peculiar index relations 2d tqft and universality of susy
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Peculiar Index Relations, 2D TQFT, and Universality of SUSY Enhancement Takahiro Nishinaka ( Ritsumeikan U. ) w/ Matt Buican, arXiv: 1907.01579 Linfeng Li <latexit

  1. Peculiar Index Relations, 2D TQFT, and Universality of SUSY Enhancement Takahiro Nishinaka ( Ritsumeikan U. ) w/ Matt Buican, arXiv: 1907.01579 Linfeng Li

  2. <latexit sha1_base64="amn46KGoKnAnbdSMIwJi7/Cydc=">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</latexit> <latexit sha1_base64="SrloNWBzSnvTqtEnaq2hwNk2N4=">ADlHichVJNaxNRFD3p+NHWr1RBTfBKLqQ4Y1UbMFsAiuSv1IU0hLmUxf4yPzxbyJEkLWQteu3bkQ94KuBF34B1z4E7oWcSPomTuJorX1wcyce+675353XS0Nhcqc+VKefQ4SNHp2dmjx0/cfJUde70qk36WaCbQRIm2VrHtzo0sW7mJg/1WpP+qEutXpLRX51mOdWZPED/NBqjcivxubRP4Oamkeg4v0EGCEFuwGCAaR0PM4j42+VW4hmWMGI9Q26zWlbu4C0qVdsLPFfJqjcufX39DsBKMle5gnVqJwjQp7pGjJw4hM9+Fm147JCS2AvHxmRkbyWnusQpcwF6fHcZtcdszLjQtFIdiPOEGnSKy+qTeqm+qI/qldpV3/fVGoqG/XV6qSXy6eQR2f/VTXb+qy4TjxpPxFsk2ZjTGDK3LfWGjgdktMR9RjmVirwl8zd/0Dxy7lyQORj2SIUpugelM/203VLxzvkH3xhd5R6XWZcz2uWM3uw8L3M/ZqRH2deI9THcq7OEFX/k4x8Yjue4KLe6KoOs+vJ3h0oFZIrstJFbdhIKp7FV3cEKXJQ0XewMk1q+0PVq+7HvG9+XrjNso1jQu4yJN7uIkG7mIFTXZ7hrd4jw/OWeWs+TcKbdOVcY1Z/DHcpZ/AhFxwgk=</latexit> <latexit sha1_base64="SrloNWBzSnvTqtEnaq2hwNk2N4=">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</latexit> <latexit sha1_base64="f0oKQ8AEcUpSlc78AU95Px64Fg=">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</latexit> [ Argyres-Seiberg ] 4d N=2 S-dualities [ Gaiotto ] [ Chacaltana-Distler ] SU(N) gauge theory w/ 2N flavors 2N 2 N 1 R 0 ,N S-dual (N>2) non-Lagrangian theory • This duality corresponds to N M5-branes wrapped on class S dualities • This interpretation led to the discovery of AGT relation etc.

  3. N=2 S-dualities w/ AD theories ( poorly understood ) ( N: odd ) [ Buican-Giacomelli-Papageorgakis-TN ] N [ Xie-Yau ] x 2 2 exotic AD AD 3 N AD N AD N S-dual mysterious AD theory Argyres-Douglas (AD) theory ( poorly understood ) w/ SU(N) flavor sym. No natural interpretation in terms of a Riemann surface!

  4. <latexit sha1_base64="amn46KGoKnAnbdSMIwJi7/Cydc=">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</latexit> <latexit sha1_base64="SrloNWBzSnvTqtEnaq2hwNk2N4=">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</latexit> <latexit sha1_base64="SrloNWBzSnvTqtEnaq2hwNk2N4=">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</latexit> <latexit sha1_base64="f0oKQ8AEcUpSlc78AU95Px64Fg=">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</latexit> Q: Any quantitative relation between these two S-dualities? top 2N 2 N 1 R 0 ,N S-dual N 2 bottom exotic AD AD 3 N AD N AD N S-dual YES!!! Our Answer : • The Schur index of the top and bottom are identical up to a simple change of variables. • This relation enables us to read off the Schur index of exotic AD

  5. Outline 1. What is ? AD N N 2. Schur index of N AD N AD N 3. Index relation in the S-duality

  6. Outline 1. What is ? AD N N 2. Schur index of N AD N AD N 3. Index relation in the S-duality

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