Related papers: Gauge theory and calibrated geometry, I
We develop a unifed theory to study geometry of manifolds with different holonomy groups. They are classified by (1) real, complex, quaternion or octonion number they are defined over and (2) being special or not. Specialty is an…
A classification of the possible symmetric principal bundles with a compact gauge group, a compact symmetry group and a base manifold which is regularly foliated by the orbits of the symmetry group is derived. A generalization of Wang's…
We describe mirror symmetry in N=2 superconformal field theories in terms of a dynamical topology changing process of the principal fiber bundle associated with a topological membrane. We show that the topological symmetries of Calabi-Yau…
Yang-Mills theory with a symmetry algebra that is the semidirect product $\mathfrak{h}\ltimes\mathfrak{h}^*$ defined by the coadjoint action of a Lie algebra $\mathfrak{h}$ on its dual $\mathfrak{h}^*$ is studied. The gauge group is the…
We develop the theory of Chern-Simons bundle 2-gerbes and multiplicative bundle gerbes associated to any principal $G$-bundle with connection and a class in $H^4(BG, \ZZ)$ for a compact semi-simple Lie group $G$. The Chern-Simons bundle…
The scalar and vector topological Yang-Mills symmetries determine a closed and consistent sector of Yang-Mills supersymmetry. We provide a geometrical construction of these symmetries, based on a horizontality condition on reducible…
Consider a vector bundle over a K\"ahler manifold which admits a Hermitian Yang-Mills connection. We show that the pullback bundle on the blowup of the K\"ahler manifold at a collection of points also admits a Hermitian Yang-Mills…
Twisted four-dimensional supersymmetric Yang-Mills theory famously gives a useful point of view on the Donaldson and Seiberg-Witten invariants of four-manifolds. In this paper we generalize the construction to include a path integral…
We study the moduli spaces of flat SL(r)- and PGL(r)-connections, or equivalently, Higgs bundles, on an algebraic curve. These spaces are noncompact Calabi-Yau orbifolds; we show that they can be regarded as mirror partners in two different…
The 3+1 dimensional Yang-Mills theory with the Pontryagin term included is studied on manifolds with a boundary. Based on the geometry of the universal bundle for Yang-Mills theory, the symplectic structure of this model is exhibited. The…
Nonlinear analysis has played a prominent role in the recent developments in geometry and topology. The study of the Yang-Mills equation and its cousins gave rise to the Donaldson invariants and more recently, the Seiberg-Witten invariants.…
The recent result of Strominger, Yau and Zaslow relating mirror symmetry to the quantum field theory notion of T-duality is reinterpreted as providing a way of geometrically characterizing which Calabi-Yau manifolds have mirror partners.…
Lagrangian classical field theory of even and odd fields is adequately formulated in terms of fibre bundles and graded manifolds. In particular, conventional Yang-Mills gauge theory is theory of connections on smooth principal bundles, but…
We study the phase structure of four-dimensional N=1 super Yang-Mills theories realized on D6-branes wrapping the RP^3 of a Z_2 orbifold of the deformed conifold. The non-trivial fundamental group of RP^3 allows for the gauge group to be…
The Jones-Witten invariants can be generalized for non-singular smooth vector fields with invariant probability measure on 3-manifolds, giving rise to new invariants of dynamical systems [22]. After a short survey of cohomological field…
Working over a pseudo-Riemannian manifold, for each vector bundle with connection we construct a sequence of three differential operators which is a complex (termed a Yang-Mills detour complex) if and only if the connection satisfies the…
We discuss the interplay between lagrangian distributions and connections in symplectic geometry, beginning with the traditional case of symplectic manifolds and then passing to the more general context of poly- and multisymplectic…
Gauge symmetric methods for data representation and analysis utilize tools from the differential geometry of vector bundles in order to achieve consistent data processing architectures with respect to local symmetry and equivariance. In…
Given a closed symplectic 4-manifold $(X,\omega)$, we define a twisted version of the Gromov-Taubes invariants for $(X,\omega)$, where the twisting coefficients are induced by the choice of a surface bundle over $X$. Given a fibered…
We study skein modules of 3-manifolds by embedding them into the Hilbert spaces of 4d ${\cal N}=4$ super-Yang-Mills theories. When the 3-manifold has reduced holonomy, we present an algorithm to determine the dimension and the list of…