Abstract
We calculate the Schur index of the ${\cal N}=4$ $U(N)$ SYM with finite $N$ via the AdS/CFT correspondence as the contribution of D3-branes wrapped on contractible cycles in $\boldsymbol{S}^5$ 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, Drukker, and Felix.
Highlights
The Schur index [1] is a specialization of the superconformal index [2] that is defined for N 1⁄4 2 superconformal theories
The N 1⁄4 4 theory, regarded as a special N 1⁄4 2 theory, has the flavor symmetry SUð2ÞF ⊂ SUð4ÞR, and we introduce the flavor fugacity u
We have found the complete agreement with the results obtained from (2). [See the Appendix for the first few terms of IUðNÞ=I Uð∞Þ calculated by (2) for small N.] For N 1⁄4 0, the “Uð0Þ” gauge theory is the trivial theory with no excitation, and the index is IUð0Þ 1⁄4 1
Summary
The Schur index [1] is a specialization of the superconformal index [2] that is defined for N 1⁄4 2 superconformal theories. It is known that for an arbitrary N 1⁄4 2 superconformal theory there is a corresponding chiral algebra and the Schur index is given as the vacuum character of the chiral algebra [6]. By using these different methods complementarily we can obtain nonperturbative information of the theory. In this work we propose another method to calculate the Schur index of the N 1⁄4 4 UðNÞ supersymmetric Yang-Mills theory based on the AdS/CFT correspondence [7]. What brane configurations should we take into account to calculate the index? In the following we calculate Iðn−k;kÞ and numerically confirm that (8) and (9) hold
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
