Surface Defects from Fractional Branes - I S. K. Ashok a , M. Bill` o b,c , M. Frau b,c , A. Lerda d,c and S. Mahato a a Institute of Mathematical Sciences, Homi Bhabha National Institute (HBNI), IV Cross Road, C.I.T. Campus, Taramani, Chennai, India 600113 b Universit`a di Torino, Dipartimento di Fisica, Via P. Giuria 1, I-10125 Torino, Italy c I.N.F.N. - 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: sashok,sujoymahato@imsc.res.in; billo,frau,lerda@to.infn.it Abstract We show that the Gukov-Witten monodromy defects of supersymmetric Yang-Mills the- ory 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 par- tially 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 Z 2 orbifold and defer the study of the most general case to a companion paper. Keywords: Surface defects, fractional branes, orbifolds