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arXiv · 1904.04766

A note on S-dual basis in free fermion system

Shinya Sasa·Akimi Watanabe·Yutaka Matsuo
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Abstract

Free fermion system is the simplest quantum field theory which has the symmetry of Ding-Iohara-Miki algebra (DIM). DIM has S-duality symmetry, known as Miki automorphism which defines the transformation of generators. In this note, we introduce the second set of the fermionic basis (S-dual basis) which implement the duality transformation. It may be interpreted as the Fourier dual of the standard basis, and the inner product between the standard and the S-dual ones is proportional to the Hopf link invariant. We also rewrite the general topological vertex in the form of Awata-Feigin-Shiraishi intertwiner and show that it becomes more symmetric for the duality transformation.

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Shinya Sasa, Akimi Watanabe, Yutaka Matsuo. 2019-04-09. A note on S-dual basis in free fermion system. https://doi.org/10.1093/ptep/ptz158

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