BPS spectra of complex knots

IF 5 2区物理与天体物理 Q1 Physics and Astronomy

Physical Review D Pub Date : 2025-05-20 DOI:10.1103/physrevd.111.106011

Vivek Kumar Singh, Nafaa Chbili

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引用次数: 0

Abstract

Marino’s Conjecture remains underexplored within the framework of SO(N) string dualities. In this article, we investigated the reformulated invariants of one-parameter families of knots [K]p derived from tangle surgery on Manolescu’s quasialternating knot diagrams [C. Manolescu, ]. Within topological string dualities, we have verified Marino’s integrality conjecture for these families of knots up to the Young diagram representation R, with |R|≤2. Furthermore, through our analysis, we have conjectured a closed structure for the extremal refined Bogomol’nyi–Prasad–Sommerfeld (BPS) integers for the torus knots [31]2p+1 and [820]2p+1, p∈Z≥0. As the parameter p of the knot diagram increases, the total crossing number of a knot exceeds 16, which we describe as a complex knot. Interestingly, we discovered the maximum number of gaps in the BPS spectra associated with complex knot families. Moreover, our observations indicated that as p increases, the size of these gaps also expands.

Published by the American Physical Society

2025

查看原文本刊更多论文

复杂结的BPS谱

Marino猜想在SO(N)弦对偶性的框架内仍未得到充分的研究。在本文中，我们研究了Manolescu 's拟交替结图[C]上由缠结手术导出的单参数结族[K]p的重新表述不变量。Manolescu]。在拓扑弦对偶性中，我们验证了这些结族的Marino的完整性猜想，直到Young图表示R，其中|R|≤2。进一步，通过分析，我们推测了环面结点[31]2p+1和[820]2p+1， p∈Z≥0的极值精化Bogomol 'nyi-Prasad-Sommerfeld （BPS）整数的封闭结构。随着结图参数p的增大，一个结的总交叉数超过16个，我们称之为复结。有趣的是，我们发现了与复杂结家族相关的BPS光谱中最大数量的间隙。此外，我们的观察表明，随着p的增加，这些差距的大小也会扩大。2025年由美国物理学会出版

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来源期刊

Physical Review D 物理-天文与天体物理

CiteScore

9.20

自引率

36.00%

发文量

审稿时长

2 months

期刊介绍： Physical Review D (PRD) is a leading journal in elementary particle physics, field theory, gravitation, and cosmology and is one of the top-cited journals in high-energy physics. PRD covers experimental and theoretical results in all aspects of particle physics, field theory, gravitation and cosmology, including: Particle physics experiments, Electroweak interactions, Strong interactions, Lattice field theories, lattice QCD, Beyond the standard model physics, Phenomenological aspects of field theory, general methods, Gravity, cosmology, cosmic rays, Astrophysics and astroparticle physics, General relativity, Formal aspects of field theory, field theory in curved space, String theory, quantum gravity, gauge/gravity duality.