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

Journal Article · 09 September 2019 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/JHEP09(2019)062 · OSTI ID:1596782

Fluder, Martin ^[1];

^[2]

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

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.

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Research Organization:: California Inst. of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

Grant/Contract Number:: SC0011632

OSTI ID:: 1596782

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 9 Vol. 2019; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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