arXiv subjects

Gao-fu Ren

Publications and source records attributed to Gao-fu Ren.

3 recordsLinked to original sources

arXiv2026

Superconformal index for $\mathcal{N} = 4$ Super Yang-Mills and Elliptic Macdonald Polynomials

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 $B_λ(p,q,t)$ and normalization constants $\mathcal{N}_λ(p,q,t)$. 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.

hep-th↗

arXiv2026

Unitary matrix models, quantized symmetric functions and spin chain

We construct a correspondence between a broad class of unitary matrix models and vacuum correlation functions in quantum spin-chain Hilbert spaces. The key step is to lift symmetric functions to operators acting on the $N$-magnon sector in a way that preserves the relevant ring structure. For any unitary matrix model whose integrand admits a factorized expansion in symmetric functions, the Schur orthogonality of the unitary group integral is then translated into the inner product of quantized Schur states. We illustrate the construction for the Gross--Witten--Wadia model, superconformal indices of $\mathcal{N}=4$ super Yang--Mills theory with classical gauge groups, and Toda tau functions. The resulting operator formulation provides a unified algebraic bridge between unitary matrix integrals, quantum integrable systems and symmetric function theory.

hep-th↗

arXiv2026

Deformed Schur Indices of BCD-type for N=4 Super Yang-Mills and Symmetric Functions

We investigate the deformed Schur index in four dimensional N=4 super Yang-Mills theories with $SO$ and $Sp$ gauge groups, generalizing Hatsuda's recent calculations. We express the deformed Schur index as integrals of Koornwinder polynomials and Macdonald polynomials, then perform the integrals in terms of the normalization constants of Macdonald polynomials. We provide explicit results for some low rank gauge groups and for expansion in a $u$ parameter. We discuss various special limits and the tests of S-duality.

hep-th↗