T-branes and defects
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Springer
Received: March 5, 2019 Accepted: April 6, 2019 Published: April 16, 2019
Fernando Marchesano,a Raffaele Savellib and Sebastian Schwiegera a
Instituto de F´ısica Te´ orica UAM-CSIC, Cantoblanco, 28049 Madrid, Spain b Dipartimento di Fisica, Universit` a di Roma “Tor Vergata” & INFN — Sezione di Roma 2, Via della Ricerca Scientifica 1, 00133 Roma, Italy
E-mail: [email protected], [email protected], [email protected] Abstract: We study T-branes on compact K¨ahler surfaces, in the presence of fields localised at curves. If such fields are treated as defects, their vevs induce delta-function sources for the 7-brane background, possibly leading to profiles with poles. We find that the presence of defect sources relaxes the constraints on globally well-defined T-brane configurations, avoiding the obstruction to building them on surfaces of positive curvature. Profiles with poles can be understood, from a 4d viewpoint, as non-trivial vevs for massive modes induced by the defects, and come with their own set of constraints. In the special case of fields localised on a self-intersection curve, we show how to retrieve the Hitchin system with defects from an ordinary global one with enhanced symmetry. Keywords: D-branes, Supersymmetric Gauge Theory, Differential and Algebraic Geometry, Superstring Vacua ArXiv ePrint: 1902.04108
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP04(2019)110
JHEP04(2019)110
T-branes and defects
Contents 1 Introduction
1
2 T-branes with defects 2.1 Compact T-brane systems 2.2 Introducing defects
3 4 7 14
4 Defects and Hitchin systems 4.1 The meromorphic scheme 4.2 The defect limits 4.3 The holomorphic scheme
19 20 23 29
5 Conclusions
31
A Lie algebra conventions
34
B BPS equations with defects
35
C 4d reduction and massive modes
37
1
Introduction
One of the open problems in string theory is to characterise the spectrum of extended BPS objects of a given string compactification. This question remains unanswered even for particularly well-studied cases of vacua, like BPS D-branes in type IIB Calabi-Yau orientifolds with O3/O7-planes, or their F-theory generalisation [1–7]. In this case one can construct an abundant set of space-time-filling BPS D-branes at large volume, by considering D3-branes located at points in the internal six-manifold B, or 7-branes wrapping holomorphic four-cycles S ⊂ B. One may even enlarge this set by endowing the 7-branes with anti-self-dual gauge bundles threading S. In some instances, these can be understood as bound states of 7-branes and D3-branes, as they carry the same charges. In general, classifying the possible BPS bound states of D-branes at a given point in closed string moduli space is where a large fraction of the problem resides. One particular set of such bound states, that have recently been the subject of attention, are stacks of 7-branes whose complex worldvolume scalar or Higgs field has an intrinsic non-Abelian profile. These objects, typically dubbed H
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