Superconformal Index on RP2 × S1 and 3D Mirror Symmetry

Nonfiction, Science & Nature, Mathematics, Algebra, Science, Physics, Quantum Theory
Cover of the book Superconformal Index on RP2 × S1 and 3D Mirror Symmetry by Akinori Tanaka, Springer Singapore
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Akinori Tanaka ISBN: 9789811013980
Publisher: Springer Singapore Publication: August 12, 2016
Imprint: Springer Language: English
Author: Akinori Tanaka
ISBN: 9789811013980
Publisher: Springer Singapore
Publication: August 12, 2016
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer Singapore

Cover of the book Education in Japan by Akinori Tanaka
Cover of the book Big Data Analytics by Akinori Tanaka
Cover of the book Intelligent Computing Paradigm: Recent Trends by Akinori Tanaka
Cover of the book Rotating Machineries by Akinori Tanaka
Cover of the book Early Study-Abroad and Identities by Akinori Tanaka
Cover of the book Manipulation of Sound Properties by Acoustic Metasurface and Metastructure by Akinori Tanaka
Cover of the book Multifunctional Molecular Magnets Based on Octacyanidometalates by Akinori Tanaka
Cover of the book Digital TV and Wireless Multimedia Communication by Akinori Tanaka
Cover of the book Inherited Neurological Disorders by Akinori Tanaka
Cover of the book Urban Development in Asia and Africa by Akinori Tanaka
Cover of the book Industry Interactive Innovations in Science, Engineering and Technology by Akinori Tanaka
Cover of the book Leading for High Performance in Asia by Akinori Tanaka
Cover of the book Man-Machine-Environment System Engineering by Akinori Tanaka
Cover of the book The Growth and Development of Astronomy and Astrophysics in India and the Asia-Pacific Region by Akinori Tanaka
Cover of the book Respiratory Endoscopy by Akinori Tanaka
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy