An infrared bootstrap of the Schur index with surface defects
- Creators
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Fluder, Martin
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Longhi, Pietro
Abstract
The infrared formula relates the Schur index of a 4d 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 various types of line and surface defects. We study BPS monodromies in the presence of vortex surface defects of arbitrary vorticity for general class SS theories of type A_1 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.
Additional Information
© 2019 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: July 30, 2019; Accepted: August 29, 2019; Published: September 10, 2019. We would like to thank Subhojoy Gupta and Shu-Heng Shao for insightful discussions and correspondence. PL is grateful for hospitality from the Simons Center for Geometry and Physics summer workshop, Caltech, and the Kavli IPMU at Tokyo University where part of this work was carried out. The work of MF is supported by the JSPS Grant-In-Aid for Scientific Research Wakate(A) 17H04837, the WPI Initiative, MEXT, Japan at IPMU, the University of Tokyo, the David and Ellen Lee Postdoctoral Scholarship, and the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number de-sc0011632. The work of PL is supported by a grant from the Swiss National Science foundation. He also acknowledges the support of the NCCR SwissMAP that is also funded by the Swiss National Science foundation. PL was also supported by the grants "Geometry and Physics" and "Exact Results in Gauge and String Theories" from the Knut and Alice Wallenberg foundation during part of this work.Attached Files
Published - Fluder-Longhi2019_Article_AnInfraredBootstrapOfTheSchurI.pdf
Submitted - 1905.02724.pdf
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Additional details
- Eprint ID
- 97012
- Resolver ID
- CaltechAUTHORS:20190709-151753573
- Japan Society for the Promotion of Science (JSPS)
- 17H04837
- Ministry of Education, Culture, Sports, Science and Technology (MEXT)
- University of Tokyo
- David and Ellen Lee Postdoctoral Scholarship
- Department of Energy (DOE)
- DE-SC0011632
- Swiss National Science Foundation (SNSF)
- Knut and Alice Wallenberg Foundation
- SCOAP3
- Created
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2019-07-09Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics
- Other Numbering System Name
- CALT-TH
- Other Numbering System Identifier
- 2019-015