Krefl, Daniel (2009): Real Mirror Symmetry and The Real Topological String. Dissertation, LMU München: Faculty of Physics 

PDF
Krefl_Daniel.pdf 1MB 
Abstract
This thesis is concerned with real mirror symmetry, that is, mirror symmetry for a CalabiYau 3fold background with a Dbrane on a special Lagrangian 3cycle defined by the real locus of an antiholomorphic involution. More specifically, we will study real mirror symmetry by means of compact 1parameter CalabiYau hypersurfaces in weighted projective space (at treelevel) and noncompact local P2 (at higher genus). For the compact models, we identify mirror pairs of Dbrane configurations in weighted projective space, derive the corresponding inhomogeneous PicardFuchs equations, and solve for the domainwall tensions as analytic functions over moduli space, thereby collecting evidence for real mirror symmetry at treelevel. A major outcome of this part is the prediction of the number of disk instantons ending on the Dbrane for these models. Further, we study real mirror symmetry at higher genus using local P2. For that, we utilize the real topological string, that is, the topological string on a background with Oplane and Dbrane on top. In detail, we calculate topological amplitudes using three complementary techniques. In the Amodel, we refine localization on the moduli space of maps with respect to the torus action preserved by the antiholomorphic involution. This leads to a computation of open and unoriented GromovWitten invariants that can be applied to any toric CalabiYau with involution. We then show that the full topological string amplitudes can be reproduced within the topological vertex formalism. Especially, we obtain the real topological vertex with trivial fixed leg. Finally, we verify that the same results arise in the Bmodel from the extended holomorphic anomaly equations, together with appropriate boundary conditions, thereby establishing local real mirror symmetry at higher genus. Significant outcomes of this part are the derivation of real GopakumarVafa invariants at high Euler number and degree for local P2 and the discovery of a new kind of gap structure of the closed and unoriented topological amplitudes at the conifold point in moduli space.
Item Type:  Thesis (Dissertation, LMU Munich) 

Keywords:  mirror symmetry, topological string theory, Dbranes, orientifold 
Subjects:  600 Natural sciences and mathematics 600 Natural sciences and mathematics > 530 Physics 
Faculties:  Faculty of Physics 
Language:  English 
Date Accepted:  2. July 2009 
1. Referee:  Lüst, Dieter 
Persistent Identifier (URN):  urn:nbn:de:bvb:19102832 
MD5 Checksum of the PDFfile:  04218d7565bb1bb6e4f5617eda9cd710 
Signature of the printed copy:  0001/UMC 17890 
ID Code:  10283 
Deposited On:  16. Jul 2009 08:20 
Last Modified:  19. Jul 2016 16:27 