Computing a categorical Gromov–Witten invariant
We compute the $g=1$, $n=1$ B-model Gromov–Witten invariant of an elliptic curve $E$ directly from the derived category $\mathsf{D}_{\mathsf{coh}}^{b}(E)$. More precisely, we carry out the computation of the categorical Gromov–Witten invariant defined by Costello using as target a cyclic $\mathscr{A}_{\infty }$ model of $\mathsf{D}_{\mathsf{coh}}^{b}(E)$ described by Polishchuk. This is the first non-trivial computation of a positive-genus categorical Gromov–Witten invariant, and the result agrees with the prediction of mirror symmetry: it matches the classical (non-categorical) Gromov–Witten invariants of a symplectic 2-torus computed by Dijkgraaf.
2005 ◽
Vol 127
(1)
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pp. 1-34
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2017 ◽
Vol 2017
(732)
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pp. 211-246
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1998 ◽
Vol 2
(2)
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pp. 443-470
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2018 ◽
Vol 2018
(743)
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pp. 245-259
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