American Mathematical Society. Clay Mathematics Institute. Clay Mathematics Monographs. Volume 4. DIRICHLETBRANES. AND MIRRORSYMMETRY. Paul S. Aspinwall. Tom Bridgeland. Alastair Craw. Michael R. Douglas. Mark Gross. Anton Kapustin. Gregory W. Moore. Graeme Segal. Balázs Szendrői. P.M.H. Wilson ...
arXiv:1612.09380v1 [math.SG] 30 Dec 2016. SYZ MirrorSymmetry for. DirichletBranes. CHUNG, Shun Wai. A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of. Master of Philosophy in. Mathematics. The Chinese University of Hong Kong. July 2016 ...
Keywords and Phrases: Superstring theory, DirichletBranes, Homological. MirrorSymmetry, stability. 1. Introduction. Let M be a complex manifold with Kähler metric, and E a vector bundle on. M. The hermitian Yang-Mills (HYM) equations are nonlinear partial differential equations for a connection
The concept of a D-brane (Dirichlet brane) in string theory had evolved considerably [?] in recent years: Original .... the Strominger-Yau-Zaslow [SYZ96] picture of mirrorsymmetry and suggests the following. Questions ... We will explain how these mathematical symmetries act on D-brane moduli
1.3 'Unifying string theories and p-branes. 2 General Formulation of Dirichlet p-Branes. 2.1 D-branes and boundary conformal field theory. 2.2 Supersymmetric cycles in Calabi-Yau manifolds. 2.3 Boundary states for D-branes ... 2.4 Exceptional supersymmetric cycles. 3 Applications to MirrorSymmetry.
a consequence of mirrorsymmetry acting on D-branes. The organization of this ... section 6 we derive, using the results of  the mirror of certain D-branes on Fano varieties in terms of D-branes in the ...... coordinate fields as (3.21), from pure Neumann to mixed Dirichlet-Neumann condition
G. Segal, B. Szendr˝oi, and P.M.H. Wilson, Dirichletbranes and mirrorsymmetry, Clay. Mathematics Monographs, vol. 4, American Mathematical Society, Providence, RI, 2009. 4. Serguei Barannikov, Semi-infinite Hodge structures and mirrorsymmetry for projective spaces, arXiv:math/0010157, 2000. 5
string theory, and give an intuitive description of string compactification,. Dirichletbranes, T-duality and the other physical concepts we will discuss in more depth, primarily in Chapters 2, 3 and 5. We then summarize the mathematics behind homological mirrorsymmetry and SYZ, which we
23. 1. The SYZ proposal. In 1996, drawing on the new idea of D-branes from string theory, Strominger,. Yau and Zaslow  made a ground-breaking proposal to explain mirrorsymmetry ...... B. Szendr˝oi, and P. M. H. Wilson, Dirichletbranes and mirrorsymmetry, Clay Mathemat- ics Monographs, vol.
D–branes and Calabi–Yaus. Topological Strings. MirrorSymmetry. Conclusions. D–branes. • D–branes are objects where open strings can end. (Dirichlet boundary conditions). • D–branes break translation invariance and supersymmetry. • The string gets additional degrees of freedom on the boundary.
