S-duality and mirror symmetry

proceedings of the Trieste Conference on S-Duality and Mirror Symmetry, ICTP, Trieste, Italy, 5-9 June 1995
  • 269 Pages
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by
North-Holland , Amsterdam
String models -- Congresses., Duality (Nuclear physics) -- Congresses., Symmetry (Physics) -- Congre
Statementedited by E. Gava, K.S. Narain, C. Vafa.
SeriesProceedings supplements, Nuclear physics B -- 46., Nuclear physics -- vol. 46.
ContributionsGava, E., Narain, Kumar Shiv., Vafa, Cumrun.
Classifications
LC ClassificationsQC173 .N88392 v.46
The Physical Object
Paginationviii, 269 p. :
ID Numbers
Open LibraryOL18084863M

S-duality is a particular example of a general notion of duality in physics. The term duality refers to a situation where two seemingly different physical systems turn out to be equivalent in a nontrivial way.

If two theories are related by a duality, it means that one theory can be transformed in some way so that it ends up looking just like. In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometric objects called Calabi–Yau 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 was originally discovered by physicists. Dirichlet Branes and Mirror Symmetry (Clay Mathematics Monographs) 0th Edition Of great research interest but not discussed in too much detail in this book is the connection between K-theory and S-duality.

D-branes are in general classified by twisted K-theory, but RR-fluxes are not quite classified by K-theory since the K-theory Cited by: Get this from a library.

S-duality and mirror symmetry: proceedings of the Trieste Conference on S-Duality and Mirror Symmetry, ICTP, Trieste, Italy, June [E. Mirror symmetry, Kobayashi's duality, and Saito's duality Article (PDF Available) in Kodai Mathematical Journal 29(3) August with 32 Reads How we measure 'reads'Author: Wolfgang Ebeling.

The mirror K3 surfaces are defined, and a link between their symmetries and the Arnold duality for the14 exceptional singularities of modality one is established.

A combinatorial description of a nonlinear change of variables is used in the study of birational geometry in the context of mirror symmetry of manifolds with trivial first Chern by: 1. S-duality for 4d N = 4 supersymmetric Yang-Mills theory predicts S-duality and mirror symmetry book the Hitchin fibration for the group G will be SYZ mirror dual to the Hitchin fibration for the Langlands dual group L G [8, Mirror symmetry translates the dimension number of the (p, q)-th differential form h p,q for the original manifold S-duality and mirror symmetry book h n-p,q of that for the counter pair manifold.

Namely, for any Calabi–Yau manifold the Hodge diamond is unchanged by a rotation by π radians and the Hodge diamonds of mirror Calabi–Yau manifolds are related by a rotation by π/2 radians.

Giving a fairly detailed overview of mirror symmetry that emphasizes both its mathematical and physical aspects, this book should be accessible to readers who are familiar with topological quantum field theory, superstring theory, and the highly esoteric mathematical constructions used in these fields.5/5.

This chapter begins with a discussion of the A-model and B-model. It then describes mirror symmetry and Hitchin's equations, Hitchin fibration, ramification, wild ramification, and Author: Edward Witten. For this reason, S-duality is called a strong-weak duality. S-duality in quantum field theory A symmetry of Maxwell's equations.

In classical physics, the behavior of the electric and magnetic field is described by a system of equations known as Maxwell's equations. Dirichlet Branes and Mirror Symmetry Share this page. Mirgor a fairly detailed overview of mirror symmetry that emphasizes both its mathematical and physical aspects, this book should be accessible to readers who are familiar with topological quantum field theory, superstring theory, and the highly esoteric mathematical constructions used in.

The four dimensional S-duality corresponds here to a mirror symmetry of these topological sigma models. Wilson and ‘t Hooft operators of the 4-d gauge theory act on the branes of the topological sigma models. Branes mapped in some sense to a multiple of themselves by these operators are called electric or magnetic “eigenbranes.

Full Description: "One appealing feature of string theory is that it provides a theory of quantum gravity. This volume is a self-contained, pedagogical exposition of this theory, its foundations and its basic results. Due to the large amount of background material, actions, solutions and bibliography contained within, this unique book can be used as a reference for research as well as a.

Symmetry, an international, peer-reviewed Open Access journal.

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Physical states represented in Hilbert space rather than phase space. Quantum mechanics defines symmetries as mappings between physical states that preserve transition amplitudes. Many new fields and concepts in Algebraic Geometry appeared when people tried to give a mathematical foundation for aspects of the mirror symmetry, for example, quantum cohomology, the complexified Kahler moduli space of a Calabi–Yau threefold, Kontsevich's definition of a stable map, and Batyrev's duality between certain toric varieties and.

