Work

Superconformal index for $$ \mathcal{N} $$ = 4 super Yang-Mills and elliptic Macdonald polynomials

Year: 2026

Type: article

Abstract: A bstract We establish a connection between the superconformal index of $$ \mathcal{N} $$ 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 λ ( p , q , t ) and normalization constants $$ {\mathcal{N}}_{\lambda}\left(p,q,t\right) $$ N λ 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.

Source: Journal of High Energy Physics

DOI: 10.1007/jhep09(2026)178

Authors: Gao-fu Ren, Min-xin Huang

Institutions: University of Science and Technology of China, Peng Huanwu Center for Fundamental Theory

Language: English

Topic: Black Holes and Theoretical Physics

Subfield: Nuclear and High Energy Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

Funder: National Natural Science Foundation of China

Awards: G2012042336, G5479278984, G767428274