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Superconformal index for $\mathcal{N} = 4$ Super Yang-Mills and Elliptic Macdonald Polynomials
High Energy Physics - Theory · Submitted 1 Apr 2026
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We establish a connection between the superconformal index of $\mathcal{N}=4$ $U(N)$ SYM and the elliptic Ruijsenaars-Schneider integrable system.
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The abstract, sentence by sentence
We establish a connection between the superconformal index of $\mathcal{N}=4$ $U(N)$ SYM and the elliptic Ruijsenaars-Schneider integrable system. The index admits an expression in terms of elliptic Macdonald polynomials, which leads to a compact summation over generalized partitions involving the structure constants $B_\lambda(p,q,t)$ and normalization constants $\mathcal{N}_\lambda(p,q,t)$. By solving the elliptic Ruijsenaars-Schneider model perturbatively in the elliptic parameter $p$, a systematic expansion of the index in powers of $p$ is obtained. We check that in various limits, namely a deformed 1/2 BPS limit and especially the large $N$ limit, our formalism reduces to previously known results.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We establish a connection between the superconformal index of $\mathcal{N}=4$ $U(N)$ SYM and the elliptic Ruijsenaars-Schneider integrable system. | contribution 0.75 | 0.94 | 0.77 | asserted 1.00 |
| s1 | The index admits an expression in terms of elliptic Macdonald polynomials, which leads to a compact summation over generalized partitions involving the structure constants $B_\lambda(p,q,t)$ and normalization constants $\mathcal{N}_\lambda(p,q,t)$. | result 0.75 | 0.87 | 0.25 | asserted 1.00 |
| s2 | By solving the elliptic Ruijsenaars-Schneider model perturbatively in the elliptic parameter $p$, a systematic expansion of the index in powers of $p$ is obtained. | method 0.87 | 0.94 | 0.12 | asserted 1.00 |
| s3 | We check that in various limits, namely a deformed 1/2 BPS limit and especially the large $N$ limit, our formalism reduces to previously known results. | result 0.72 | 0.90 | 0.08 | asserted 0.99 |
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Original abstract
We establish a connection between the superconformal index of $\mathcal{N}=4$ $U(N)$ SYM and the elliptic Ruijsenaars-Schneider integrable system. The index admits an expression in terms of elliptic Macdonald polynomials, which leads to a compact summation over generalized partitions involving the structure constants $B_\lambda(p,q,t)$ and normalization constants $\mathcal{N}_\lambda(p,q,t)$. By solving the elliptic Ruijsenaars-Schneider model perturbatively in the elliptic parameter $p$, a systematic expansion of the index in powers of $p$ is obtained. We check that in various limits, namely a deformed 1/2 BPS limit and especially the large $N$ limit, our formalism reduces to previously known results.
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References
How the literature uses it
2 arXiv papers cite this in 7 sentences
Papers citing it · 6 sentences without a confident label
Cites it as background 1 paper
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The deep connections between classical symmetric functions and superconformal indices [ref] were mentioned in the introduction.
Unitary matrix models, quantized symmetric functions and spin chain · Outlook · 0.95
What it cites · 15 sentences without a confident label
Builds on 1 paper
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We generalize the novel method of [ref] to the case of full index, using elliptic Macdonald polynomials.
Deformed Schur indices and Macdonald polynomials · Introduction · 0.97
Uses the method or tool of 1 paper
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To proceed further, we define an expectation value and an inner product with respect to the non-elliptic Macdonald weight function, following [ref] : [equation] where $ω()$ is the ordinary Macdonald weight.
Deformed Schur indices and Macdonald polynomials · Large $N$ limit · 0.97
Compares with 1 paper
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The sum can be rewritten as [equation] Assuming convergence, each geometric series can be summed, yielding [equation] Thus, based on symmetric function methods, we have checked the exact expression for the $𝒩=4$ $U(N)$ SYM superconformal index in the large-$N$ limit [equation] which was first derived in [ref] .
An Index for 4 dimensional Super Conformal Theories · Large $N$ limit · 0.84
Cites as background 28 papers
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In another perspective, the deep interplay between superconformal indices and integrable systems has emerged as a powerful theme in theoretical physics, particularly in the context of $=2$ superconformal field theories of class $𝒮$ [ref] .
The superconformal index of theories of class $\cal S$ · Introduction · 0.93
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In another perspective, the deep interplay between superconformal indices and integrable systems has emerged as a powerful theme in theoretical physics, particularly in the context of $=2$ superconformal field theories of class $𝒮$ [ref] .
Gauge Theories and Macdonald Polynomials · Introduction · 0.93
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In another perspective, the deep interplay between superconformal indices and integrable systems has emerged as a powerful theme in theoretical physics, particularly in the context of $=2$ superconformal field theories of class $𝒮$ [ref] .
On the N=2 superconformal index and eigenfunctions of the elliptic RS model · Introduction · 0.93
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