Sequencing BPS spectra

Gukov, Sergei; Nawata, Satoshi; Saberi, Ingmar; Stošić, Marko; Sułkowski, Piotr

doi:10.1007/JHEP03(2016)004

Title: Sequencing BPS spectra

Abstract

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:

Gukov, Sergei ^[1]; Nawata, Satoshi ^[2]; Saberi, Ingmar ^[3]; Stošić, Marko ^[4]; Sułkowski, Piotr ^[5]

California Inst. of Technology (CalTech), Pasadena, CA (United States); Max-Planck-Institut fur Mathematik, Bonn (Germany)
California Inst. of Technology (CalTech), Pasadena, CA (United States); Aarhus Univ. (Denmark)
California Inst. of Technology (CalTech), Pasadena, CA (United States)
Instituto Superior Tecnico, Lisbon (Portugal); Mathematical Institute SANU, Belgrade (Serbia)
California Inst. of Technology (CalTech), Pasadena, CA (United States); Univ. of Warsaw (Poland)

Publication Date:: Wed Mar 02 00:00:00 EST 2016

Research Org.:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1327009

Grant/Contract Number:: SC0011632

Resource 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

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

Citation Formats


                    Gukov, Sergei, Nawata, Satoshi, Saberi, Ingmar, Stošić, Marko, and Sułkowski, Piotr. Sequencing BPS spectra.  United States: N. p., 2016. 
Web.  doi:10.1007/JHEP03(2016)004.

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                    Gukov, Sergei, Nawata, Satoshi, Saberi, Ingmar, Stošić, Marko, & Sułkowski, Piotr. Sequencing BPS spectra.  United States.  https://doi.org/10.1007/JHEP03(2016)004

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                    Gukov, Sergei, Nawata, Satoshi, Saberi, Ingmar, Stošić, Marko, and Sułkowski, Piotr. Wed .  
"Sequencing BPS spectra".  United States.  https://doi.org/10.1007/JHEP03(2016)004.  https://www.osti.gov/servlets/purl/1327009.

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@article{osti_1327009,

  title        = {Sequencing BPS spectra},

  author       = {Gukov, Sergei and Nawata, Satoshi and Saberi, Ingmar and Stošić, Marko and Sułkowski, Piotr},

  abstractNote = {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 study their properties.},

  doi          = {10.1007/JHEP03(2016)004},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 3,

  volume       = 2016,

  place        = {United States},

  year         = {Wed Mar 02 00:00:00 EST 2016},

  month        = {Wed Mar 02 00:00:00 EST 2016}

}

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Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that vebrane compacti cations provide a universal description of various old and new homological invariants of 3-manifolds. In terms of 3d/3d correspondence, such invariants are given by the Q-cohomology of the Hilbert space of partially topologically twisted 3d N = 2 theory T[M₃] on a Riemann surface with defects. We demonstrate this by concrete and explicit calculations in the case of monopole/Heegaard Floer homology and a 3-manifold analog of Khovanov-Rozansky link homology. The latter gives a categori cation of Chern-Simons partition function. Finally,more »« less
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Title: Sequencing BPS spectra

Abstract

Citation Formats

Algebras, BPS states, and strings journal, March 1996

Khovanov-Rozansky Homology and Topological Strings journal, October 2005

Seiberg-Witten Prepotential from Instanton Counting journal, January 2003

Gauge Theories and Macdonald Polynomials journal, November 2012

sl(3) link homology journal, January 2004

A unified Witten–Reshetikhin–Turaev invariant for integral homology spheres journal, September 2007

The colored Jones polynomials and the simplicial volume of a knot journal, January 2001

Differential Forms in Algebraic Topology book, January 1982

Refined knot invariants and Hilbert schemes journal, September 2015

Polynomial Invariants for Torus Knots¶and Topological Strings journal, March 2001

Computing Khovanov–Rozansky homology and defect fusion journal, January 2014

Gauge Theories Labelled by Three-Manifolds journal, December 2013

On the characteristic and deformation varieties of a knot conference, September 2004

Quantum ( sl n , ∧V n ) link invariant and matrix factorizations journal, December 2011

Calculation of BRS cohomology with spectral sequences journal, August 1991

Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial journal, March 2005

Large N Duality, Lagrangian Cycles, and Algebraic Knots journal, October 2012

Plane curves associated to character varieties of 3-manifolds journal, December 1994

A link-splitting spectral sequence in Khovanov homology journal, April 2015

On the quantum sl 2 invariants of knots and integral homology spheres conference, September 2002

Evolution method and “differential hierarchy” of colored knot polynomials conference, January 2013

Refined Hopf link revisited journal, April 2012

Chiral Rings and Anomalies in Supersymmetric Gauge Theory journal, December 2002

Torus Knots and the Topological Vertex journal, March 2014

Knot Invariants from Topological Recursion on Augmentation Varieties journal, December 2014

