Critical dimension in d-matrix theory and its application in SU(2) subsector of N=4 SYM

by Prof. Yang Lei (Soochow University)

Monday 18 May 2026, 15:00 → 16:00 Asia/Shanghai

B105 (CHEP)

Supersymmetric sectors of N=4 super-Yang-Mills theory motivate the study of the partition function for the counting of gauge-invariant functions of d=2,3 matrices transforming under the adjoint action of U(N). The partition function \mathcal{Z}_d(x) in the large N limit has a known Hagedorn phase transition at x=d^{−1} which provides a simple model for the phase structure of the thermal partition function of SYM. We study the all-orders asymptotic expansion of \mathcal{Z}_d(x) based on a geometric picture of concentric circles of poles in the complex plane accumulating in a natural boundary at ∣x∣=1. We find that the order by order structure has a precise combinatorial interpretation organized in terms of increasing cycle size of permutations arising in the enumeration of the invariants. We refer to this organization as small-cycle dominance, and find that it extends to refined versions of the partition functions depending on several complex variables. An analysis of the coefficients in the asymptotic expansion of \mathcal{Z}_d(x) using the modular property of the Dedekind eta function reveals that the asymptotic expansion is actually convergent for d≥d_crit=13.

Bio:
Prof. Yang Lei is now working as an associate professor in Soochow University. He graduated from Peking University in 2011 with dual degrees in physics and math. He acquired PhD degree in Durham University, and did postdoc researches in Chinese Academy of Science, University of Witwatersrand, Niels Bohr Institute and Kavli Institute of Theoreical Science. His recent research interests include applying combinatorics method to study quantum gravity and supersymmetric field theory, also non-relativistic holography, and black hole physics.