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Schur index of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>U</mml:mi><mml:mo mathvariant="bold" stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo mathvariant="bold" stretchy="false">)</mml:mo></mml:mrow></mml:math> supersymmetric Yang-Mills theory via the AdS/CFT correspondence

Reona Arai, Shota Fujiwara, Yosuke Imamura, Tatsuya Mori

2020Physical review. D/Physical review. D.46 citationsDOIOpen Access PDF

Abstract

We calculate the Schur index of the $\mathcal{N}=4$ $U(N)$ supersymmetric Yang-Mills theory with finite $N$ via the AdS/CFT correspondence as the contribution of $\mathrm{D}3$-branes wrapped on contractible cycles in ${\mathbit{S}}^{5}$ on some assumptions motivated by preliminary analyses. As far as we have checked numerically it agrees with the index calculated on the gauge theory side. In a certain limit it reproduces the analytic result given by Bourdier, et al.

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Schur index of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>U</mml:mi><mml:mo mathvariant="bold" stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo mathvariant="bold" stretchy="false">)</mml:mo></mml:mrow></mml:math> supersymmetric Yang-Mills theory via the AdS/CFT correspondence | Litcius