Mirror Symmetry

By K. Hori, C. Vafa. 2000

1,777 citations recorded by the source corpus.

We prove mirror symmetry for supersymmetric sigma models on Kahler manifolds in 1+1 dimensions. The proof involves establishing the equivalence of the gauged linear sigma model, embedded in a theory with an enlarged gauge symmetry, with a Landau-Ginzburg theory of Toda type. Standard R ->1/R duality and dynamical generation of superpotential by vortices are crucial in the derivation. This provides not only a proof of mirror symmetry in the case of (local and global) Calabi-Yau manifolds, but also for sigma models on manifolds with positive first Chern class, including deformations of the action by holomorphic isometries.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f87f25e74cb71ad15a73f170ae6fb7767ecb3502

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. C. Vafa
2. Marcos Mariño
3. P. Seidel
4. E. Witten
5. D. Auroux
6. A. Klemm
7. Sergei Gukov
8. L. Katzarkov

In Nuclear and High Energy Physics

1. C. Vafa
2. Marcos Mariño
3. Eran Palti
4. Thomas W. Grimm
5. Frederik Denef
6. E. Witten
7. A. Klemm
8. F. Benini

In Statistical and Nonlinear Physics

1. Marcos Mariño
2. C. Vafa
3. A. Klemm
4. Mina Aganagic
5. E. Witten
6. K. Hori
7. P. Seidel
8. B. Eynard

Citations in the corpus

• Super-moonshine for Conway's largest sporadic group (2005, background): “From [KO03], [Sch98] for example, we have the following Theorem 6.”
• Disk Instantons, Mirror Symmetry and the Duality Web (2001, background): “The mirror theory is given in terms of n + k dual C∗ fields Y i [10], where”
• The reduced genus 1 Gromov-Witten invariants of Calabi-Yau hypersurfaces (2007, positive): “4 of [MirSym], also comes from the components of ZΓ in the following sense.”
• Partition Functions of $${\mathcal{N}=(2,2)}$$N=(2,2) Gauge Theories on S2 and Vortices (2012, background): “The mirror description is in terms of Σ, Y1, Y2 and twisted superpotential [39]:”
• D-Branes And Mirror Symmetry (2000, methodology): “Moreover, if we choose different paths the vanishing cycle we get is a linear combination of the above and the relation between them is known through the Picard Lefshetz theory as we will now review.”
• Homological mirror symmetry for punctured spheres (2011, background): “X(n),W) In this section we describe mirror Landau-Ginzburg (LG) models W : X(n) → C for n≥ 3.These mirrors are toric, and their construction can be justified by a physics argument due to Hori and Vafa [21], see also [22, Section 3]. (Mathematically, this construction can be construed as a duality bet”
• On geometry and matrix models (2002, methodology): “As was demonstrated in [26,27] the B-model mirrors are given by vv + F (e, e) = 0”
• Resurgence and trans-series in Quantum Field Theory: the $\mathbb{C}{{\mathbb{P}}^{N-1 }}$ model (2012, methodology): “Our proposal, valid for both supersymmetric and non-supersymmetric theories, is also consistent with arguments based on mirror symmetry [55] and appropriate generalization of the quantum chiral ring relations [56] in the minimal supersymmetric case, as discussed below in Section 5.”
• Building a better racetrack (2004, background): “” In [54, 65, 19, 46] it was proposed, based on the study of examples, that such divisors are always “exceptional” in the sense that there exist birational transformations of Calabi-Yau fourfolds which contract these divisors.”
• Review of geometry and analysis (2000, methodology): “When the deformation space is multidimensional, the calculation requires a new method and this was carried out independently by Hosono-Klemm-Thiesen-Yau [99] and by Candelas-de la Ossa-Font-Katz-Morrison [30].”