Quantum Field Theory on Affine Bundles

Unstable Bundles in Quantum Field Theory

The relation between connections on 2-dimensional manifolds and holomorphic bundles provides a new perspective on the role of classical gauge fields in quantum field theory in two, three and four dimensions. In particular we show that there is a close relation between unstable bundles and monopoles, sphalerons and instantons. Some of these classical configurations emerge as nodes of quantum vac...

Recent developments in affine Toda quantum field theory

Affine Toda Field Theory

We present one loop boundary reflection matrix for d (1) 4 Toda field theory defined on a half line with the Neumann boundary condition. This result demonstrates a nontrivial cancellation of non-meromorphic terms which are present when the model has a particle spectrum with more than one mass. Using this result, we determine uniquely the exact boundary reflection matrix which turns out to be ‘n...

Flat Bundles on Affine Manifolds

We review some recent results in the theory of affine manifolds and bundles on them. Donaldson–Uhlenbeck–Yau type correspondences for flat vector bundles and principal bundles are shown. We also consider flat Higgs bundles and flat pairs on affine manifolds. A bijective correspondence between polystable flat Higgs bundles and solutions of the Yang–Mills–Higgs equation in the context of affine m...

Jacobi structures on affine bundles

We study affine Jacobi structures (brackets) on an affine bundle π : A→M , i.e. Jacobi brackets that close on affine functions. We prove that if the rank of A is non-zero, there is a one-to-one correspondence between affine Jacobi structures on A and Lie algebroid structures on the vector bundle A = ⋃ p∈M Aff(Ap,R) of affine functionals. In the case rank A = 0, it is shown that there is a one-t...