Twisted moduli spaces and Duistermaat–Heckman measures

Zerouali, Ahmed J.

doi:10.1016/j.geomphys.2020.104042

Cited by 1 publication

(3 citation statements)

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“…Factorisation homology on surfaces equipped with non-trivial Out(G)-bundles has also a natural field theoretical interpretation: The value of factorisation homology describes the coupling of the quantum character field theory to non-trivial Out(G)-background fields. In [MSS19] the topological limit of the partition function of 2-dimensional Yang-Mills theory coupled to an Out(G)-background field ϕ : Σ −→ B Out(G) was related to the symplectic volume of the moduli space of flat ϕ-twisted G-bundles M ρ (Σ) [Mei17,Zer21]. We will show the analogous statement for quantum character stacks, i.e.…”

Section: Introductionmentioning

confidence: 78%

“…We first recollect some background about twisted bundles in the differential geometric setting, see for example [Mei17] and [Zer21] for more details and [MSS19] for the non-flat version. Let Σ be an oriented surface equipped with a principal Out(G)-bundle P −→ Σ.…”

Section: The Moduli Space Of Flat Twisted Bundlesmentioning

confidence: 99%

“…Remark 4.1. The moduli space of flat Out(G)-twisted bundles on a closed surface Σ was studied in the differential geometric setting in [Mei17,Zer21]. In particular, it is shown in loc.…”

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confidence: 99%

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Finite symmetries of quantum character stacks

Keller¹,

Müller²

2021

Preprint

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For a finite group D, we study categorical factorisation homology on oriented surfaces equipped with principal D-bundles, which 'integrates' a (linear) balanced braided category A with D-action over those surfaces. For surfaces with at least one boundary component, we identify the value of factorisation homology with the category of modules over an explicit algebra in A, extending the work of Ben-Zvi, Brochier and Jordan to surfaces with D-bundles. Furthermore, we show that the value of factorisation homology on annuli, boundary conditions, and point defects can be described in terms of equivariant representation theory.Our main example comes from an action of Dynkin diagram automorphisms on representation categories of quantum groups. We show that in this case factorisation homology gives rise to a quantisation of the moduli space of flat twisted bundles.

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Section: Introductionmentioning

confidence: 78%