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Browsing by Author "Sharpe, E."

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    Hidden exceptional symmetry in the pure spinor superstring
    Eager, R.; Lockhart, G.; Sharpe, E. (2020-01-06)
    The pure spinor formulation of superstring theory includes an interacting sector of central charge c(lambda) = 22, which can be realized as a curved beta gamma system on the cone over the orthogonal Grassmannian OG(+) (5,10). We find that the spectrum of the beta gamma system organizes into representations of the g = e(6) affine algebra at level -3, whose so(10)(-3) circle plus u(1)(-4) subalgebra encodes the rotational and ghost symmetries of the system. As a consequence, the pure spinor partition function decomposes as a sum of affine e(6) characters. We interpret this as an instance of a more general pattern of enhancements in curved beta gamma systems, which also includes the cases g = so(8) and e(7), corresponding to target spaces that are cones over the complex Grassmannian Gr(2, 4) and the complex Cayley plane OP2. We identify these curved beta gamma systems with the chiral algebras of certain two-dimensional (2D) (0,2) conformal field theories arising from twisted compactification of 4D N = 2 superconformal field theories on S-2.
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    Notes on gauging noninvertible symmetries. Part I. Multiplicity-free cases
    Perez-Lona, Alonso; Robbins, D.; Sharpe, E.; Vandermeulen, T.; Yu, X. (2024-02-21)
    In this paper we discuss gauging noninvertible zero-form symmetries in two dimensions. We specialize to certain gaugeable cases, specifically, fusion categories of the form for a suitable Hopf algebra (which includes the special case Rep(G) for G a finite group). We also specialize to the case that the fusion category is multiplicity-free. We discuss how to construct a modular-invariant partition function from a choice of Frobenius algebra structure on . We discuss how ordinary G orbifolds for finite groups G are a special case of the construction, corresponding to the fusion category Vec(G) = Rep(ℂ[G]*). For the cases Rep(S3), Rep(D4), and Rep(Q8), we construct the crossing kernels for general intertwiner maps. We explicitly compute partition functions in the examples of Rep(S3), Rep(D4), Rep(Q8), and , and discuss applications in c = 1 CFTs. We also discuss decomposition in the special case that the entire noninvertible symmetry group acts trivially.