A modified melting crystal model and the Ablowitz–Ladik hierarchy

• 高崎, 金久

抄録

This paper addresses the issue of integrable structure in a modified melting crystal model of topological string theory on the resolved conifold. The partition function can be expressed as the vacuum expectation value of an operator on the Fock space of 2D complex free fermion fields. The quantum torus algebra of fermion bilinears behind this expression is shown to have an extended set of 'shift symmetries'. They are used to prove that the partition function (deformed by external potentials) is essentially a tau function of the 2D Toda hierarchy. This special solution of the 2D Toda hierarchy can also be characterized by a factorization problem of [Z x Z] matrices. The associated Lax operators turn out to be quotients of first-order difference operators. This implies that the solution of the 2D Toda hierarchy in question is actually a solution of the Ablowitz–Ladik (equivalently, the relativistic Toda) hierarchy. As a byproduct, the shift symmetries are shown to be related to matrix-valued quantum dilogarithmic functions.

収録刊行物

• Journal of Physics A: Mathematical and Theoretical

  Journal of Physics A: Mathematical and Theoretical 46 (24), 2013-05-24

  IOP Publishing

詳細情報

• CRID: 1050282810749079296
• NII論文ID: 120005296111
• NII書誌ID: AA12185372
• ISSN: 17518113
• HANDLE: 2433/175510
• 本文言語コード: en
• 資料種別: journal article
• データソース種別:
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  • CiNii Articles
  • KAKEN