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DOE OSTI · 3005946

A universal inequality on the unitary 2D CFT partition function

Dey, Indranil [Tata Institute of Fundamental Research, Mumbai (India)] (ORCID:000900052688972X)·Pal, Sridip [California Institute of Technology (CalTech), Pasadena, CA (United States)] (ORCID:0000000238139513)·Qiao, Jiaxin [École Polytechnique Fédérale de Lausanne (Switzerland)] (ORCID:0000000193425662)
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Abstract

We prove the conjecture proposed by Hartman, Keller and Stoica (HKS) [1]: the grand-canonical free energy of a unitary 2D CFT with a sparse spectrum below the scaling dimension $\frac{c}{12}$ + ϵ and below the twist $\frac{c}{12}$ is universal in the large c limit for all β L β R ≠ 4π 2 . The technique of the proof allows us to derive a one-parameter (with parameter α ∈ (0, 1]) family of universal inequalities on the unitary 2D CFT partition function with general central charge c ⩾ 0, using analytical modular bootstrap. We derive an iterative equation for the domain of validity of the inequality on the (β L , β R ) plane. The infinite iteration of this equation gives the boundary of maximal-validity domain, which depends on the parameter α in the inequality.

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Dey, Indranil [Tata Institute of Fundamental Research, Mumbai (India)] (ORCID:000900052688972X), Pal, Sridip [California Institute of Technology (CalTech), Pasadena, CA (United States)] (ORCID:0000000238139513), Qiao, Jiaxin [École Polytechnique Fédérale de Lausanne (Switzerland)] (ORCID:0000000193425662). 2025-07-15. A universal inequality on the unitary 2D CFT partition function. https://doi.org/10.1007/jhep07(2025)163

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