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:
-
- California Inst. of Technology (CalTech), Pasadena, CA (United States); Univ. of Tokyo (Japan)
- ETH Zurich (Switzerland)
- Publication Date:
- 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. doi:10.1007/JHEP09(2019)062.
Fluder, Martin, & Longhi, Pietro. An infrared bootstrap of the Schur index with surface defects. United States. https://doi.org/10.1007/JHEP09(2019)062
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.
@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}
}
Web of Science
Works referenced in this record:
Phases of N = 2 theories in two dimensions
journal, August 1993
- Witten, Edward
- Nuclear Physics B, Vol. 403, Issue 1-2
N = 2 dualities
journal, August 2012
- Gaiotto, Davide
- Journal of High Energy Physics, Vol. 2012, Issue 8
Spectral Networks
journal, March 2013
- Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew
- Annales Henri Poincaré, Vol. 14, Issue 7
On classification ofN=2 supersymmetric theories
journal, December 1993
- Cecotti, Sergio; Vafa, Cumrun
- Communications in Mathematical Physics, Vol. 158, Issue 3
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
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
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
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
Seiberg-Witten Prepotential from Instanton Counting
journal, January 2003
- Nekrasov, Nikita A.
- Advances in Theoretical and Mathematical Physics, Vol. 7, Issue 5
A new supersymmetric index
journal, November 1992
- Cecotti, Sergio; Fendley, Paul; Intriligator, Ken
- Nuclear Physics B, Vol. 386, Issue 2
Jenkins–Strebel differentials with poles
journal, January 2008
- Liu, Jinsong
- Commentarii Mathematici Helvetici
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
Integrable systems and supersymmetric gauge theory
journal, January 1996
- Martinec, Emil J.; Warner, Nicholas P.
- Nuclear Physics B, Vol. 459, Issue 1-2
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
Gauge Theories and Macdonald Polynomials
journal, November 2012
- Gadde, Abhijit; Rastelli, Leonardo; Razamat, Shlomo S.
- Communications in Mathematical Physics, Vol. 319, Issue 1
Surface defects and instanton–vortex interaction
journal, July 2017
- Gorsky, A.; Le Floch, B.; Milekhin, A.
- Nuclear Physics B, Vol. 920
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
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
On the phase transition towards permanent quark confinement
journal, June 1978
- 't Hooft, G.
- Nuclear Physics B, Vol. 138, Issue 1
Refined, Motivic, and Quantum
journal, November 2009
- Dimofte, Tudor; Gukov, Sergei
- Letters in Mathematical Physics, Vol. 91, Issue 1
Solutions of four-dimensional field theories via M-theory
journal, September 1997
- Witten, Edward
- Nuclear Physics B, Vol. 500, Issue 1-3
Spectral Networks with Spin
journal, August 2015
- Galakhov, Dmitry; Longhi, Pietro; Moore, Gregory W.
- Communications in Mathematical Physics, Vol. 340, Issue 1
Geometry and integrability of topological-antitopological fusion
journal, March 1993
- Dubrovin, B.
- Communications in Mathematical Physics, Vol. 152, Issue 3
Branes and N = 2 theories in two dimensions
journal, March 1998
- Hanany, Amihay; Hori, Kentaro
- Nuclear Physics B, Vol. 513, Issue 1-2
Tinkertoys for Gaiotto duality
journal, November 2010
- Chacaltana, Oscar; Distler, Jacques
- Journal of High Energy Physics, Vol. 2010, Issue 11
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
S-duality and 2d topological QFT
journal, March 2010
- Gadde, Abhijit; Pomoni, Elli; Rastelli, Leonardo
- Journal of High Energy Physics, Vol. 2010, Issue 3
ADE spectral networks
journal, August 2016
- Longhi, Pietro; Park, Chan Y.
- Journal of High Energy Physics, Vol. 2016, Issue 8
Supersymmetric Yang-Mills theory and integrable systems
journal, February 1996
- Donagi, Ron; Witten, Edward
- Nuclear Physics B, Vol. 460, Issue 2
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
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
Ising model andN=2 supersymmetric theories
journal, October 1993
- Cecotti, Sergio; Vafa, Cumrun
- Communications in Mathematical Physics, Vol. 157, Issue 1
5D SYM on 3D sphere and 2D YM
journal, October 2012
- Kawano, Teruhiko; Matsumiya, Nariaki
- Physics Letters B, Vol. 716, Issue 3-5
Topological—anti-topological fusion
journal, December 1991
- Cecotti, Sergio; Vafa, Cumrun
- Nuclear Physics B, Vol. 367, Issue 2
Framed BPS states
journal, January 2013
- Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew
- Advances in Theoretical and Mathematical Physics, Vol. 17, Issue 2
Rigid Surface Operators
journal, January 2010
- Gukov, Sergei; Witten, Edward
- Advances in Theoretical and Mathematical Physics, Vol. 14, Issue 1
General Argyres-Douglas theory
journal, January 2013
- Xie, Dan
- Journal of High Energy Physics, Vol. 2013, Issue 1
Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory
journal, September 1994
- Seiberg, N.; Witten, E.
