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 The Case for Repatriating China’s Cultural Objects by Akinori Tanaka
Cover of the book Wearable and Wireless Systems for Healthcare I by Akinori Tanaka
Cover of the book Conceptualizing Soft Power of Higher Education by Akinori Tanaka
Cover of the book Digital Signal Processing with Matlab Examples, Volume 3 by Akinori Tanaka
Cover of the book Function Spaces and Inequalities by Akinori Tanaka
Cover of the book The Palgrave Handbook of Local Governance in Contemporary China by Akinori Tanaka
Cover of the book Ophthalmic Instruments and Surgical Tools by Akinori Tanaka
Cover of the book Geomorphology of Lake-Catchment Systems by Akinori Tanaka
Cover of the book A Study of Attitudes of Dialect Speakers Towards the Speak Mandarin Campaign in Singapore by Akinori Tanaka
Cover of the book Synthesis of Functionalized Organoboron Compounds Through Copper(I) Catalysis by Akinori Tanaka
Cover of the book Structural Change and Dynamics of Labor Markets in Bangladesh by Akinori Tanaka
Cover of the book Intelligent Visual Surveillance by Akinori Tanaka
Cover of the book Uncertain Portfolio Optimization by Akinori Tanaka
Cover of the book Strategic Marketing and Innovation for Indian MSMEs by Akinori Tanaka
Cover of the book The Future of Technology Education 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