Year: 2026
Type: preprint
Abstract: For every integer $s$ and every $n \geq 1$, we construct a symmetric monoidal $(\infty,n)$-category $\mathrm{Leg}_n^s$ whose objects are $s$-shifted contact derived Artin stacks and whose $i$-morphisms are $i$-fold Legendrian correspondences. The construction is based on the fact that an $s$-shifted contact structure on a derived Artin stack $X$ is an $s$-shifted symplectic structure on $X$ relative to $B\mathbb{G}_m$, twisted by the weight-one line bundle, and that Legendrian structures are the corresponding relative Lagrangian structures. This lets us obtain the $(\infty,n)$-categories $\mathrm{Leg}_n^s$ as twisted forms over $B\mathbb{G}_m$ of the $(\infty,n)$-categories of iterated Lagrangian correspondences of Calaque, Haugseng and Scheimbauer, with the fiber product over $B\mathbb{G}_m$ as tensor product. For an $s$-shifted contact stack $X$, we then obtain the derived Legendrian category $\mathcal{F}_{c}(X)$. Its objects are Legendrian morphisms into $X$, and its mapping categories are categories of Legendrians in derived Legendrian intersections, which carry $(s-1)$-shifted contact structures. The AKSZ construction gives oriented extended topological field theories with values in $\mathrm{Leg}_n^s$, as well as shifted contact structures on the quotient mapping stacks $[\mathrm{Map}(Y,\widetilde X)/\mathbb{G}_m]$. Our definitions of contact and Legendrian structures agree with those of Berktav where both are defined, for every shift.
Source: arXiv (Cornell University)
Authors: İzbudak, Efe, Berktav, Kadri İlker
Institution: Middle East Technical University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162446768