Surface defects from fractional branes. Part I
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Springer
Received: May 25, 2020 Accepted: June 18, 2020 Published: July 8, 2020
Surface defects from fractional branes. Part I
a
Institute of Mathematical Sciences, Homi Bhabha National Institute (HBNI), IV Cross Road, C.I.T. Campus, Taramani, Chennai, 600113 India b Universit` a di Torino, Dipartimento di Fisica, Via P. Giuria 1, I-10125 Torino, Italy c INFN — Sezione di Torino, Via P. Giuria 1, I-10125 Torino, Italy d Universit` a del Piemonte Orientale, Dipartimento di Scienze e Innovazione Tecnologica Viale T. Michel 11, I-15121 Alessandria, Italy
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: We show that the Gukov-Witten monodromy defects of supersymmetric YangMills theory can be realized in perturbative string theory by considering an orbifold background of the Kanno-Tachikawa type and placing stacks of fractional D3-branes whose world-volume partially extends along the orbifold directions. In particular, we show that turning on a constant background value for some scalar fields in the closed string twisted sectors induces a non-trivial profile for the gauge field and one of the complex scalars of the world-volume theory, and that this profile exactly matches the singular behavior that one expects for a Gukov-Witten surface defect in the N = 4 super Yang-Mills theory. To keep the presentation as simple as possible, in this work we restrict our analysis to surface defects corresponding to a Z2 orbifold and defer the study of the most general case to a companion paper. Keywords: D-branes, Extended Supersymmetry, Nonperturbative Effects, Duality in Gauge Field Theories ArXiv ePrint: 2005.02050
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)051
JHEP07(2020)051
S.K. Ashok,a M. Bill` o,b,c M. Frau,b,c A. Lerdac,d and S. Mahatoa
Contents 1
2 Review and outline 2.1 Monodromy defects 2.2 Monodromy defects from fractional branes
3 3 5
3 Closed strings in the Z2 orbifold 3.1 Twisted closed string sectors 3.1.1 Massless states in the NS/NS sector 3.1.2 Massless states in the R/R sector
7 7 8 10
4 Fractional D3-branes in the Z2 orbifold 4.1 Boundary states 4.2 The open string spectrum
11 12 13
5 Open/closed correlators 5.1 Correlators with NS/NS twisted fields 5.2 Correlators with R/R twisted fields
15 15 19
6 Continuous parameters of surface operators from world-sheet correlators 20 7 Conclusions
24
A Dirac matrices A.1 4d A.2 6d
25 25 26
B Reflection rules
27
1
Introduction
Non-local operators have traditionally played an important role in quantum field theory since they can provide valuable information especially at the non-perturbative level. In this work we consider surface defects in 4d supersymmetric Yang-Mills theories and study their explicit realization in string theory. From the gauge theory point of view, there are several ways to analyze surface defects. The original approach of Gukov and Witten (GW) in [1, 2] was to treat them as monodromy defects, in which one specifie
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