Moreover, for a special value of the parameter, four-dimensional S-duality acts as two-dimensional mirror symmetry. The third main idea, developed in section 6, is that Wilson and ’t Hooft line operators are topological operators that act on the branes of the two-dimensional sigma-model in a natural fashion.

Here we consider an operator that maps.

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Cite this chapter as: Kapustin A. () Gauge Theory, Mirror Symmetry, and the Geometric Langlands Program. In: Homological Mirror by: 1. See: John Baez: Duality in Logic and Physics I am studying the various cases of duality in math.

I imagine that at the heart is the duality between zero and infinity by way of one as in God's y is the basis for logic, and mathematics gives the ways of deviating from duality.

@article{osti_, title = {Modularity, quaternion-Kähler spaces, and mirror symmetry}, author = {Alexandrov, Sergei and Banerjee, Sibasish}, abstractNote = {We provide an explicit twistorial construction of quaternion-Kähler manifolds obtained by deformation of c-map spaces and carrying an isometric action of the modular group SL(2,Z).

Electric-Magnetic Duality And The Geometric Langlands Program Electric-magnetic duality and the geometric Langlands program 3 Generalizations Of The c.c.

Brane And Twisted of the parameter, four-dimensional S-duality acts as two-dimensional mirror symmetry. The third main idea, developed in section 6, is that Wilson and. Mirror symmetry Heterotic string theory on Calabi{Yau three-folds K3 compacti cations and more string dualities Manifolds with G2 and Spin(7) holonomy 10 Flux compacti cations Flux compacti cations and Calabi{Yau four-folds Flux compacti cations of the type IIB theory The field theory results of [] were obtained from string theory and generalized.

Specifically, the mirror symmetry of three-dimensional gauge theories which relates hy- permultiplets and vector multiplets of two different theories was seen as a result of the S-duality of type by: Supergravity and Superstrings - A Geometric Perspective.

World Scientific, on supergravity and string theory with an emphasis on the D'Auria-Fré formulation of supergravity, based on. Riccardo D'Auria, Pietro Fré Geometric Supergravity in D=11 and its. Vortices and Mirror Symmetry 89 Swapping Vortices and Electrons 89 Vortex Strings 91 4.

Domain Walls 94 The Basics 94 Domain Wall Equations 95 An Example 96 Classification of Domain Walls 97 The Moduli Space 98 The Moduli Space Metric 98 Examples of Domain Wall Moduli Spaces 99 Dyonic.

We construct a class of exactly solved (0,2) heterotic compactifications, similar to the (2,2) models constructed by Gepner. We identify these as special poi. tain categories of sheaves in Section 3. In Section 4 we will turn to the S-duality in topological twisted N = 4 super{Yang{Mills theory.

Its dimensional reduction gives rise to the Mirror Symmetry of two-dimensional sigma models associated to the Hitchin 1. We will use the notation Gfor a complex Lie group and G c for its compact form. Note that. Mirror symmetry does arise through a genuine Z 2 action on the Hodge diamond, but then a Z 2-action by itself doesn׳t need to be called a duality.

For example, reflecting a plane in a line, we don׳t speak of a duality between reflected by: 6.

Description S-duality and mirror symmetry PDF

Mirror symmetry (string theory) From Wikipedia, the free encyclopedia String theory Fundamental objects[show] Perturbative string theory[show] Non-perturbative results[show] Phenomenology[show] Mathematics[show] Related concepts[show] Theorists[show] History Glossary v t e In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometric objects called Calabi.

Geometry, Symmetry, and Physics 8 Duality Symmetries and BPS states 9 BPS states 9 Topological string theory 10 3-manifolds, 3d mirror symmetry, and symplectic duality 11 Knot theory 12 Special holonomy in six, seven, and eight dimensions 13 Hyperk¨ahler and Quaternionic-Ka¨hler geometry.

This chapter presents Nigel Hitchin's recollections about the themes that emerged in his own mathematical development. The aim is to explain how the links between physics and geometry, which seem to underlie much of Nigel Hitchin's work, came about.

Hitchin's claims that it is specific problems that have engaged him in research projects, and that theoretical physics is perhaps the richest Author: Nigel Hitchin.Homological Mirror Symmetry, the study of dualities of certain quantum field theories in a mathematically rigorous form, has developed into a flourishing subject on its own over the past years.

The present volume bridges a gap in the literature by providing a set of lectures and reviews that both introduce and representatively review the state.Michael Bird on notions of how symmetry, the Doppelgänger, duality and mirror images have played a part in the way artists view themselves and the world around them, starting with his first viewing of the Jacobean painting The Cholmondeley Ladies c–10 when he was eleven, and continuing to look at Barnett Newman’s Onement I, and Frida Kahlo’s double self-portrait The Two.