- Nuclear Physics B, Vol. 426, Issue 1
Liouville Correlation Functions from Four-Dimensional Gauge Theories
journal, January 2010
- Alday, Luis F.; Gaiotto, Davide; Tachikawa, Yuji
- Letters in Mathematical Physics, Vol. 91, Issue 2
Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops
journal, May 2012
- Pestun, Vasily
- Communications in Mathematical Physics, Vol. 313, Issue 1
Loop operators and S-duality from curves on Riemann surfaces
journal, September 2009
- Drukker, Nadav; Morrison, David R.; Okuda, Takuya
- Journal of High Energy Physics, Vol. 2009, Issue 09
Loop and surface operators in $ \mathcal{N} = 2 $ gauge theory and Liouville modular geometry
journal, January 2010
- Alday, Luis F.; Gaiotto, Davide; Gukov, Sergei
- Journal of High Energy Physics, Vol. 2010, Issue 1
Gauge theory loop operators and Liouville theory
journal, February 2010
- Drukker, Nadav; Gomis, Jaume; Okuda, Takuya
- Journal of High Energy Physics, Vol. 2010, Issue 2
Surface operators in $ \mathcal{N} $ = 2 4d gauge theories
journal, November 2012
- Gaiotto, Davide
- Journal of High Energy Physics, Vol. 2012, Issue 11
NILPOTENT ORBITS AND CODIMENSION-2 DEFECTS OF 6d${\mathcal N} = (2, 0)$ THEORIES
journal, February 2013
- Chacaltana, Oscar; Distler, Jacques; Tachikawa, Yuji
- International Journal of Modern Physics A, Vol. 28, Issue 03n04
Four Dimensional Superconformal Index from -Deformed Two Dimensional Yang-Mills Theory
journal, June 2011
- Gadde, Abhijit; Rastelli, Leonardo; Razamat, Shlomo S.
- Physical Review Letters, Vol. 106, Issue 24
Counting chiral primaries in , superconformal field theories
journal, July 2006
- Römelsberger, Christian
- Nuclear Physics B, Vol. 747, Issue 3
Wall Crossing Invariants from Spectral Networks
journal, December 2017
- Longhi, Pietro
- Annales Henri Poincaré, Vol. 19, Issue 3
BPS degeneracies and superconformal index in diverse dimensions
journal, November 2014
- Iqbal, Amer; Vafa, Cumrun
- Physical Review D, Vol. 90, Issue 10
Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory
journal, July 2010
- Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew
- Communications in Mathematical Physics, Vol. 299, Issue 1
Quantum Wall Crossing in $${{\mathcal N}=2}$$ Gauge Theories
journal, October 2010
- Dimofte, Tudor; Gukov, Sergei; Soibelman, Yan
- Letters in Mathematical Physics, Vol. 95, Issue 1
Bootstrapping the superconformal index with surface defects
journal, January 2013
- Gaiotto, Davide; Rastelli, Leonardo; Razamat, Shlomo S.
- Journal of High Energy Physics, Vol. 2013, Issue 1
Surface defects, the superconformal index and q-deformed Yang-Mills
journal, October 2013
- Alday, Luis F.; Bullimore, Mathew; Fluder, Martin
- Journal of High Energy Physics, Vol. 2013, Issue 10
Infrared computations of defect Schur indices
journal, November 2016
- Córdova, Clay; Gaiotto, Davide; Shao, Shu-Heng
- Journal of High Energy Physics, Vol. 2016, Issue 11
Surface defect indices and 2d-4d BPS states
journal, December 2017
- Córdova, Clay; Gaiotto, Davide; Shao, Shu-Heng
- Journal of High Energy Physics, Vol. 2017, Issue 12
Surface defects and chiral algebras
journal, May 2017
- Córdova, Clay; Gaiotto, Davide; Shao, Shu-Heng
- Journal of High Energy Physics, Vol. 2017, Issue 5
Line defect Schur indices, Verlinde algebras and U(1)r fixed points
journal, November 2017
- Neitzke, Andrew; Yan, Fei
- Journal of High Energy Physics, Vol. 2017, Issue 11
The BPS spectrum generator in 2D-4D systems
journal, November 2012
- Longhi, Pietro
- Journal of High Energy Physics, Vol. 2012, Issue 11
Spectral Networks and Fenchel–Nielsen Coordinates
journal, May 2016
- Hollands, Lotte; Neitzke, Andrew
- Letters in Mathematical Physics, Vol. 106, Issue 6
2d SCFTs from M2-branes
journal, November 2013
- Hori, Kentaro; Park, Chan Y.; Tachikawa, Yuji
- Journal of High Energy Physics, Vol. 2013, Issue 11
ADE spectral networks and decoupling limits of surface defects
journal, February 2017
- Longhi, Pietro; Park, Chan Y.
