We extend the notion of (branched) holomorphic Cartan geometry on a complex manifold to the context of Sasakian manifolds. Branched holomorphic Cartan geometries on Sasakian Calabi–Yau manifolds are investigated in particular.

The path integral for the partition function of Chern–Simons gauge theory with a compact gauge group is evaluated on a general Seifert $3$-manifold. This extends previous results and relies on abelianisation, a background field method and local application of the Kawasaki Index theorem.

For any positive integer $n$ and any Lie group $\mathfrak{G}$, given a definite symmetric bilinear form on $\mathbb{R}^n$ and an Ad‑invariant scalar product on the Lie algebra of $\mathfrak{G}$, we construct a variational problem on fields defined on an arbitrary oriented $(n + \operatorname{dim} \mathfrak{G})$-dimensional manifold $\mathcal{Y}$. We show that, if $\mathfrak{G}$ is compact and simply

The 2d gauged linear sigma model (GLSM) gives a UV model for quantum cohomology on a Kähler manifold $X$, which is reproduced in the IR limit. We propose and explore a 3d lift of this correspondence, where the UV model is the $\mathcal{N} = 2$ supersymmetric 3d gauge theory and the IR limit is given by Givental’s permutation equivariant quantum K‑theory on $X$. This gives a one-parameter deformation

We investigate F-theory models with a discrete $\mathbb{Z}_2$ gauge symmetry and $SU(n)$ gauge symmetries. We utilize a class of rational elliptic surfaces lacking a global section, known as Halphen surfaces of index $2$, to yield genus-one fibered K3 surfaces with a bisection, but lacking a global section. We consider F‑theory compactifications on these K3 surfaces times a K3 surface to build such

In these notes we will give an overview and road map for a definition and characterization of (relative) entropy for both classical and quantum systems. In other words, we will provide a consistent treatment of entropy which can be applied within the recently developed Orlicz space based approach to large systems. This means that the proposed approach successfully provides a refined framework for the