Mirror Symmetry In Three Dimensional Supersymmetric Gauge Theories
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| Author | : Anindya Dey (Ph. D.) |
| Publisher | : |
| Total Pages | : 520 |
| Release | : 2015 |
| Genre | : |
| ISBN | : |
Download Mirror Symmetry in Three Dimensional Supersymmetric Gauge Theories Book in PDF, Epub and Kindle
The basic objective of this thesis is to apply techniques of supersymmetric localization for studying Mirror Symmetry in N = 4 gauge theories in three space-time dimensions. We start by discussing an M-theory/Type IIA description of Mirror Symmetry for affine quiver gauge theories and present a neat classification of various infinite families of dual theories that arise in this fashion. We then perform an extremely non-trivial check of Mirror Symmetry for a large class of affine A and D type quivers and their truncated versions using partition function on a round sphere as a function of hypermultiplet masses and FI parameters. The computation allows one to explicitly derive the "mirror map" -- a linear map relating masses of a theory with FI parameters of the dual and vice-versa. In addition, we demonstrate that there exists a one-to-one correspondence between the various "building blocks" of the partition function of a given theory and String Theory objects in the Type IIB description of such theories. In the next part of the thesis, we introduce the idea that a very large class of dual quiver gauge theories may be systematically generated starting from dual pairs consisting only of simple linear quivers by appropriately gauging avor symmetries on one side of the duality. The gauging operation on one side of the duality results in a corresponding "ungauging" on the other side. We show that this program can be carried out to obtain various known as well as new families of mirror pairs -- including affine quivers of A-D-E type, star-shaped quivers and quivers with symplectic gauge groups. S3 partition function turns out to be a particularly convenient tool to implement the gauging procedure since it easily generalizes to any arbitrary shape of the quiver as well as arbitrary rank of the gauge group at a given node in the quiver. Additional checks on the new mirror pairs obtained in this fashion are performed using Hilbert Series computation on the Coulomb and Higgs branches of the dual theories in question. Remarkably, we find that our prescription gives a straightforward recipe to construct "good" duals in certain cases where naive mirror duals obtained via S-duality from Type IIB brane construction are "bad" in the Gaiotto-Witten sense.
| Author | : Akinori Tanaka |
| Publisher | : Springer |
| Total Pages | : 91 |
| Release | : 2016-08-12 |
| Genre | : Science |
| ISBN | : 9811013985 |
Download Superconformal Index on RP2 × S1 and 3D Mirror Symmetry Book in PDF, Epub and Kindle
The author introduces the supersymmetric localization technique, a new approach for computing path integrals in quantum field theory on curved space (time) defined with interacting Lagrangian. The author focuses on a particular quantity called the superconformal index (SCI), which is defined by considering the theories on the product space of two spheres and circles, in order to clarify the validity of so-called three-dimensional mirror symmetry, one of the famous duality proposals. In addition to a review of known results, the author presents a new definition of SCI by considering theories on the product space of real-projective space and circles. In this book, he explains the concept of SCI from the point of view of quantum mechanics and gives localization computations by reducing field theoretical computations to many-body quantum mechanics. He applies his new results of SCI with real-projective space to test three-dimensional mirror symmetry, one of the dualities of quantum field theory. Real-projective space is known to be an unorientable surface like the Mobius strip, and there are many exotic effects resulting from Z2 holonomy of the surface. Thanks to these exotic structures, his results provide completely new evidence of three-dimensional mirror symmetry. The equivalence expected from three-dimensional mirror symmetry is transformed into a conjectural non-trivial mathematical identity through the new SCI, and he performs the proof of the identity using a q-binomial formula.
| Author | : Jörg Teschner |
| Publisher | : Springer |
| Total Pages | : 467 |
| Release | : 2015-11-17 |
| Genre | : Science |
| ISBN | : 3319187694 |
Download New Dualities of Supersymmetric Gauge Theories Book in PDF, Epub and Kindle
This book reviews a number of spectacular advances that have been made in the study of supersymmetric quantum field theories in the last few years. Highlights include exact calculations of Wilson loop expectation values, and highly nontrivial quantitative checks of the long-standing electric-magnetic duality conjectures The book starts with an introductory article presenting a survey of recent advances, aimed at a wide audience with a background and interest in theoretical physics. The following articles are written for advanced students and researchers in quantum field theory, string theory and mathematical physics, our goal being to familiarize these readers with the forefront of current research. The topics covered include recent advances in the classification and vacuum structure of large families of N=2 supersymmetric field theories, followed by an extensive discussion of the localisation method, one of the most powerful tools for exact studies of supersymmetric field theories. The quantities that have been studied in this way are partition functions, expectation values of line operators, and supersymmetric indices. The book also reviews recently discovered connections between SUSY field theories in four dimensions and two-dimensional conformal field theory. These connections have a counterpart in relations between three-dimensional gauge theories and Chern-Simons theory; the book’s closing chapters explore connections with string theory.
