Finite- N corrections to the M-brane indices
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Springer
Received: July 21, 2020 Accepted: October 2, 2020 Published: November 18, 2020
Finite-N corrections to the M-brane indices
a
Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan b Department of Physics, Meiji University, Kanagawa 214-8571, Japan
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: We investigate finite-N corrections to the superconformal indices of the theories realized on M2- and M5-branes. For three-dimensional theories realized on a stack of N M2-branes we calculate the finite-N corrections as the contribution of extended M5-branes in the dual geometry AdS4 ×S 7 . We take only M5-brane configurations with a single wrapping into account, and neglect multiple-wrapping configurations. We compare the results with the indices calculated from the ABJM theory, and find agreement up to expected errors due to the multiple wrapping. For six-dimensional theories on N M5-branes we calculate the indices by analyzing extended M2-branes in AdS7 × S 4 . Again, we include only configurations with single wrapping. We first compare the result for N = 1 with the index of the free tensor multiplet to estimate the order of the error due to multiple wrapping. We calculate first few terms of the index of AN −1 theories explicitly, and confirm that they can be expanded by superconformal representations. We also discuss multiple-wrapping contributions to the six-dimensional Schur-like index. Keywords: AdS-CFT Correspondence, Extended Supersymmetry, M-Theory ArXiv ePrint: 2007.05213
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP11(2020)093
JHEP11(2020)093
Reona Arai,a Shota Fujiwara,a Yosuke Imamura,a Tatsuya Moria and Daisuke Yokoyamab
Contents 1 Introduction
1 4 4 5 10 11 12 13
3 6d N = (2, 0) superconformal theories 3.1 Superconformal index 3.2 Wrapped M2-branes 3.3 Results and consistency check 3.4 Schur-like index
14 14 15 17 20
4 Summary and discussions
22
A Index of the ABJM theory
24
B Full B.1 B.2 B.3
25 25 27 29
expressions of the indices in section 2 k=1 k=2 k=3
C Technical remarks on superconformal representations
1
31
Introduction
In typical utilization of the AdS/CFT correspondence [1] we calculate quantities in the boundary theory by using the gravity or string theory in the bulk. For this to be possible it is necessary that the quantum gravitational effect is suppressed because we do not have enough knowledge to carry out quantitative analysis of quantum gravity. Due to this restriction the majority of works about the AdS/CFT correspondence assume the large-N limit. However, there is a possibility that some physical quantities in supersymmetric theories are protected from the quantum gravity corrections and we can perform an analysis on the gravity side even if N is finite. An example of such a quantity is the BPS partition function of the four-dimensional N = 4 supersymmetric Yang-Mills theory. It was shown
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