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Title: Sequencing BPS spectra

In this article, we provide 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 Poincar e polynomials in numerous examples. Among these structural properties is a novel "sliding" property, which can be explained by using (re fined) modular S-matrix. This leads to the identi fication of modular transformations in Chern-Simons theory and 3d N = 2 theory via the 3d/3d correspondence. In conclusion, we introduce the notion of associated varieties as classical limits of recursion relations of colored superpolynomials of links, and studymore » their properties.« less
Authors:
 [1] ;  [2] ;  [3] ;  [4] ;  [5]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States); Max-Planck-Institut fur Mathematik, Bonn (Germany)
  2. California Inst. of Technology (CalTech), Pasadena, CA (United States); Aarhus Univ. (Denmark)
  3. California Inst. of Technology (CalTech), Pasadena, CA (United States)
  4. Instituto Superior Tecnico, Lisbon (Portugal); Mathematical Institute SANU, Belgrade (Serbia)
  5. California Inst. of Technology (CalTech), Pasadena, CA (United States); Univ. of Warsaw (Poland)
Publication Date:
OSTI Identifier:
1327009
Grant/Contract Number:
SC0011632
Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 3; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Research Org:
California Inst. of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS differential and algebraic geometry; supersymmetry and duality; topological field theories; topological strings