國立虎尾科技大學 |

Superconformal index on RP2 × S1 and 3D mirror symmetry

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Superconformal index on RP2 × S1 and 3D mirror symmetry/ by Akinori Tanaka.
Author:	Tanaka, Akinori.
Published:	Singapore :Springer Singapore : : 2016.,
Description:	xii, 83 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Supersymmetry. -
Online resource:	http://dx.doi.org/10.1007/978-981-10-1398-0
ISBN:	9789811013980

Superconformal index on RP2 × S1 and 3D mirror symmetry
Tanaka, Akinori.

Superconformal index on RP2 × S1 and 3D mirror symmetry[electronic resource] /by Akinori Tanaka. - Singapore :Springer Singapore :2016. - xii, 83 p. :ill., digital ;24 cm. - Springer theses,2190-5053. - Springer theses..

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.

ISBN: 9789811013980

Standard No.: 10.1007/978-981-10-1398-0doiSubjects--Topical Terms:

579993
Supersymmetry.

LC Class. No.: QC174.17.S9

Dewey Class. No.: 530.1423

Superconformal index on RP2 × S1 and 3D mirror symmetry
LDR:02479nam a2200313 a 4500 001 866664
003 DE-He213
005 20170220104933.0
006 m d
007 cr nn 008maaau
008 170720s2016 si s 0 eng d
020 $a 9789811013980 $q (electronic bk.)
020 $a 9789811013966 $q (paper)
024 7 $a 10.1007/978-981-10-1398-0 $2 doi
035 $a 978-981-10-1398-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QC174.17.S9
072 7 $a PHS $2 bicssc
072 7 $a SCI057000 $2 bisacsh
082 0 4 $a 530.1423 $2 23
090 $a QC174.17.S9 $b T161 2016
100 1 $a Tanaka, Akinori. $3 1112996
245 1 0 $a Superconformal index on RP2 × S1 and 3D mirror symmetry $h [electronic resource] / $c by Akinori Tanaka.
260 $a Singapore : $c 2016. $b Springer Singapore : $b Imprint: Springer,
300 $a xii, 83 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer theses, $x 2190-5053
520 $a 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.
650 0 $a Supersymmetry. $3 579993
650 0 $a Quantum field theory. $3 579915
650 0 $a S-matrix theory. $3 856782
650 1 4 $a Physics. $3 564049
650 2 4 $a Quantum Field Theories, String Theory. $3 768973
650 2 4 $a Field Theory and Polynomials. $3 672025
650 2 4 $a Mathematical Applications in the Physical Sciences. $3 786649
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a Springer theses. $3 831604
856 4 0 $u http://dx.doi.org/10.1007/978-981-10-1398-0
950 $a Physics and Astronomy (Springer-11651)