$ {\text{SL}}\left( {2,\mathbb{R}} \right) $ Chern-Simons, Liouville, and gauge theory on duality walls journal, August 2011

B-type defects in Landau-Ginzburg models journal, August 2007

Super-A-polynomial for knots and BPS states journal, February 2013

The Superpolynomial for Knot Homologies journal, January 2006

Vortex Counting and Lagrangian 3-Manifolds journal, October 2011

Stability of Landau-Ginzburg branes journal, August 2005

Superpolynomials for torus knots from evolution induced by cut-and-join operators journal, March 2013

BRST analysis of physical states for 2D gravity coupled toc≦1 matter journal, April 1992

3d TQFT from 6d SCFT journal, August 2013

Combinatorial knot contact homology and transverse knots journal, August 2011

Supersymmetry and Morse theory journal, January 1982

Character Expansion for Homfly Polynomials iii: all 3-Strand Braids in the First Symmetric Representation journal, July 2012

A-polynomial, B-model, and quantization journal, February 2012

Patterns in Knot Cohomology, I journal, January 2003

Walls, lines, and spectral dualities in 3d gauge theories journal, May 2014

The colored Jones function is q-holonomic journal, January 2005

Topological strings, D-model, and knot contact homology journal, January 2014

Torus Knots and Mirror Symmetry journal, March 2012

Link polynomial calculus and the AENV conjecture journal, April 2014

Distinguishing Mutants by knot Polynomials journal, April 1996

Multiple series Rogers-Ramanujan type identities journal, January 1984

Geometric engineering of quantum field theories journal, July 1997

Categorifying fractional Euler characteristics, Jones–Wenzl projectors and 3j-symbols journal, January 2012

Categorification of the Jones–Wenzl projectors journal, January 2012

The refined topological vertex journal, October 2009

Knots, links and branes at large N journal, November 2000

On the Invariants of Torus Knots Derived from Quantum Groups journal, March 1993

Elliptic Genera of Two-Dimensional $${\mathcal{N} = 2}$$ N = 2 Gauge Theories with Rank-One Gauge Groups journal, November 2013

Matrix factorizations and link homology II journal, January 2008

Dynamical breaking of supersymmetry journal, October 1981

Phases of N = 2 theories in two dimensions journal, August 1993

Colored Homfly Polynomials from Chern-Simons Theory journal, November 2013

Volume conjecture: refined and categorified journal, January 2012

Torus knots and the rational DAHA journal, November 2014

Khovanov homology and the slice genus journal, September 2010

Surface operators and separation of variables journal, January 2016

Knot invariants and topological strings journal, June 2000

Modular invariance for conformal full field algebras journal, December 2009

Ribbon graphs and their invaraints derived from quantum groups journal, January 1990

:{unav) journal, January 1997

A categorification of the Jones polynomial journal, February 2000

Character expansion for HOMFLY polynomials. II. Fundamental representation. Up to five strands in braid journal, March 2012

On the Landau-Ginzburg Description of n=2 Minimal Models journal, October 1994

An endomorphism of the Khovanov invariant journal, November 2005

Lagrangians for the Gopakumar–Vafa conjecture journal, January 2001

Khovanov homology of torus links journal, January 2009

Framed knot contact homology journal, February 2008

3d Chern-Simons theory from M5-branes journal, December 2013

Braid group actions on derived categories of coherent sheaves journal, May 2001

On the modularity of the unified WRT invariants of certain Seifert manifolds journal, January 2011

Gauge theory and knot homologies journal, May 2007

Four‐dimensional topological quantum field theory, Hopf categories, and the canonical bases journal, October 1994

Algebras, BPS states, and strings
journal, March 1996

Khovanov-Rozansky Homology and Topological Strings
journal, October 2005

Seiberg-Witten Prepotential from Instanton Counting
journal, January 2003

Gauge Theories and Macdonald Polynomials
journal, November 2012

sl(3) link homology
journal, January 2004

A unified Witten–Reshetikhin–Turaev invariant for integral homology spheres
journal, September 2007

The colored Jones polynomials and the simplicial volume of a knot
journal, January 2001

Differential Forms in Algebraic Topology
book, January 1982

Refined knot invariants and Hilbert schemes
journal, September 2015

Polynomial Invariants for Torus Knots¶and Topological Strings
journal, March 2001

Computing Khovanov–Rozansky homology and defect fusion
journal, January 2014

Gauge Theories Labelled by Three-Manifolds
journal, December 2013

On the characteristic and deformation varieties of a knot
conference, September 2004

Quantum ( sl _n , ∧V _n ) link invariant and matrix factorizations
journal, December 2011

