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In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometric objects called Calabi–Yau manifolds.The term refers to a situation where two Calabi–Yau manifolds look very different geometrically but are nevertheless equivalent when employed as extra dimensions of string theory.
Mirror Symmetry Cumrun Vafa and Eric Zaslow, Editors 1 AMS CMI www.ams.org www.claymath.org Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has significant mathematical consequences, the most familiar of which involves the
Overview of mirror symmetry 7 1. Enumerative mirror symmetry 7 1.1. Topological twists 8 1.2. Useful calculations 8 1.3. Homological mirror symmetry 9 1.4. Proving numerical mirror symmetry 9 1.5. Proving HMS 9 1.6. Modern state 9 1.7. Plan for the class 9 Chapter 1. Mirror symmetry for the quintic 10 1. The quintic threefold, its mirror, and ...
string theory. A mathematical realization of a SCFT is given by a sigma model, a construction depending upon the choice of: a Calabi-Yau threefold X; a complexified Kahler class ω. Renzo Cavalieri Mirror Symmetry
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string theory on Z(Z), respectively. Various 4dgauge theories can be geometrically engineered [15, 16] and mirror symmetry can be used to compute their exact e ective actions. (See also [17] and references therein.) The prepotential is the genus zero free energy of topological string theory, which is de ned
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MIRROR SYMMETRY: LECTURE 1 DENIS AUROUX Goal of the class: this is not always going to be the most rigorous class, but the goal is to tell the story of mirror symmetry. 1. Physical Origins Mirror symmetry comes from statements in supersymmetric string theory. Ba sic idea of string theory: replace particles with vibrating strings, which propogate
In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometric objects called Calabi–Yau manifolds. The term refers to a situation where two Calabi–Yau manifolds look very different geometrically but are nevertheless equivalent when employed as extra dimensions of string theory.
