We define integrability preserving Yang-Baxter deformations of symmetric space sigma models with non-semi-simple symmetry group, in particular the flat string, using only essential structures a model. For homogeneous deformations, Lax connection is same form as semi-simple case, although R operator no longer satisfies freestanding equation. inhomogeneous needs to be relaxed, by modifying underl...

We present some generalizations of a recently proposed alternative approach to nonabelian gauge theories based on the causal Epstein-Glaser method in perturbative quantum field theory. Nonabelian gauge invariance is defined by a simple commutator relation in every order of perturbation theory separately, using only the linear (abelian) BRStransformations of the asymptotic fields. This condition...

In matrix models, higher dimensional D-branes are obtained by imposing a noncommutative relation to coordinates of lower dimensional D-branes. On the other hand, a dual description of this noncommutative space is provided by higher dimensional D-branes with gauge fields. Fuzzy spheres can appear as a configuration of lower dimensional D-branes in a constant R-R field strength background. In thi...

Abstract We prove the abelian–nonabelian correspondence for quasimap $I$-functions. That is, if $Z$ is an affine l.c.i. variety with action by a complex reductive group $G$, we explicit formula relating $I$-functions of geometric invariant theory quotients $Z\mathord{/\mkern -6mu/}_{\theta } G$ and T$ where $T$ maximal torus $G$. apply to compute $J$-functions some Grassmannian bundles on varie...