Overview
- Nominated as an outstanding contribution by Osaka University's Physics Department in 2014
- Localization technique provides an exact way to calculate the path integral of quantum field theory
- Introduces the result of the localization technique in a comprehensive manner
- Provides exact results of (2+1)-dimensional quantum field theory on unorientable Euclidean space-time
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Theses (Springer Theses)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.Authors and Affiliations
About the author
Dr.Akinori Tanaka
Particle Physics Theory Group, Physics Department, Osaka University
Bibliographic Information
Book Title: Superconformal Index on RP2 × S1 and 3D Mirror Symmetry
Authors: Akinori Tanaka
Series Title: Springer Theses
DOI: https://doi.org/10.1007/978-981-10-1398-0
Publisher: Springer Singapore
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer Science+Business Media Singapore 2016
Hardcover ISBN: 978-981-10-1396-6Published: 22 August 2016
Softcover ISBN: 978-981-10-9346-3Published: 15 June 2018
eBook ISBN: 978-981-10-1398-0Published: 12 August 2016
Series ISSN: 2190-5053
Series E-ISSN: 2190-5061
Edition Number: 1
Number of Pages: XII, 83
Topics: Quantum Field Theories, String Theory, Field Theory and Polynomials, Mathematical Applications in the Physical Sciences