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Title: Surface defect indices and 2d-4d BPS states

Abstract

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 defect indices and line defect indices. We illustrate our results in the example of su(2) super Yang-Mills coupled to the CP1 sigma model defect.

Authors:
 [1];  [2];  [1]
  1. Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
  2. Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
Publication Date:
Research Org.:
Institute for Advanced Study, Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1502495
Grant/Contract Number:  
SC0009988
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: 2017; Journal Issue: 12; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal and W Symmetry; Supersymmetric Gauge Theory

Citation Formats

Córdova, Clay, Gaiotto, Davide, and Shao, Shu-Heng. Surface defect indices and 2d-4d BPS states. United States: N. p., 2017. Web. doi:10.1007/jhep12(2017)078.
Córdova, Clay, Gaiotto, Davide, & Shao, Shu-Heng. Surface defect indices and 2d-4d BPS states. United States. doi:10.1007/jhep12(2017)078.
Córdova, Clay, Gaiotto, Davide, and Shao, Shu-Heng. Thu . "Surface defect indices and 2d-4d BPS states". United States. doi:10.1007/jhep12(2017)078. https://www.osti.gov/servlets/purl/1502495.
@article{osti_1502495,
title = {Surface defect indices and 2d-4d BPS states},
author = {Córdova, Clay and Gaiotto, Davide and Shao, Shu-Heng},
abstractNote = {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 defect indices and line defect indices. We illustrate our results in the example of su(2) super Yang-Mills coupled to the CP1 sigma model defect.},
doi = {10.1007/jhep12(2017)078},
journal = {Journal of High Energy Physics (Online)},
number = 12,
volume = 2017,
place = {United States},
year = {2017},
month = {12}
}

Journal Article:
Free Publicly Available Full Text
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Cited by: 10 works
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Figures / Tables:

Figure 1 Figure 1: The unwrapping process of a surface defect to a sum of lines. Starting in the upper left we have a surface defect $\mathbb{S}$ (shown in blue) wrapping an equator in $S$3 as well as the $S$1 which is not shown. The defect is cut open using a resolutionmore » of the identity with left and right boundary conditions $B$$\alpha$ and $B$$\alpha$. The boundary conditions are then parallel transported around the equator using the operator $R$2$π$. When they collide the surface defect is gone and a sum of line defects $L$$i$ remains.« less

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    Works referencing / citing this record:

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