An infrared bootstrap of the Schur index with surface defects

Fluder, Martin; Longhi, Pietro

doi:10.1007/JHEP09(2019)062

Title: An infrared bootstrap of the Schur index with surface defects

Abstract

The infrared formula relates the Schur index of a 4d $$\mathcal{N}$$ = 2 theory to its wall-crossing invariant, a.k.a. BPS monodromy. A further extension of this formula, proposed by Córdova, Gaiotto and Shao, includes contributions by many types of line and surface defects. We study BPS monodromies in the presence of vortex surface defects of arbitrary vorticity for general class $$\mathcal{S}$$ theories of type A₁ engineered by UV curves with at least one regular puncture. The trace of these defect BPS monodromies is shown to coincide with the action of certain q-difference operators acting on the trace of the (pure) 4d BPS monodromy. We use these operators to develop a “bootstrap” (of traces) of BPS monodromies, relying only on their infrared properties, thereby reproducing the very general ultraviolet characterization of the Schur index.

Authors:

Fluder, Martin ^[1];

^[2]

California Inst. of Technology (CalTech), Pasadena, CA (United States); Univ. of Tokyo (Japan)
ETH Zurich (Switzerland)

Publication Date:: 2019-09-10

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

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

OSTI Identifier:: 1596782

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: 2019; Journal Issue: 9; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Fluder, Martin, and Longhi, Pietro. An infrared bootstrap of the Schur index with surface defects.  United States: N. p., 2019. 
Web.  https://doi.org/10.1007/JHEP09(2019)062.

Copy to clipboard


                    Fluder, Martin, & Longhi, Pietro. An infrared bootstrap of the Schur index with surface defects.  United States.  https://doi.org/10.1007/JHEP09(2019)062

Copy to clipboard


                    Fluder, Martin, and Longhi, Pietro. Tue .  
"An infrared bootstrap of the Schur index with surface defects".  United States.  https://doi.org/10.1007/JHEP09(2019)062.  https://www.osti.gov/servlets/purl/1596782.

Copy to clipboard


                    
@article{osti_1596782,

  title        = {An infrared bootstrap of the Schur index with surface defects},

  author       = {Fluder, Martin and Longhi, Pietro},

  abstractNote = {The infrared formula relates the Schur index of a 4d $\mathcal{N}$ = 2 theory to its wall-crossing invariant, a.k.a. BPS monodromy. A further extension of this formula, proposed by Córdova, Gaiotto and Shao, includes contributions by many types of line and surface defects. We study BPS monodromies in the presence of vortex surface defects of arbitrary vorticity for general class $\mathcal{S}$ theories of type A1 engineered by UV curves with at least one regular puncture. The trace of these defect BPS monodromies is shown to coincide with the action of certain q-difference operators acting on the trace of the (pure) 4d BPS monodromy. We use these operators to develop a “bootstrap” (of traces) of BPS monodromies, relying only on their infrared properties, thereby reproducing the very general ultraviolet characterization of the Schur index.},

  doi          = {10.1007/JHEP09(2019)062},

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

  number       = 9,

  volume       = 2019,

  place        = {United States},

  year         = {2019},

  month        = {9}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1007/JHEP09(2019)062

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 3 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD
journal, December 1994

Seiberg, N.; Witten, E.
Nuclear Physics B, Vol. 431, Issue 3
DOI: 10.1016/0550-3213(94)90214-3

N = 2 dualities
journal, August 2012

Gaiotto, Davide
Journal of High Energy Physics, Vol. 2012, Issue 8
DOI: 10.1007/JHEP08(2012)034

Seiberg-Witten Prepotential from Instanton Counting
journal, January 2003

Nekrasov, Nikita A.
Advances in Theoretical and Mathematical Physics, Vol. 7, Issue 5
DOI: 10.4310/ATMP.2003.v7.n5.a4

Spectral Networks
journal, March 2013

Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew
Annales Henri Poincaré, Vol. 14, Issue 7
DOI: 10.1007/s00023-013-0239-7

Tinkertoys for Gaiotto duality
journal, November 2010

Chacaltana, Oscar; Distler, Jacques
Journal of High Energy Physics, Vol. 2010, Issue 11
DOI: 10.1007/JHEP11(2010)099

