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SUMMARY:Critical dimension in d-matrix theory and its application in SU(2)
  subsector of N=4 SYM
DTSTART;VALUE=DATE-TIME:20260518T070000Z
DTEND;VALUE=DATE-TIME:20260518T080000Z
DTSTAMP;VALUE=DATE-TIME:20260523T135500Z
UID:indico-event-29540@indico.ihep.ac.cn
DESCRIPTION:Speakers: Yang  Lei (Soochow University)\nSupersymmetric secto
 rs of N=4 super-Yang-Mills theory motivate the study of the partition func
 tion for the counting of gauge-invariant functions of d=2\,3 matrices tran
 sforming under the adjoint action of U(N). The partition function \\mathca
 l{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 ther
 mal partition function of SYM. We study the all-orders asymptotic expansio
 n 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 combinatori
 al interpretation organized in terms of increasing cycle size of permutati
 ons arising in the enumeration of the invariants. We refer to this organiz
 ation as small-cycle dominance\, and find that it extends to refined versi
 ons 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 t
 he asymptotic expansion is actually convergent for d≥d_crit=13.\n\nBio:\
 nProf. Yang Lei is now working as an associate professor in Soochow Univer
 sity. He graduated from Peking University in 2011 with dual degrees in phy
 sics and math. He acquired PhD degree in Durham University\, and did postd
 oc researches in Chinese Academy of Science\, University of Witwatersrand\
 , Niels Bohr Institute and Kavli Institute of Theoreical Science. His rece
 nt research interests include applying combinatorics method to study quant
 um gravity and supersymmetric field theory\, also non-relativistic hologra
 phy\, and black hole physics.\nhttps://indico.ihep.ac.cn/event/29540/
LOCATION:B105 (CHEP)
URL:https://indico.ihep.ac.cn/event/29540/
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