Calculation of BRS cohomology with spectral sequences
journal, August 1991

Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial
journal, March 2005

Large N Duality, Lagrangian Cycles, and Algebraic Knots
journal, October 2012

Plane curves associated to character varieties of 3-manifolds
journal, December 1994

A link-splitting spectral sequence in Khovanov homology
journal, April 2015

On the quantum sl 2 invariants of knots and integral homology spheres
conference, September 2002

Evolution method and “differential hierarchy” of colored knot polynomials
conference, January 2013

Refined Hopf link revisited
journal, April 2012

Chiral Rings and Anomalies in Supersymmetric Gauge Theory
journal, December 2002

Torus Knots and the Topological Vertex
journal, March 2014

Knot Invariants from Topological Recursion on Augmentation Varieties
journal, December 2014

$ {\text{SL}}\left( {2,\mathbb{R}} \right) $ Chern-Simons, Liouville, and gauge theory on duality walls
journal, August 2011

B-type defects in Landau-Ginzburg models
journal, August 2007

Super-A-polynomial for knots and BPS states
journal, February 2013

The Superpolynomial for Knot Homologies
journal, January 2006

Vortex Counting and Lagrangian 3-Manifolds
journal, October 2011

Stability of Landau-Ginzburg branes
journal, August 2005

Superpolynomials for torus knots from evolution induced by cut-and-join operators
journal, March 2013

BRST analysis of physical states for 2D gravity coupled toc≦1 matter
journal, April 1992

3d TQFT from 6d SCFT
journal, August 2013

Combinatorial knot contact homology and transverse knots
journal, August 2011

Supersymmetry and Morse theory
journal, January 1982

Character Expansion for Homfly Polynomials iii: all 3-Strand Braids in the First Symmetric Representation
journal, July 2012

A-polynomial, B-model, and quantization
journal, February 2012

Patterns in Knot Cohomology, I
journal, January 2003

Walls, lines, and spectral dualities in 3d gauge theories
journal, May 2014

The colored Jones function is q-holonomic
journal, January 2005

Topological strings, D-model, and knot contact homology
journal, January 2014

Torus Knots and Mirror Symmetry
journal, March 2012

Link polynomial calculus and the AENV conjecture
journal, April 2014

Distinguishing Mutants by knot Polynomials
journal, April 1996

Multiple series Rogers-Ramanujan type identities
journal, January 1984

Geometric engineering of quantum field theories
journal, July 1997

Categorifying fractional Euler characteristics, Jones–Wenzl projectors and 3j-symbols
journal, January 2012

Categorification of the Jones–Wenzl projectors
journal, January 2012

The refined topological vertex
journal, October 2009

Knots, links and branes at large N
journal, November 2000

On the Invariants of Torus Knots Derived from Quantum Groups
journal, March 1993

Elliptic Genera of Two-Dimensional $${\mathcal{N} = 2}$$ N = 2 Gauge Theories with Rank-One Gauge Groups
journal, November 2013

Matrix factorizations and link homology II
journal, January 2008

Dynamical breaking of supersymmetry
journal, October 1981

Phases of N = 2 theories in two dimensions
journal, August 1993

Colored Homfly Polynomials from Chern-Simons Theory
journal, November 2013

Volume conjecture: refined and categorified
journal, January 2012

Torus knots and the rational DAHA
journal, November 2014

Khovanov homology and the slice genus
journal, September 2010

Surface operators and separation of variables
journal, January 2016

Knot invariants and topological strings
journal, June 2000

Modular invariance for conformal full field algebras
journal, December 2009

Ribbon graphs and their invaraints derived from quantum groups
journal, January 1990

:{unav)
journal, January 1997

A categorification of the Jones polynomial
journal, February 2000

Character expansion for HOMFLY polynomials. II. Fundamental representation. Up to five strands in braid
journal, March 2012

On the Landau-Ginzburg Description of n=2 Minimal Models
journal, October 1994

An endomorphism of the Khovanov invariant
journal, November 2005

Lagrangians for the Gopakumar–Vafa conjecture
journal, January 2001

Khovanov homology of torus links
journal, January 2009

Framed knot contact homology
journal, February 2008

3d Chern-Simons theory from M5-branes
journal, December 2013

Braid group actions on derived categories of coherent sheaves
journal, May 2001

On the modularity of the unified WRT invariants of certain Seifert manifolds
journal, January 2011

Gauge theory and knot homologies
journal, May 2007

Four‐dimensional topological quantum field theory, Hopf categories, and the canonical bases
journal, October 1994

Counting chiral primaries in , superconformal field theories
journal, July 2006

Super-A-polynomials for twist knots
journal, November 2012

Knot Homology and Refined Chern–Simons Index
journal, November 2014