Authors: Gukov, Sergei
Nawata, Satoshi
Saberi, Ingmar
Stošić, Marko 
Sułkowski, Piotr
Title: Sequencing BPS spectra
Journal: Journal of High Energy Physics
Volume: 2016
Issue: 3
Issue Date: 1-Mar-2016
Rank: M21
ISSN: 1029-8479
DOI: 10.1007/JHEP03(2016)004
This paper provides both a detailed study of color-dependence of link homologies, as realized in physics as certain spaces of BPS states, and a broad study of the behavior of BPS states in general. We consider how the spectrum of BPS states varies as continuous parameters of a theory are perturbed. This question can be posed in a wide variety of physical contexts, and we answer it by proposing that the relationship between unperturbed and perturbed BPS spectra is described by a spectral sequence. These general considerations unify previous applications of spectral sequence techniques to physics, and explain from a physical standpoint the appearance of many spectral sequences relating various link homology theories to one another. We also study structural properties of colored HOMFLY homology for links and evaluate Poincaré polynomials in numerous examples. Among these structural properties is a novel “sliding” property, which can be explained by using (refined) modular S-matrix. This leads to the identification of modular transformations in Chern-Simons theory and 3d (Formula presented.) theory via the 3d/3d correspondence. Lastly, we introduce the notion of associated varieties as classical limits of recursion relations of colored superpolynomials of links, and study their properties.
Keywords: Differential and Algebraic Geometry | Supersymmetry and Duality | Topological Field Theories | Topological Strings
Publisher: Springer Link
Project: Quantum fields and knot homologies 
SUPERSYMMETRY: a window to non-perturbative physics 
Geometry, Education and Visualization With Applications 

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