Over the past year, Dirichletbranes (D-branes) which do not preserve supersymmetry, and therefore do not saturate the ... to make progress in analysing the possible dualities of theories without supersymmetry†, we have to develop ..... of the string that stretches between the D5-brane and its
the comprehensive MirrorSymmetry monograph [Clay03] and the more recent Dirichlet. Branes and MirrorSymmetry monograph [Clay09], the recent survey article by Mark Gross. [CDM] and the expository article [GS08] should both be reasonably accessible to workshop participants. (Chap. 6 through 8
Duality symmetries, D-brane categories, and extended field theory. 2. 3. ... The duality symmetries here are primarily mirrorsymmetry and S-duality. D-branes are connected to two central developments in this area of Mathematics: 1. .....  J. Polchinski, “DirichletBranes and Ramond-Ramond
D-Branes on Calabi-Yau Manifolds. Michael R. Douglas. Abstract. We give an overview of recent work on Dirichletbranes on Calabi-. Yau threefolds which makes contact with Kontsevich's homological mirrorsymmetry proposal, proposes a new definition of stability which is appropriate in string theory
Mirrorsymmetry has proven to be a powerful and fascinating area of string theory. (for a review see Ref. ... branes wrapped around supersymmetric cycles in these manifolds have world-volume theories which are ..... In particular, this means that Dirichlet p-branes which are reduced from ten
The homological mirrorsymmetry (HMS) conjecture, proposed by Kontsevich in his 1994 ICM address ... provides a geometric explanation for mirrorsymmetry – the celebrated SYZ conjec- ture asserts that a pair ...... MR 2914956. 33. P. Aspinwall et al., Dirichletbranes and mirrorsymmetry, Clay
(15) with P. Aspinwall et al, DirichletBranes and MirrorSymmetry, Clay. Mathematics Monographs, x+681 pp. Hardback 684 pp. (2009). (16) with David Stern, Helices on del Pezzo surfaces and tilting Calabi-Yau algebras,. Adv. Math. 224 1672–1716 (2010). (17) Hall algebras and curve-counting
markable conjecture (Conjecture 2.3), which builds a bridge between mirrorsymmetry for the ... by gluing the underlying affine base manifolds of X1 and X2 in SYZ mirrorsymmetry. This is based ...... Szendr˝oi B., Wilson P.M.H., Dirichletbranes and mirrorsymmetry, Clay Mathematics Monographs
D-BRANES. ANTON KAPUSTIN AND DMITRI ORLOV. Abstract. This paper is an introduction to Homological MirrorSymmetry, derived cat- egories, and topological D-branes aimed mainly at a mathematical audience. In the paper we explain ..... For example, one can impose Dirichlet boundary conditions (i.e
Dirichlet boundary condition on some fields living on the worldsheet (open strings). Now, there are again two types of D-branes (boundary conditions) that may be as- sociated with the A-model and the B-model, respectively. We would like for the boundary condition to preserve as many symmetries
MirrorSymmetry can also be extended on the case when 2-dimensional world-sheet has boundaries (see e.g. ). This generalization leads to the notion of a D-brane, which plays a very important role in string the- ory . A D-brane is a nice boundary condition for the SCQFT. For example, one can
The present mathematical challenges of mirrorsymmetry include making the statements (1.3), (1.4) more precise, proving them, and finding relations between either of them and (1.2). All these conjectures are strongly backed by physical ideas from string theory, centrally involving D-branes. D
 P. S. Aspinwall, T. Bridgeland, A. Craw, M. R. Douglas, M. Gross, A. Kapustin, G. W.. Moore, G. Segal, B. Szendr˝oi, and P. M. H. Wilson, Dirichletbranes and mirrorsymmetry, Clay. Mathematics Monographs 4, American Mathematical Society, Providence, RI, 2009, ISBN 978-0-8218-. 3848-8.
mann branes and Dirichletbranes on these manifolds. ... For C-VCPs, there are two types of branes corresponding to the Dirichlet type ... Relations to Mirror. Symmetry will also be discussed there. 2. Instantons and branes. In this section we introduce and study instantons and branes on manifolds
I am interested in algebraic geometry with applications to mirrorsymmetry. I use methods of ... which both sides of mirrorsymmetry have been understood deeply and with explicit methods. The method in ..... G. Segal, B. Szendröi, P.M.H. Wilson: Dirichletbranes and mirrorsymmetry, Clay Math
on the homological mirrorsymmetry conjecture. This note can be read without ... end product of a conden- sation process is generally not a Dirichlet brane, since it typically cannot be described ... on Dirichletbranes, and – in a slightly less direct manner – also in the case of generalized. D
open string mirrorsymmetry for the simplest compact Calabi–Yau, the torus. ..... (Dirichlet conditions). Dirichlet boundary conditions have been ignored in string theory for a long time since there were no suitable objects in the theory for the open string to end ... Generic D–brane configurations
Dirichletbranes, effective actions and supersymmetry. Eenink, Martijn Gerard Christian. IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. Document Version. Publisher's PDF, also known
small resolution in IIA string theory. The image under mirrorsymmetry of the 3-branes wrapping the S. 3 providing additional non-perurbative massless states is the 2-branes of the IIA theory wrapping the S. 2. 's again giving additional massless states. On the “other side” of the conifold
Algebraic geometry— Seattle 2005. Part 1, 149–192, Proc. Sympos. Pure Math.,. 80, AMS, Providence, RI, 2009.  With Aspinwall et al, “Dirichletbranes and mirrorsymmetry,” Clay Mathe- matics Monographs, 4, American Mathematical Society, Providence, RI; Clay. Mathematics Institute, Cambridge, MA