| Author | : Misha Shifman |
| Publisher | : World Scientific |
| Total Pages | : 636 |
| Release | : 2005 |
| Genre | : Condensed matter |
| ISBN | : 9812561145 |
Download From Fields to Strings Book in PDF, Epub and Kindle
This volume is a collection of dedicated reviews covering all aspects of theoretical high energy physics and some aspects of solid state physics. Some of the papers are broad reviews of topics that span the entire field while others are surveys of authors' personal achievements. This is the most comprehensive review collection reflecting state of the art at the end of 2004. An important and unique aspect is a special effort the authors have invested in making the presentation pedagogical
| Author | : Eric D'Hoker |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 394 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 0821833359 |
Download Mirror Symmetry IV Book in PDF, Epub and Kindle
This book presents contributions of participants of a workshop held at the Centre de Recherches Mathematiques (CRM), University of Montreal. It can be viewed as a sequel to Mirror Symmetry I (1998), Mirror Symmetry II (1996), and Mirror Symmetry III (1999), copublished by the AMS and International Press. The volume presents a broad survey of many of the noteworthy developments that have taken place in string theory, geometry, and duality since the mid 1990s. Some of the topics emphasized include the following: Integrable models and supersymmetric gauge theories; theory of M- and D-branes and noncommutative geometry; duality between strings and gauge theories; and elliptic genera and automorphic forms. Several introductory articles present an overview of the geometric and physical aspects of mirror symmetry and of corresponding developments in symplectic geometry. The book provides an efficient way for a very broad audience of mathematicians and physicists to explore the frontiers of research into this rapidly expanding area.
| Author | : Kentaro Hori |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 954 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 0821829556 |
Download Mirror Symmetry Book in PDF, Epub and Kindle
This thorough and detailed exposition is the result of an intensive month-long course on mirror symmetry sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives with the aim of furthering interaction between the two fields. The material will be particularly useful for mathematicians and physicists who wish to advance their understanding across both disciplines. 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 enumeration of holomorphic curves inside complex manifolds by solving differential equations obtained from a ``mirror'' geometry. The inclusion of D-brane states in the equivalence has led to further conjectures involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds: the Gopakumar-Vafa invariants. This book gives a single, cohesive treatment of mirror symmetry. Parts 1 and 2 develop the necessary mathematical and physical background from ``scratch''. The treatment is focused, developing only the material most necessary for the task. In Parts 3 and 4 the physical and mathematical proofs of mirror symmetry are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory can be described geometrically, and thus mirror symmetry gives rise to a ``pairing'' of geometries. The proof involves applying $R\leftrightarrow 1/R$ circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Gromov-Witten theory in the algebraic setting, beginning with the moduli spaces of curves and maps, and uses localization techniques to show that certain hypergeometric functions encode the Gromov-Witten invariants in genus zero, as is predicted by mirror symmetry. Part 5 is devoted to advanced topi This one-of-a-kind book is suitable for graduate students and research mathematicians interested in mathematics and mathematical and theoretical physics.
| Author | : Sergio Cecotti |
| Publisher | : Cambridge University Press |
| Total Pages | : 425 |
| Release | : 2015-01-08 |
| Genre | : Mathematics |
| ISBN | : 1107053811 |
Download Supersymmetric Field Theories Book in PDF, Epub and Kindle
Adopting an elegant geometrical approach, this advanced pedagogical text describes deep and intuitive methods for understanding the subtle logic of supersymmetry while avoiding lengthy computations. The book describes how complex results and formulae obtained using other approaches can be significantly simplified when translated to a geometric setting. Introductory chapters describe geometric structures in field theory in the general case, while detailed later chapters address specific structures such as parallel tensor fields, G-structures, and isometry groups. The relationship between structures in supergravity and periodic maps of algebraic manifolds, Kodaira-Spencer theory, modularity, and the arithmetic properties of supergravity are also addressed. Relevant geometric concepts are introduced and described in detail, providing a self-contained toolkit of useful techniques, formulae and constructions. Covering all the material necessary for the application of supersymmetric field theories to fundamental physical questions, this is an outstanding resource for graduate students and researchers in theoretical physics.