Gauge Theories and Macdonald Polynomials
journal, November 2012

Gadde, Abhijit; Rastelli, Leonardo; Razamat, Shlomo S.
Communications in Mathematical Physics, Vol. 319, Issue 1
DOI: 10.1007/s00220-012-1607-8

An Index for 4 Dimensional Super Conformal Theories
journal, June 2007

Kinney, Justin; Maldacena, Juan; Minwalla, Shiraz
Communications in Mathematical Physics, Vol. 275, Issue 1
DOI: 10.1007/s00220-007-0258-7

BPS graphs: from spectral networks to BPS quivers
journal, July 2017

Gabella, Maxime; Longhi, Pietro; Park, Chan Y.
Journal of High Energy Physics, Vol. 2017, Issue 7
DOI: 10.1007/JHEP07(2017)032

Schur indices, BPS particles, and Argyres-Douglas theories
journal, January 2016

Córdova, Clay; Shao, Shu-Heng
Journal of High Energy Physics, Vol. 2016, Issue 1
DOI: 10.1007/JHEP01(2016)040

On classification ofN=2 supersymmetric theories
journal, December 1993

Cecotti, Sergio; Vafa, Cumrun
Communications in Mathematical Physics, Vol. 158, Issue 3
DOI: 10.1007/BF02096804

Framed BPS states
journal, January 2013

Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew
Advances in Theoretical and Mathematical Physics, Vol. 17, Issue 2
DOI: 10.4310/ATMP.2013.v17.n2.a1

Wall-crossing in coupled 2d-4d systems
journal, December 2012

Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew
Journal of High Energy Physics, Vol. 2012, Issue 12
DOI: 10.1007/JHEP12(2012)082

ADE spectral networks
journal, August 2016

Longhi, Pietro; Park, Chan Y.
Journal of High Energy Physics, Vol. 2016, Issue 8
DOI: 10.1007/JHEP08(2016)087

A new supersymmetric index
journal, November 1992

Cecotti, Sergio; Fendley, Paul; Intriligator, Ken
Nuclear Physics B, Vol. 386, Issue 2
DOI: 10.1016/0550-3213(92)90572-S

Ising model andN=2 supersymmetric theories
journal, October 1993

Cecotti, Sergio; Vafa, Cumrun
Communications in Mathematical Physics, Vol. 157, Issue 1
DOI: 10.1007/BF02098023

Refined, Motivic, and Quantum
journal, November 2009

Dimofte, Tudor; Gukov, Sergei
Letters in Mathematical Physics, Vol. 91, Issue 1
DOI: 10.1007/s11005-009-0357-9

The Self-Duality Equations on a Riemann Surface
journal, July 1987

Hitchin, N. J.
Proceedings of the London Mathematical Society, Vol. s3-55, Issue 1
DOI: 10.1112/plms/s3-55.1.59

Supersymmetric Yang-Mills theory and integrable systems
journal, February 1996

Donagi, Ron; Witten, Edward
Nuclear Physics B, Vol. 460, Issue 2
DOI: 10.1016/0550-3213(95)00609-5

Integrable systems and supersymmetric gauge theory
journal, January 1996

Martinec, Emil J.; Warner, Nicholas P.
Nuclear Physics B, Vol. 459, Issue 1-2
DOI: 10.1016/0550-3213(95)00588-9

Classification of complete $N = 2$ supersymmetric theories in 4 dimensions
journal, January 2013

Cecotti, Sergio; Vafa, Cumrun
Surveys in Differential Geometry, Vol. 18, Issue 1
DOI: 10.4310/SDG.2013.v18.n1.a2

On the phase transition towards permanent quark confinement
journal, June 1978

't Hooft, G.
Nuclear Physics B, Vol. 138, Issue 1
DOI: 10.1016/0550-3213(78)90153-0

Rigid Surface Operators
journal, January 2010

Gukov, Sergei; Witten, Edward
Advances in Theoretical and Mathematical Physics, Vol. 14, Issue 1
DOI: 10.4310/ATMP.2010.v14.n1.a3

