TH Friday Meeting

Friday 18 Oct 2024, 11:00 → 13:00 Europe/Zurich

4/S-030 (CERN)

ArXiv + Presentation [Jiaxin Qiao: A universal inequality on the unitary 2D CFT partition function]

Title: 
A universal inequality on the unitary 2D CFT partition function

Abstract: 
We prove the conjecture proposed by Hartman,  Keller and Stoica (HKS [1405.5137]): the  grand-canonical free energy of a unitary 2D CFT with a sparse spectrum below the scaling dimension c/12+ε and below the twist c/12 is universal in the large c limit for all $\beta_L\beta_R \neq 4\pi^2$.
The technique of the proof allows us to derive a one-parameter (with parameter α btween 0 and 1) family of universal inequalities on the unitary 2D CFT partition function with general central charge,  using analytical modular bootstrap.  We derive an iterative equation for the domain of validity of the inequality on the $(\beta_L,\beta_R)$ plane.  The infinite iteration of this equation gives the boundary of maximal-validity domain, which depends on the parameter α in the inequality.
In the large c limit,  with additional assumption of having a sparse spectrum below the scaling dimension c/12+ε and below the twist αc/12 (with α fixed between 0 and 1), our inequality implies that the grand-canonical free energy has universal large c behavior in the maximal-validity domain, which does not encompass the entire $(\beta_L,\beta_R)$ plane,  except in the case of α= 1.  For α=1, this proves the conjecture by HKS and for α<1,  this quantifies how sparseness in twist affects the regime of universality. This further implies a precise lower bound on near extremal BTZ black hole’s temperature at which we can confidently trust the black hole thermodynamics.