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Award ID contains: 1901876

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  1. ; (, International Journal of Modern Physics A)
    In this paper, we discuss decomposition in the context of three-dimensional Chern–Simons theories. Specifically, we argue that a Chern–Simons theory with a gauged noneffectively-acting one-form symmetry is equivalent to a disjoint union of Chern–Simons theories, with discrete theta angles coupling to the image under a Bockstein homomorphism of a canonical degree-two characteristic class. On three-manifolds with boundary, we show that the bulk discrete theta angles (coupling to bundle characteristic classes) are mapped to choices of discrete torsion in boundary orbifolds. We use this to verify that the bulk three-dimensional Chern–Simons decomposition reduces on the boundary to known decompositions of two-dimensional (WZW) orbifolds, providing a strong consistency test of our proposal. 
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  2. ; ; ; (, Journal of High Energy Physics)
    A bstract In this paper we study three-dimensional orbifolds by 2-groups with a trivially-acting one-form symmetry group BK . These orbifolds have a global two-form symmetry, and so one expects that they decompose into (are equivalent to) a disjoint union of other three-dimensional theories, which we demonstrate. These theories can be interpreted as sigma models on 2-gerbes, whose formal structures reflect properties of the orbifold construction. 
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  3. ; (, Algebraic Geometry)
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  4. ; (, Panoramas et synthèses)
    Cantat, S.; Massart, P; Dalibard, A.-L.; Mezard, A; Guillin, A.; Rigot, S.; Remy, B. (Ed.)
    We give a quick introduction to derived algebraic geometry (DAG) sampling basic constructions and techniques. We discuss affine derived schemes, derived algebraic stacks, and the Artin-Lurie representability theorem. Through the example of deformations of smooth and proper schemes, we explain how DAG sheds light on classical deformation theory. In the last two sections, we introduce differential forms on derived stacks, and then specialize to shifted symplectic forms, giving the main existence theorems proved in [17]. 
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  5. ; (, Publications of the Research Institute for Mathematical Sciences)
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