Citation

BibTex format

@article{Alday:2024:10.1007/jhep05(2024)044,
author = {Alday, LF and Chester, SM and Dorigoni, D and Green, MB and Wen, C},
doi = {10.1007/jhep05(2024)044},
journal = {Journal of High Energy Physics},
title = {Relations between integrated correlators in N=4 supersymmetric Yang-Mills theory},
url = {http://dx.doi.org/10.1007/jhep05(2024)044},
volume = {2024},
year = {2024}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Integrated correlation functions in $\mathcal{N}=4$ supersymmetric Yang--Mills theory with gauge group $SU(N)$ can be expressed in terms of the localised $S^4$ partition function, $Z_N$, deformed by a mass $m$. Two such cases are $\mathcal{C}_N=(\text{Im} τ)^2 \partial_τ\partial_{\barτ} \partial_m^2\log Z_N\vert_{m=0}$ and $\mathcal{H}_N=\partial_m^4\log Z_N\vert_{m=0}$, which are modular invariant functions of the complex coupling $τ$. While $\mathcal{C}_N$ was recently written in terms of a two-dimensional lattice sum for any $N$ and $τ$, $\mathcal{H}_N$ has only been evaluated up to order $1/N^3$ in a large-$N$ expansion in terms of modular invariant functions with no known lattice sum realisation. Here we develop methods for evaluating $\mathcal{H}_N$ to any desired order in $1/N$ and finite $τ$. We use this new data to constrain higher loop corrections to the stress tensor correlator, and give evidence for several intriguing relations between $\mathcal{H}_N$ and $\mathcal{C}_N$ to all orders in $1/N$. We also give evidence that the coefficients of the $1/N$ expansion of $\mathcal{H}_N$ can be written as lattice sums to all orders. Lastly, these large $N$ and finite $τ$ results are used to accurately estimate the integrated correlators at finite $N$ and finite $τ$.
AU  - Alday,LF
AU  - Chester,SM
AU  - Dorigoni,D
AU  - Green,MB
AU  - Wen,C
DO  - 10.1007/jhep05(2024)044
PY  - 2024///
SN  - 1029-8479
TI  - Relations between integrated correlators in N=4 supersymmetric Yang-Mills theory
T2  - Journal of High Energy Physics
UR  - http://dx.doi.org/10.1007/jhep05(2024)044
UR  - https://arxiv.org/abs/2310.12322v1
UR  - https://doi.org/10.1007/jhep05(2024)044
VL  - 2024
ER  -
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