are represented by (1,1)-forms on M\u3b6 and provide a basis for the cohomology group H2(M\u3b6 ). We also discuss the relation with conjugacy classes of \u393 and we provide the explicit construction of several examples emphasizing the role of a general- ized McKay correspondence. The case of the ALE manifold resolution of C2/\u393 singularities is utilized as a comparison term and new formulae related with the complex presentation of Gibbons-Hawking metrics are exhibited
Semistable Higgs bundles on Calabi-Yau manifolds
We provide a partial classification of semistable Higgs bundles over a simply connected Calabi-Yau manifolds. Applications to a conjecture about a special class of semistable Higgs bundles are given. In particular, the conjecture is proved for K3 and Enriques surfaces, and some related classes of surfaces
Gauge fixing and equivariant cohomology
The supersymmetric model developed by Witten to study the equivariant
cohomology of a manifold with an isometric circle action is derived from the
BRST quantization of a simple classical model. The gauge-fixing process is
carefully analysed, and demonstrates that different choices of gauge-fixing
fermion can lead to different quantum theories.Comment: 18 pages LaTe
Parafermionic Liouville field theory and instantons on ALE spaces
In this paper we study the correspondence between the
coset conformal field
theories and SU(n) gauge theories on
. Namely we check the correspondence between the
SU(2) Nekrasov partition function on and the
conformal blocks of the parafermion algebra (in and modules).
We find that they are equal up to the U(1)-factor as it was in all cases of
AGT-like relations. Studying the structure of the instanton partition function
on we also find some evidence that this
correspondence with arbitrary takes place up to the U(1)-factor.Comment: 21 pages, 6 figures, misprints corrected, references added, version
to appear in JHE
Yang-Mills-Higgs connections on Calabi-Yau manifolds
Let be a compact connected K"ahler--Einstein manifold with . If there is a semistable Higgs vector bundle on with , then we show that ; any satisfying this condition is called a Calabi--Yau manifold, and it admits a Ricci--flat K"ahler form cite{Ya}. Let be a polystable Higgs vector bundle on a compact Ricci--flat K"ahler manifold . Let be an Hermitian structure on satisfying the Yang--Mills--Higgs equation for . We prove that also satisfies the Yang--Mills--Higgs equation for . A similar result is proved for Hermitian structures on principal Higgs bundles on satisfying the Yang--Mills--Higgs equation. \ua9 2016 International Press
On semistable principal bundles over a complex projective manifold, II
Let (X, \omega) be a compact connected Kaehler manifold of complex dimension
d and E_G a holomorphic principal G-bundle on X, where G is a connected
reductive linear algebraic group defined over C. Let Z (G) denote the center of
G. We prove that the following three statements are equivalent: (1) There is a
parabolic subgroup P of G and a holomorphic reduction of the structure group of
E_G to P (say, E_P) such that the bundle obtained by extending the structure
group of E_P to L(P)/Z(G) (where L(P) is the Levi quotient of P) admits a flat
connection; (2) The adjoint vector bundle ad(E_G) is numerically flat; (3) The
principal G-bundle E_G is pseudostable, and the degree of the charateristic
class c_2(ad(E_G) is zero.Comment: 15 page
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