Surface defects and instanton–vortex interaction
journal, July 2017

Gorsky, A.; Le Floch, B.; Milekhin, A.
Nuclear Physics B, Vol. 920
DOI: 10.1016/j.nuclphysb.2017.04.010

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

Witten, Edward
Nuclear Physics B, Vol. 403, Issue 1-2
DOI: 10.1016/0550-3213(93)90033-L

Branes and N = 2 theories in two dimensions
journal, March 1998

Hanany, Amihay; Hori, Kentaro
Nuclear Physics B, Vol. 513, Issue 1-2
DOI: 10.1016/S0550-3213(97)00754-2

Solutions of four-dimensional field theories via M-theory
journal, September 1997

Witten, Edward
Nuclear Physics B, Vol. 500, Issue 1-3
DOI: 10.1016/S0550-3213(97)00416-1

Topological—anti-topological fusion
journal, December 1991

Cecotti, Sergio; Vafa, Cumrun
Nuclear Physics B, Vol. 367, Issue 2
DOI: 10.1016/0550-3213(91)90021-O

Geometry and integrability of topological-antitopological fusion
journal, March 1993

Dubrovin, B.
Communications in Mathematical Physics, Vol. 152, Issue 3
DOI: 10.1007/BF02096618

Jenkins–Strebel differentials with poles
journal, January 2008

Liu, Jinsong
Commentarii Mathematici Helvetici
DOI: 10.4171/CMH/123

Self-dual strings and N = 2 supersymmetric field theory
journal, October 1996

Klemm, Albrecht; Lerche, Wolfgang; Mayr, Peter
Nuclear Physics B, Vol. 477, Issue 3
DOI: 10.1016/0550-3213(96)00353-7

The structure of BPS spectra
text, January 2015

Longhi, Pietro
No Publisher Supplied
DOI: 10.7282/T3FQ9ZMF

New phenomena in SU(3) supersymmetric gauge theory
journal, August 1995

Argyres, Philip C.; Douglas, Michael R.
Nuclear Physics B, Vol. 448, Issue 1-2
DOI: 10.1016/0550-3213(95)00281-V

New = 2 superconformal field theories in four dimensions
journal, February 1996

Argyres, Philip C.; Ronen Plesser, M.; Seiberg, Nathan
Nuclear Physics B, Vol. 461, Issue 1-2
DOI: 10.1016/0550-3213(95)00671-0

General Argyres-Douglas theory
journal, January 2013

Xie, Dan
Journal of High Energy Physics, Vol. 2013, Issue 1
DOI: 10.1007/JHEP01(2013)100

S-duality and 2d topological QFT
journal, March 2010

Gadde, Abhijit; Pomoni, Elli; Rastelli, Leonardo
Journal of High Energy Physics, Vol. 2010, Issue 3
DOI: 10.1007/JHEP03(2010)032

5D SYM on 3D sphere and 2D YM
journal, October 2012

Kawano, Teruhiko; Matsumiya, Nariaki
Physics Letters B, Vol. 716, Issue 3-5
DOI: 10.1016/j.physletb.2012.08.055

2d TQFT structure of the superconformal indices with outer-automorphism twists
journal, March 2013

Mekareeya, Noppadol; Song, Jaewon; Tachikawa, Yuji
Journal of High Energy Physics, Vol. 2013, Issue 3
DOI: 10.1007/JHEP03(2013)171

Works referencing / citing this record:

Testing Macdonald index as a refined character of chiral algebra
journal, February 2020

Watanabe, Akimi; Zhu, Rui-Dong
Journal of High Energy Physics, Vol. 2020, Issue 2
DOI: 10.1007/jhep02(2020)004

Similar Records in DOE PAGES and OSTI.GOV collections:

Surface defect indices and 2d-4d BPS states

Journal Article Córdova, Clay ; Gaiotto, Davide ; Shao, Shu-Heng - Journal of High Energy Physics (Online)

We conjecture a formula for the Schur index of four-dimensional N=2 theories coupled to (2, 2) surface defects in terms of the 2d-4d BPS spectrum in the Coulomb phase of the theory. The key ingredient in our conjecture is a refined 2d-4d wall-crossing invariant, which we also formulate. Our result intertwines recent conjectures expressing the four-dimensional Schur index in terms of infrared BPS particles, with the Cecotti-Vafa formula for limits of the elliptic genus in terms of two-dimensional BPS solitons. We extend our discussion to framed 2d-4d BPS states, and use this to demonstrate a general relationship between surface defectmore »« less
Cited by 10
https://doi.org/10.1007/jhep12(2017)078