- Journal of High Energy Physics, Vol. 2017, Issue 2
Orbifold Schur index and IR formula
journal, April 2018
- Imamura, Yosuke
- Progress of Theoretical and Experimental Physics, Vol. 2018, Issue 4
Line defects, tropicalization, and multi-centered quiver quantum mechanics
journal, September 2014
- Córdova, Clay; Neitzke, Andrew
- Journal of High Energy Physics, Vol. 2014, Issue 9
Geometric engineering of (framed) BPS states
journal, January 2014
- Chuang, Wu-Yen; Diaconescu, Duiliu-Emanuel; Manschot, Jan
- Advances in Theoretical and Mathematical Physics, Vol. 18, Issue 5
About the Absence of Exotics and the Coulomb Branch Formula
journal, November 2017
- Del Zotto, Michele; Sen, Ashoke
- Communications in Mathematical Physics, Vol. 357, Issue 3
BPS Quivers and Spectra of Complete $${\mathcal{N} = 2}$$ N = 2 Quantum Field Theories
journal, August 2013
- Alim, Murad; Cecotti, Sergio; Córdova, Clay
- Communications in Mathematical Physics, Vol. 323, Issue 3
$\mathcal{N} = 2$ quantum field theories and their BPS quivers
journal, January 2014
- Alim, Murad; Cecotti, Sergio; Córdova, Clay
- Advances in Theoretical and Mathematical Physics, Vol. 18, Issue 1
Wilson-’t Hooft operators in four-dimensional gauge theories and -duality
journal, July 2006
- Kapustin, Anton
- Physical Review D, Vol. 74, Issue 2
Reading between the lines of four-dimensional gauge theories
journal, August 2013
- Aharony, Ofer; Seiberg, Nathan; Tachikawa, Yuji
- Journal of High Energy Physics, Vol. 2013, Issue 8
Surface operators and separation of variables
journal, January 2016
- Frenkel, Edward; Gukov, Sergei; Teschner, Jörg
- Journal of High Energy Physics, Vol. 2016, Issue 1
Exact WKB analysis and cluster algebras
journal, November 2014
- Iwaki, Kohei; Nakanishi, Tomoki
- Journal of Physics A: Mathematical and Theoretical, Vol. 47, Issue 47
2d index and surface operators
journal, March 2014
- Gadde, Abhijit; Gukov, Sergei
- Journal of High Energy Physics, Vol. 2014, Issue 3
Surface defects and resolvents
journal, September 2013
- Gaiotto, Davide; Gukov, Sergei; Seiberg, Nathan
- Journal of High Energy Physics, Vol. 2013, Issue 9
The superconformal index and an elliptic algebra of surface defects
journal, October 2014
- Bullimore, Mathew; Fluder, Martin; Hollands, Lotte
- Journal of High Energy Physics, Vol. 2014, Issue 10
The BPS spectra of two-dimensional supersymmetric gauge theories with twisted mass terms
journal, November 1998
- Dorey, Nick
- Journal of High Energy Physics, Vol. 1998, Issue 11
Wild quiver gauge theories
journal, February 2012
- Bonelli, Giulio; Maruyoshi, Kazunobu; Tanzini, Alessandro
- Journal of High Energy Physics, Vol. 2012, Issue 2
Classification of Argyres-Douglas theories from M5 branes
journal, September 2016
- Wang, Yifan; Xie, Dan
- Physical Review D, Vol. 94, Issue 6
Central charges and RG flow of strongly-coupled $ \mathcal{N}=2 $ theory
journal, March 2013
- Xie, Dan; Zhao, Peng
- Journal of High Energy Physics, Vol. 2013, Issue 3
Infinite Chiral Symmetry in Four Dimensions
journal, January 2015
- Beem, Christopher; Lemos, Madalena; Liendo, Pedro
- Communications in Mathematical Physics, Vol. 336, Issue 3
Nekrasov-Shatashvili limit of the 5D superconformal index
journal, August 2016
- Papageorgakis, Constantinos; Pini, Alessandro; Rodríguez-Gómez, Diego
- Physical Review D, Vol. 94, Issue 4
Exponential networks and representations of quivers
journal, August 2017
- Eager, Richard; Selmani, Sam Alexandre; Walcher, Johannes
- Journal of High Energy Physics, Vol. 2017, Issue 8
S-duality and the $ \mathcal{N}=2 $ lens space index
journal, October 2013
- Razamat, Shlomo S.; Yamazaki, Masahito
- Journal of High Energy Physics, Vol. 2013, Issue 10
Down the rabbit hole with theories of class S $$ \mathcal{S} $$
journal, October 2014
- Razamat, Shlomo S.; Willett, Brian
- Journal of High Energy Physics, Vol. 2014, Issue 10
Heterotic surface defects and dualities from 2d/4d indices
journal, October 2014
- Chen, Heng-Yu; Chen, Hsiao-Yi
- Journal of High Energy Physics, Vol. 2014, Issue 10
N
=
1 $$ \mathcal{N}=1 $$ theories of class S
k $$ {\mathcal{S}}_k $$
journal, July 2015
- Gaiotto, Davide; Razamat, Shlomo S.
