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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:
 [1]; ORCiD logo [2]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States); Univ. of Tokyo (Japan)
  2. 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. https://doi.org/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}
}

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    Works referencing / citing this record:

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