Six-Dimensional Superconformal Field Theories and Their Torus Compactifications, Kantaro Ohmori
Автор: Tanaka Название: Superconformal Index on RP2 ? S1 and 3D Mirror Symmetry ISBN: 9811013969 ISBN-13(EAN): 9789811013966 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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.
Описание: This monograph presents in detail the reduction method for studying the unification of fundamental actions. The book presents the basic ideas and the calculations in detail and should be of interest to researchers and graduate students in mathematical physics.
Автор: Grana, Mariana Triendl, Hagen Название: String theory compactifications ISBN: 3319543156 ISBN-13(EAN): 9783319543154 Издательство: Springer Рейтинг: Цена: 7685.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Chapter 1 Lecture 1: Introduction to String Theory.- Chapter 2 Lecture 2: Compactifications on tori.- Chapter 3 Lecture 3: Calabi-Yau Compactifications.- Chapter 4 Lecture 4: Fluxes and Generalized Geometry.- Chapter 5 Lecture 5: 4D Effective actions for compactifications on manifolds of reduced structure.- Chapter 6 Lecture 6: Open problems in phenomenology
Описание: This book treats the two-dimensional non-linear supersymmetric sigma model or spinning string from the perspective of supergeometry. The objective is to understand its symmetries as geometric properties of super Riemann surfaces, which are particular complex super manifolds of dimension 1|1.The first part gives an introduction to the super differential geometry of families of super manifolds. Appropriate generalizations of principal bundles, smooth families of complex manifolds and integration theory are developed.The second part studies uniformization, U(1)-structures and connections on Super Riemann surfaces and shows how the latter can be viewed as extensions of Riemann surfaces by a gravitino field. A natural geometric action functional on super Riemann surfaces is shown to reproduce the action functional of the non-linear supersymmetric sigma model using a component field formalism. The conserved currents of this action can be identified as infinitesimal deformations of the super Riemann surface. This is in surprising analogy to the theory of Riemann surfaces and the harmonic action functional on them.This volume is aimed at both theoretical physicists interested in a careful treatment of the subject and mathematicians who want to become acquainted with the potential applications of this beautiful theory.
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