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arxiv: 1309.6262 · v1 · pith:P5XV3MY3new · submitted 2013-09-24 · 🧮 math.AG · hep-th· math-ph· math.MP

A Landau-Ginzburg/Calabi-Yau correspondence for the mirror quintic

classification 🧮 math.AG hep-thmath-phmath.MP
keywords mirrorquinticlandau-ginzburgcalabi-yaucorrespondenceprovetheoryanalytic
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We prove a version of the Landau-Ginzburg/Calabi-Yau correspondence for the mirror quintic. In particular we calculate the genus-zero FJRW theory for the pair (W, G) where W is the Fermat quintic polynomial and G = SL(W). We identify it with the Gromov-Witten theory of the mirror quintic three-fold via an explicit analytic continuation and symplectic transformation. In the process we prove a mirror theorem for the corresponding Landau-Ginzburg model (W,G).

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