A. N. Kapustin, D. O. Orlov, “Lectures on mirror symmetry, derived categories, and $D$-branes”, Russian Math. Surveys, 59:5 (2004), 907

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Russian Mathematical Surveys, 2004, Volume 59, Issue 5, Pages 907–940
DOI: https://doi.org/10.1070/RM2004v059n05ABEH000772 (Mi rm772)

This article is cited in 13 scientific papers (total in 13 papers)

Lectures on mirror symmetry, derived categories, and

$D$ -branes

A. N. Kapustin^a, D. O. Orlov^b

^a California Institute of Technology
^b Steklov Mathematical Institute, Russian Academy of Sciences

English version PDF (446 kB) Citations (13) Russian version article

References:

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DOI: https://doi.org/10.1070/RM2004v059n05ABEH000772

Abstract: This paper, mainly intended for a mathematical audience, is an introduction to homological mirror symmetry, derived categories, and topological

$D$ -branes. Mirror symmetry from the point of view of physics is explained, along with the relationship between symmetry and derived categories, and the reason why the Fukaya category must be extended by using co-isotropic

$A$ -branes. There is also a discussion of how to extend the definition of the Floer homology to these objects and a description of mirror symmetry for flat tori. The paper consists of four lectures given at the Institute of Pure and Applied Mathematics (Los Angeles) in March 2003, as a part of the programme “Symplectic Geometry and Physics”.

Received: 05.08.2004

Bibliographic databases:

Document Type: Article

UDC: 512.7+514.7

MSC: Primary 14J32, 18E30; Secondary 14F05, 53D12, 57R58, 81T30, 32Q25, 81T45, 57R56

Language: English

Original paper language: Russian

Citation: A. N. Kapustin, D. O. Orlov, “Lectures on mirror symmetry, derived categories, and

$D$ -branes”, Russian Math. Surveys, 59:5 (2004), 907–940

Citation in format AMSBIB

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\jour Russian Math. Surveys

\yr 2004

\vol 59

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\pages 907--940

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Linking options:

https://www.mathnet.ru/eng/rm772

https://doi.org/10.1070/RM2004v059n05ABEH000772

https://www.mathnet.ru/eng/rm/v59/i5/p101

This publication is cited in the following 13 articles:

Kazushi Kobayashi, “On a B-field Transform of Generalized Complex Structures over Complex Tori”, Journal of Geometry and Physics, 2024, 105336
NaiChung Conan Leung, YuTung Yau, “Hidden ${\text {Sp}}(1)$ -Symmetry and Brane Quantization on HyperKähler Manifolds”, Commun. Math. Phys., 405:12 (2024)
Kazushi Kobayashi, “A gerby deformation of complex tori and the homological mirror symmetry”, Kodai Math. J., 46:3 (2023)
Aharony O., Feldman A., Honda M., “A String Dual For Partially Topological Chern-Simons-Matter Theories”, J. High Energy Phys., 2019, no. 6, 104
Omer H., “Matrix factorizations and elliptic fibrations”, Nucl. Phys. B, 910 (2016), 431–457
Khoroshkov Yu.V., “Mirror Symmetry as a Basis For Constructing a Space-Time Continuum”, 60, no. 5, 2015, 468–477
M. Herbst, “On higher rank coisotropic $A$ -branes”, J. Geom. Phys., 62:2 (2012), 156–169
B. Keller, W. Lowen, P. Nicolás, “On the (non)vanishing of some “derived” categories of curved dg algebras”, J. Pure Appl. Algebra, 214:7 (2010), 1271–1284
A. Kapustin, L. Katzarkov, D. Orlov, M. Yotov, “Homological mirror symmetry for manifolds of general type”, Centr. Eur. J. Math., 7:4 (2009), 571–605
M. Aldi, “Twisted homogeneous coordinate rings of abelian surfaces via mirror symmetry”, Proc. Amer. Math. Soc., 137:8 (2009), 2741–2747
R. Bocklandt, “Graded Calabi Yau algebras of dimension 3”, J. Pure Appl. Algebra, 212:1 (2008), 14–32
H. Jockers, W. Lerche, “Matrix Factorizations, D-branes and their deformations”, Nuclear Physics B - Proceedings Supplements, 171 (2007), 196
Martin Schlichenmaier, Theoretical and Mathematical Physics, An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces, 2007, 183

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	1725
Russian version PDF:	956
English version PDF:	71
References:	120
First page:	4

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