| Author | : Kodŭng Kwahagwŏn (Korea). International Conference |
| Publisher | : World Scientific |
| Total Pages | : 940 |
| Release | : 2001 |
| Genre | : Mirror symmetry |
| ISBN | : 9789812799821 |
Download Symplectic Geometry and Mirror Symmetry Book in PDF, Epub and Kindle
In 1993, M. Kontsevich proposed a conceptual framework for explaining the phenomenon of mirror symmetry. Mirror symmetry had been discovered by physicists in string theory as a duality between families of three-dimensional Calabi–Yau manifolds. Kontsevich's proposal uses Fukaya's construction of the A∞-category of Lagrangian submanifolds on the symplectic side and the derived category of coherent sheaves on the complex side. The theory of mirror symmetry was further enhanced by physicists in the language of D-branes and also by Strominger–Yau–Zaslow in the geometric set-up of (special) Lagrangian torus fibrations. It rapidly expanded its scope across from geometry, topology, algebra to physics. In this volume, leading experts in the field explore recent developments in relation to homological mirror symmetry, Floer theory, D-branes and Gromov–Witten invariants. Kontsevich-Soibelman describe their solution to the mirror conjecture on the abelian variety based on the deformation theory of A∞-categories, and Ohta describes recent work on the Lagrangian intersection Floer theory by Fukaya–Oh–Ohta–Ono which takes an important step towards a rigorous construction of the A∞-category. There follow a number of contributions on the homological mirror symmetry, D-branes and the Gromov–Witten invariants, e.g. Getzler shows how the Toda conjecture follows from recent work of Givental, Okounkov and Pandharipande. This volume provides a timely presentation of the important developments of recent years in this rapidly growing field.
| Author | : Kenji Fukaya |
| Publisher | : World Scientific |
| Total Pages | : 510 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 9810247141 |
Download Symplectic Geometry and Mirror Symmetry Book in PDF, Epub and Kindle
In 1993, M Kontsevich proposed a conceptual framework for explaining the phenomenon of mirror symmetry. Mirror symmetry had been discovered by physicists in string theory as a duality between families of three-dimensional Calabi-Yau manifolds. Kontsevich's proposal uses Fukaya's construction of the Aì-category of Lagrangian submanifolds on the symplectic side and the derived category of coherent sheaves on the complex side. The theory of mirror symmetry was further enhanced by physicists in the language of D-branes and also by Strominger-Yau-Zaslow in the geometric set-up of (special) Lagrangian torus fibrations. It rapidly expanded its scope across from geometry, topology, algebra to physics.In this volume, leading experts in the field explore recent developments in relation to homological mirror symmetry, Floer theory, D-branes and Gromov-Witten invariants. Kontsevich-Soibelman describe their solution to the mirror conjecture on the abelian variety based on the deformation theory of Aì-categories, and Ohta describes recent work on the Lagrangian intersection Floer theory by Fukaya-Oh-Ohta-Ono which takes an important step towards a rigorous construction of the Aì-category. There follow a number of contributions on the homological mirror symmetry, D-branes and the Gromov-Witten invariants, e.g. Getzler shows how the Toda conjecture follows from recent work of Givental, Okounkov and Pandharipande. This volume provides a timely presentation of the important developments of recent years in this rapidly growing field.
| Author | : Kenji Fukaya |
| Publisher | : World Scientific |
| Total Pages | : 510 |
| Release | : 2001-11-19 |
| Genre | : Mathematics |
| ISBN | : 9814490407 |
Download Symplectic Geometry And Mirror Symmetry - Proceedings Of The 4th Kias Annual International Conference Book in PDF, Epub and Kindle
In 1993, M Kontsevich proposed a conceptual framework for explaining the phenomenon of mirror symmetry. Mirror symmetry had been discovered by physicists in string theory as a duality between families of three-dimensional Calabi-Yau manifolds. Kontsevich's proposal uses Fukaya's construction of the A∞-category of Lagrangian submanifolds on the symplectic side and the derived category of coherent sheaves on the complex side. The theory of mirror symmetry was further enhanced by physicists in the language of D-branes and also by Strominger-Yau-Zaslow in the geometric set-up of (special) Lagrangian torus fibrations. It rapidly expanded its scope across from geometry, topology, algebra to physics.In this volume, leading experts in the field explore recent developments in relation to homological mirror symmetry, Floer theory, D-branes and Gromov-Witten invariants. Kontsevich-Soibelman describe their solution to the mirror conjecture on the abelian variety based on the deformation theory of A∞-categories, and Ohta describes recent work on the Lagrangian intersection Floer theory by Fukaya-Oh-Ohta-Ono which takes an important step towards a rigorous construction of the A∞-category. There follow a number of contributions on the homological mirror symmetry, D-branes and the Gromov-Witten invariants, e.g. Getzler shows how the Toda conjecture follows from recent work of Givental, Okounkov and Pandharipande. This volume provides a timely presentation of the important developments of recent years in this rapidly growing field.