Full Text Available
Infrared computations of defect Schur indices

Journal Article Córdova, Clay ; Gaiotto, Davide ; Shao, Shu-Heng - Journal of High Energy Physics (Online)

We conjecture a formula for the Schur index of four-dimensional N = 2 theories in the presence of boundary conditions and/or line defects, in terms of the low-energy effective Seiberg-Witten description of the system together with massive BPS excitations. We test our proposal in a variety of examples for SU(2) gauge theories, either conformal or asymptotically free. We use the conjecture to compute these defect-enriched Schur indices for theories which lack a Lagrangian description, such as Argyres-Douglas theories. We demonstrate in various examples that line defect indices can be expressed as sums of characters of the associated two-dimensional chiral algebramore »« less
Cited by 10
https://doi.org/10.1007/JHEP11(2016)106

Full Text Available
Superconformal index, BPS monodromy and chiral algebras

Journal Article Cecotti, Sergio ; Song, Jaewon ; Vafa, Cumrun ; ... - Journal of High Energy Physics (Online)

We show that specializations of the 4d N = 2 superconformal index labeled by an integer N is given by Tr MN where M is the Kontsevich-Soibelman monodromy operator for BPS states on the Coulomb branch. We provide evidence that the states enumerated by these limits of the index lead to a family of 2d chiral algebras A_N. This generalizes the recent results for the N = –1 case which corresponds to the Schur limit of the superconformal index. We show that this specialization of the index leads to the same integrand as that of the elliptic genus of compactificationmore »« less
Cited by 15
https://doi.org/10.1007/jhep11(2017)013

Full Text Available
Coulomb branch operators and mirror symmetry in three dimensions

Journal Article Dedushenko, Mykola ; Fan, Yale ; Pufu, Silviu S. ; ... - Journal of High Energy Physics (Online)

We develop new techniques for computing exact correlation functions of a class of local operators, including certain monopole operators, in three-dimensional N = 4 abelian gauge theories that have superconformal infrared limits. These operators are position-dependent linear combinations of Coulomb branch operators. They form a one-dimensional topological sector that encodes a deformation quantization of the Coulomb branch chiral ring, and their correlation functions completely fix the (n ≤ 3)-point functions of all half-BPS Coulomb branch operators. Using these results, we provide new derivations of the conformal dimension of half-BPS monopole operators as well as new and detailed tests of mirrormore »« less
Cited by 18
https://doi.org/10.1007/jhep04(2018)037

Full Text Available
Surface defects and chiral algebras

Journal Article Córdova, Clay ; Gaiotto, Davide ; Shao, Shu-Heng - Journal of High Energy Physics (Online)

Here, we investigate superconformal surface defects in four-dimensional N = 2 superconformal theories. Each such defect gives rise to a module of the associated chiral algebra and the surface defect Schur index is the character of this module. Various natural chiral algebra operations such as Drinfield-Sokolov reduction and spectral flow can be interpreted as constructions involving four-dimensional surface defects. We compute the index of these defects in the free hypermultiplet theory and Argyres-Douglas theories, using both infrared techniques involving BPS states, as well as renormalization group flows onto Higgs branches. We find perfect agreement with the predicted characters, in eachmore » case.« less
Cited by 20
https://doi.org/10.1007/JHEP05(2017)140

