Solar energy paper index
3d-3d correspondence for knot complements with finite and large $N$
One-line summary
A solar energy research paper on 3d-3d correspondence for knot complements with finite and large $N$.
Engineering notes
Engineering notes will be added by the Power for Solar editorial team.
Chinese explanation / 中文解读
中文解读待补充：本站会优先为光伏效率、钙钛矿太阳能电池、储能技术、太阳能热利用、BIPV、并网技术等高价值论文补充中文说明。
Original abstract
For $G=SU(N)$ at finite and large $N$, with a totally symmetric representation, we realize the homological block $F_K$ for a knot complement $S^3 \backslash K$, given in the form of the inverted Habiro series, as a half-index of a 3d $\mathcal{N}=2$ theory $T[M_3]$ by studying some examples, which we expect to extend to general knots. From the half-index expression, it is also possible to realize the colored HOMFLY-PT polynomial by taking a certain set of poles. Through the half-index realization, we describe a method for obtaining the $G=SU(N)$ homological block and its $a$-deformed version for $S^3 \backslash K$ from a Habiro series expression for the colored HOMFLY-PT polynomial. We also discuss some properties of partition functions for arbitrary $N$.
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