 # Mirror symmetry

Kentaro Hori

Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence bas significant mathematical consequences, the most familiar of which involves the enumeration of holomorphic curves inside complex manifolds by solving differential equations obtained from a mirror geometry. The inclusion of D-brane states in the equivalence bas led to further conjectures involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds : the Gopakumar Vafa invariants. This book aims to give a single, cohesive treatment of mirror symmetry from both the mathematical and physical viewpoint. Parts 1 and 2 develop the necessary mathematical and physical background from scratch , and are intended for readers trying to learn across disciplines. The treatment is focussed, developing only the material most necessary for the task. In Parts 3 and 4 the physical and mathematical proofs of mirror symmetry are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory can be described geometrically, and thus mirror symmetry gives rise to a pairing of geometries. The proof involves applying R-1/R circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Gromov-Witten theory in the algebraic setting, beginning with the moduli spaces of curves and maps, and uses localization techniques to show that certain hypergeometric functions encode the Gromov-Witten invariants in genus zero, as is predicted by mirror symmetry. Part 5 is devoted to advanced topics in mirror symmetry, including the role of D-branes in the context of mirror symmetry, and some of their applications in physics and mathematics : topological strings and large N Chern-Simons theory

ag.algebraic geometry - Roadmap for Mirror … I am interested in learning Mirror Symmetry, both from the SYZ and Homological point of view. I am taking a reading course in Mirror Symmetry, which will focus on the SYZ side. I know basic Complex geometry, Kahler manifolds, Symplectic manifolds in the geometric side and also reading some material for my course on SYZ conjecture. My major concern is Homological side, about which I have little

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9780821829554 ISBN
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## Notes actuelles Sofya Voigtuh

Lectures on Mirror Symmetry and Topological String Theory Murad Alim Je erson Physical Laboratory, Harvard University, Cambridge, MA 02138, USA Abstract These are notes of a series of lectures on mirror symmetry and topological string theory given at the Mathematical Sciences Center at Tsinghua University. The N= 2 superconformal algebra, its deformations and its chiral ring are reviewed. A Mattio Müllers

Mirror symmetry | Definition of Mirror symmetry at ... Mirror symmetry definition at Dictionary.com, a free online dictionary with pronunciation, synonyms and translation. Look it up now! Noels Schulzen

Mirror symmetry definition and meaning | Collins … Jason Leghmann

Mirror symmetry may refer to: Mirror symmetry (string theory), a relation between two Calabi-Yau manifolds in string theory; Homological mirror symmetry, a mathematical conjecture about Calabi-Yau manifolds made by Maxim Kontsevich; Reflection symmetry, a geometrical symmetry with respect to reflection; This disambiguation page lists articles associated with the same title. If an internal link Jessica Kolhmann

9 Jun 2019 ... In this form mirror symmetry remains a conjecture, not the least because for the moment there is no complete construction of these SCFTs. But to ...