9 papers
Higher abelian gauge theory in BV formalism
Shuhan Jiang
A BV structure is constructed on the space of zero modes of a quadratic elliptic higher abelian gauge theory. The associated BV integral is shown to be independent of the choice of…
From algebroids to spaces: Part I
Alberto S. Cattaneo, Shuhan Jiang
The notion of spaces over dg manifolds is developed. An equivalence between the category of transitive algebroids and that of spaces is established…
Homotopy theory for curved spaces
Shuhan Jiang
This paper proves that spaces over a dg manifold form a category of fibrant objects. Together with the first main result of the companion paper [CJ26], this implies that…
Almost Vector Bundles over Perfectoid Spaces
Yuntong Cui, Guo Li, Shuhan Jiang +1
In this paper, we define vector bundles within the framework of almost mathematics (referred to as almost vector bundles) and establish the -descent theorem together with a stru…
Equivariant localization in Batalin-Vilkovisky formalism
Alberto S. Cattaneo, Shuhan Jiang
We derive equivariant localization formulas of Atiyah--Bott and cohomological field theory types in the Batalin-Vilkovisky formalism and discuss their applications in Poisson geome…
Cohomological field theories and generalized Seiberg-Witten equations
Shuhan Jiang, Jürgen Jost
We introduce a formalism for constructing cohomological field theories (CohFT) out of nonlinear PDEs based on the first author's previous work (arXiv:2202.12425). We apply the form…
Variational aspects of the generalized Seiberg-Witten functional
Wanjun Ai, Shuhan Jiang, Jürgen Jost
In this paper, as a step towards a unified mathematical treatment of the gauge functionals from quantum field theory that have found profound applications in mathematics, we genera…
A coadjoint orbit-like construction for Jordan superalgebras
Florio M. Ciaglia, Shuhan Jiang, Jürgen Jost +1
We investigate the canonical pseudo-Riemannian metrics associated with Jordan-analogues of the coadjoint orbits for pseudo-Euclidean Jordan superalgebras.
Cohomological Lagrangian field theory
Shuhan Jiang
This paper introduces a geometric framework for classical cohomological field theories based on -algebras and gauge natural field theories. A BV-BFV extension of the fra…