Open string amplitudes of closed topological vertex
Kanehisa Takasaki, Toshio Nakatsu
备注：
latex2e, package amsmath,amssymb,amsthm,graphicx, 10 figures; (v2) Typos are corrected, the beginning of "Introduction'' is slightly expanded, and "Remark 5" is added in the end of Section 6
发表信息：
J. Phys. A: Math. Theor. 49 (2016), 025201 (28 pages)
The closed topological vertex is the simplest ``off-strip'' case of non-compact toric Calabi-Yau threefolds with acyclic web diagrams. By the diagrammatic method of topological vertex, open string amplitudes of topological string theory therein can be obtained by gluing a single topological vertex to an ``on-strip'' subdiagram of the tree-like web diagram. If non-trivial partitions are assigned to just two parallel external lines of the web diagram, the amplitudes can be calculated with the aid of techniques borrowed from the melting crystal models. These amplitudes are thereby expressed as matrix elements, modified by simple prefactors, of an operator product on the Fock space of 2D charged free fermions. This fermionic expression can be used to derive $q$-difference equations for generating functions of special subsets of the amplitudes. These $q$-difference equations may be interpreted as the defining equation of a quantum mirror curve.
Nonlinear equations for p-adic open, closed, and open-closed strings
我们研究了一维非线性伪微分方程组边值问题的解的结构，该方程组描述了标量快子场的p-adic开弦、闭弦和开闭弦的动力学（滚动）。对于开闭弦，我们证明了该方法收敛的形式p= 4 n +1的奇值p的条件下，封闭字符串的解决方案是已知的。当p=2时，讨论了边值问题解的存在性和不存在性，并指出了出现间断解的可能性.