- Journal of High Energy Physics, Vol. 2015, Issue 7
Surface defects as transfer matrices
journal, November 2016
- Maruyoshi, Kazunobu; Yagi, Junya
- Progress of Theoretical and Experimental Physics, Vol. 2016, Issue 11
Surface defects and elliptic quantum groups
journal, June 2017
- Yagi, Junya
- Journal of High Energy Physics, Vol. 2017, Issue 6
Surface Defects in E-String Compactifications and the van Diejen Model
journal, April 2018
- Nazzal, Belal; Razamat, Shlomo S.
- Symmetry, Integrability and Geometry: Methods and Applications
Flavored surface defects in 4d $$\mathcal{N}=1$$ N = 1 SCFTs
journal, December 2018
- Razamat, Shlomo S.
- Letters in Mathematical Physics, Vol. 109, Issue 6
On the correspondence between surface operators in Argyres-Douglas theories and modules of chiral algebra
journal, March 2019
- Nishinaka, Takahiro; Sasa, Shinya; Zhu, Rui-Dong
- Journal of High Energy Physics, Vol. 2019, Issue 3
5D SYM and 2D q-deformed YM
journal, April 2013
- Fukuda, Yasutaka; Kawano, Teruhiko; Matsumiya, Nariaki
- Nuclear Physics B, Vol. 869, Issue 3
A brief review of the 2d/4d correspondences
journal, October 2017
- Tachikawa, Yuji
- Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 44
On the superconformal index of Argyres–Douglas theories
journal, December 2015
- Buican, Matthew; Nishinaka, Takahiro
- Journal of Physics A: Mathematical and Theoretical, Vol. 49, Issue 1
Argyres-Douglas theories, the Macdonald index, and an RG inequality
journal, February 2016
- Buican, Matthew; Nishinaka, Takahiro
- Journal of High Energy Physics, Vol. 2016, Issue 2
Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT
journal, February 2016
- Song, Jaewon
- Journal of High Energy Physics, Vol. 2016, Issue 2
On irregular singularity wave functions and superconformal indices
journal, September 2017
- Buican, Matthew; Nishinaka, Takahiro
- Journal of High Energy Physics, Vol. 2017, Issue 9
Enhancement of Supersymmetry via Renormalization Group Flow and the Superconformal Index
journal, April 2017
- Maruyoshi, Kazunobu; Song, Jaewon
- Physical Review Letters, Vol. 118, Issue 15
N = 1 $$ \mathcal{N}=1 $$ deformations and RG flows of N = 2 $$ \mathcal{N}=2 $$ SCFTs
journal, February 2017
- Maruyoshi, Kazunobu; Song, Jaewon
- Journal of High Energy Physics, Vol. 2017, Issue 2
N $$ \mathcal{N} $$ =1 Deformations and RG flows of N $$ \mathcal{N} $$ =2 SCFTs, part II: non-principal deformations
journal, December 2016
- Agarwal, Prarit; Maruyoshi, Kazunobu; Song, Jaewon
- Journal of High Energy Physics, Vol. 2016, Issue 12
S-duality and 2d Topological QFT
text, January 2009
- Gadde, Abhijit; Pomoni, Elli; Rastelli, Leonardo
- arXiv
Schur Indices, BPS Particles, and Argyres-Douglas Theories
text, January 2015
- Cordova, Clay; Shao, Shu-Heng
- arXiv
BPS Graphs: From Spectral Networks to BPS Quivers
text, January 2017
- Gabella, Maxime; Longhi, Pietro; Park, Chan Y.
- arXiv
An Index for 4 dimensional Super Conformal Theories
text, January 2005
- Kinney, Justin; Maldacena, Juan; Minwalla, Shiraz
- arXiv
A New Supersymmetric Index
text, January 1992
- Cecotti, Sergio; Fendley, Paul; Intriligator, Ken
- arXiv
New N=2 Superconformal Field Theories in Four Dimensions
text, January 1995
- Argyres, P. C.; Plesser, M. R.; Seiberg, N.
- arXiv
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