Full Text Available

Similar Records

Title: An infrared bootstrap of the Schur index with surface defects

Abstract

Citation Formats

Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD journal, December 1994

N = 2 dualities journal, August 2012

Seiberg-Witten Prepotential from Instanton Counting journal, January 2003

Spectral Networks journal, March 2013

Tinkertoys for Gaiotto duality journal, November 2010

Gauge Theories and Macdonald Polynomials journal, November 2012

An Index for 4 Dimensional Super Conformal Theories journal, June 2007

BPS graphs: from spectral networks to BPS quivers journal, July 2017

Schur indices, BPS particles, and Argyres-Douglas theories journal, January 2016

On classification ofN=2 supersymmetric theories journal, December 1993

Framed BPS states journal, January 2013

Wall-crossing in coupled 2d-4d systems journal, December 2012

ADE spectral networks journal, August 2016

A new supersymmetric index journal, November 1992

Ising model andN=2 supersymmetric theories journal, October 1993

Refined, Motivic, and Quantum journal, November 2009

The Self-Duality Equations on a Riemann Surface journal, July 1987

Supersymmetric Yang-Mills theory and integrable systems journal, February 1996

Integrable systems and supersymmetric gauge theory journal, January 1996

Classification of complete $N = 2$ supersymmetric theories in 4 dimensions journal, January 2013

On the phase transition towards permanent quark confinement journal, June 1978

Rigid Surface Operators journal, January 2010

Surface defects and instanton–vortex interaction journal, July 2017

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

Branes and N = 2 theories in two dimensions journal, March 1998

Solutions of four-dimensional field theories via M-theory journal, September 1997

Topological—anti-topological fusion journal, December 1991

Geometry and integrability of topological-antitopological fusion journal, March 1993

Jenkins–Strebel differentials with poles journal, January 2008

Self-dual strings and N = 2 supersymmetric field theory journal, October 1996

The structure of BPS spectra text, January 2015

New phenomena in SU(3) supersymmetric gauge theory journal, August 1995

New = 2 superconformal field theories in four dimensions journal, February 1996

General Argyres-Douglas theory journal, January 2013

S-duality and 2d topological QFT journal, March 2010

5D SYM on 3D sphere and 2D YM journal, October 2012

2d TQFT structure of the superconformal indices with outer-automorphism twists journal, March 2013

Testing Macdonald index as a refined character of chiral algebra journal, February 2020

Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD
journal, December 1994

N = 2 dualities
journal, August 2012

Seiberg-Witten Prepotential from Instanton Counting
journal, January 2003

Spectral Networks
journal, March 2013

Tinkertoys for Gaiotto duality
journal, November 2010

Gauge Theories and Macdonald Polynomials
journal, November 2012

An Index for 4 Dimensional Super Conformal Theories
journal, June 2007

BPS graphs: from spectral networks to BPS quivers
journal, July 2017

Schur indices, BPS particles, and Argyres-Douglas theories
journal, January 2016

On classification ofN=2 supersymmetric theories
journal, December 1993

Framed BPS states
journal, January 2013

Wall-crossing in coupled 2d-4d systems
journal, December 2012

ADE spectral networks
journal, August 2016

A new supersymmetric index
journal, November 1992

Ising model andN=2 supersymmetric theories
journal, October 1993

Refined, Motivic, and Quantum
journal, November 2009

The Self-Duality Equations on a Riemann Surface
journal, July 1987

Supersymmetric Yang-Mills theory and integrable systems
journal, February 1996

Integrable systems and supersymmetric gauge theory
journal, January 1996

Classification of complete $N = 2$ supersymmetric theories in 4 dimensions
journal, January 2013

On the phase transition towards permanent quark confinement
journal, June 1978

Rigid Surface Operators
journal, January 2010

Surface defects and instanton–vortex interaction
journal, July 2017

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

Branes and N = 2 theories in two dimensions
journal, March 1998

Solutions of four-dimensional field theories via M-theory
journal, September 1997

Topological—anti-topological fusion
journal, December 1991

Geometry and integrability of topological-antitopological fusion
journal, March 1993

Jenkins–Strebel differentials with poles
journal, January 2008

Self-dual strings and N = 2 supersymmetric field theory
journal, October 1996

The structure of BPS spectra
text, January 2015

New phenomena in SU(3) supersymmetric gauge theory
journal, August 1995

New = 2 superconformal field theories in four dimensions
journal, February 1996

General Argyres-Douglas theory
journal, January 2013

S-duality and 2d topological QFT
journal, March 2010

5D SYM on 3D sphere and 2D YM
journal, October 2012

2d TQFT structure of the superconformal indices with outer-automorphism twists
journal, March 2013

Testing Macdonald index as a refined character of chiral algebra
journal, February 2020