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<p>In this article, we investigate the BPS invariants associated with framed links. We extend the relationship between the algebraic curve (i.e. dual <i>A</i>-polynomial) and the BPS invariants of a knot investigated in [14] to the case of a framed knot. With the help of the framing change formula for the dual <i>A</i>-polynomial of a framed knot, we give several explicit formulas for the extremal <i>A</i>-polynomials and the BPS invariants of framed knots. As to the framed links, we present several numerical calculations for the Ooguri-Vafa invariants and BPS invariants for framed Whitehead links and Borromean rings and verify the integrality property for them.</p>

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BPS invariants from framed links

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月12日

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  • Kai Wang,
  • Shengmao Zhu

摘要

In this article, we investigate the BPS invariants associated with framed links. We extend the relationship between the algebraic curve (i.e. dual A-polynomial) and the BPS invariants of a knot investigated in [14] to the case of a framed knot. With the help of the framing change formula for the dual A-polynomial of a framed knot, we give several explicit formulas for the extremal A-polynomials and the BPS invariants of framed knots. As to the framed links, we present several numerical calculations for the Ooguri-Vafa invariants and BPS invariants for framed Whitehead links and Borromean rings and verify the integrality property for them.