Flavored surface defects in 4d \(\mathcal{N}=1\) SCFTs

  • Shlomo S. Razamat


We discuss supersymmetric surface defects in compactifications of six-dimensional minimal conformal matter of types SU(3) and SO(8) to four dimensions. The relevant field theories in four dimensions are \(\mathcal{N}=1\) quiver gauge theories with SU(3) and SU(4) gauge groups, respectively. The defects are engineered by giving space-time-dependent vacuum expectation values to baryonic operators. We find evidence that in the case of SU(3) minimal conformal matter, the defects carry SU(2) flavor symmetry which is not a symmetry of the four-dimensional model. The simplest case of a model in this class is SU(3) SQCD with nine flavors, and thus the results suggest that this admits natural surface defects with SU(2) flavor symmetry. We analyze the defects using the superconformal index and derive analytic difference operators introducing the defects into the index computation. The duality properties of the four-dimensional theories imply that the index of the models is a kernel function for such difference operators. In turn, checking the kernel property constitutes an independent check of the dualities and the dictionary between six- dimensional compactifications and four-dimensional models.


Supersymmetric theories Duality Integrable models 

Mathematics Subject Classification

81T60 81T99 



We would like to thank Simon Ruijsenaars and Gabi Zafrir for comments and relevant discussions. The research was supported by the Israel Science Foundation under Grant No. 1696/15 and by the I-CORE Program of the Planning and Budgeting Committee.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Physics DepartmentTechnionHaifaIsrael

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