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The holographic contributions to the sphere free energy
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13130_2022_Article_17663.pdf
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Author(s)
Binder, Damon J.
Freedman, Daniel Z.
Pufu, Silviu S.
Zan, Bernardo
Date Issued
January 28, 2022
Publisher
Springer Berlin Heidelberg
Citation
Journal of High Energy Physics. 2022 Jan 28;2022(1):171
Version
Final published version
Abstract
Abstract
We study which bulk couplings contribute to the S3 free energy F(
m
$$ \mathfrak{m} $$
) of three-dimensional
N
$$ \mathcal{N} $$
= 2 superconformal field theories with holographic duals, potentially deformed by boundary real-mass parameters m. In particular, we show that F(
m
$$ \mathfrak{m} $$
) is independent of a large class of bulk couplings that include non-chiral F-terms and all D-terms. On the other hand, in general, F(
m
$$ \mathfrak{m} $$
) does depend non-trivially on bulk chiral F-terms, such as prepotential interactions, and on bulk real-mass terms. These conclusions can be reached solely from properties of the AdS super-algebra,
osp
$$ \mathfrak{osp} $$
(2|4). We also consider massive vector multiplets in AdS, which in the dual field theory correspond to long single-trace superconformal multiplets of spin zero. We provide evidence that F(
m
$$ \mathfrak{m} $$
) is insensitive to the vector multiplet mass and to the interaction couplings between the massive vector multiplet and massless ones. In particular, this implies that F(
m
$$ \mathfrak{m} $$
) does not contain information about scaling dimensions or OPE coefficients of single-trace long scalar
N
$$ \mathcal{N} $$
= 2 superconformal multiplets.
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DOI of Published Version
https://doi.org/10.1007/JHEP01(2022)171
