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Sequencing BPS Spectra

Gukov, Sergei and Nawata, Satoshi and Saberi, Ingmar and Stošić, Marko and Sułkowski, Piotr (2016) Sequencing BPS Spectra. Journal of High Energy Physics, 2016 (03). Art. No. 004. ISSN 1126-6708. doi:10.1007/JHEP03(2016)004.

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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 N=2 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.

Item Type:Article
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URLURL TypeDescription Paper
Gukov, Sergei0000-0002-9486-1762
Sułkowski, Piotr0000-0002-6176-6240
Additional Information:© 2016 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: January 9, 2016; Accepted: February 15, 2016; Published: March 2, 2016. S.N. would like to express deep gratitude to the previous institutions, NIKHEF Amsterdam, University of Warsaw and Max Planck Institute for Mathematics at Bonn where most of this work was carried out. This work has been supported by the ERC Starting Grant no. 335739 "Quantum fields and knot homologies", funded by the European Research Council under the European Union's Seventh Framework Programme, and by Walter Burke Institute for Theoretical Physics, California Institute of Technology. The work of S.G. is partially supported by the DOE Grant DE-SC0011632. The work of S.N. is partially supported by the ERC Advanced Grant no. 246974, "Supersymmetry: a window to non-perturbative physics", and also partially supported by the center of excellence grant "Center for Quantum Geometry of Moduli Spaces (QGM)" from the Danish National Research Foundation. M.S. was also partially supported by the Ministry of Education of Serbia, grant no. 174012. P.S. acknowledges the support of the Foundation for Polish Science.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
European Research Council (ERC)335739
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Department of Energy (DOE)DE-SC0011632
European Research Council (ERC)246974
Danish Research CouncilUNSPECIFIED
Ministry of Education (Serbia)174012
Foundation for Polish ScienceUNSPECIFIED
Subject Keywords:Differential and Algebraic Geometry, Supersymmetry and Duality, Topological Field Theories, Topological Strings
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Issue or Number:03
Record Number:CaltechAUTHORS:20160113-131017250
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:63644
Deposited By: Joy Painter
Deposited On:13 Jan 2016 21:31
Last Modified:10 Nov 2021 23:19

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