2018/09/30 by Takuya Kanazawa, Mario Kieburg · 6 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Eigenvalues and eigenvectors #Gaussian #Law #Limit (mathematics) #Mathematical physics #Mathematics #Particle physics #Particle physics theoretical and experimental studies #Physics #Pion #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Random matrix #Theoretical physics #Unitary state #hep-lat #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/jhep11(2018)205
published in Journal of High Energy Physics 2018(11) (Springer Nature) · 42 pages, 3 figures, PACS numbers: 02.10.Yn,05.50.+q,11.15.Ex,11.15.Ha,12.38.-t
arxiv created 2018/10/09 · openalex publication_date 2018/11/01 · arxiv updated 2018/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A bstract We consider a random matrix model in the hard edge limit (local spectral statistics at the origin in the limit of large matrix size) which interpolates between the Gaussian unitary ensemble (GUE) and the chiral Gaussian unitary ensemble (chGUE). We show that this model is equivalent to the low-energy limit of certain QCD-like theories in the epsilon-regime. Moreover, we present a detailed derivation of the microscopic level density as well as the partially quenched and unquenched partition functions. Some of these results have been announced in a former letter by us. Our derivation relies on the supersymmetry method and is performed here step by step. Additionally, we compute the chiral condensate and the pion condensate for the quenched as well as unquenched settings. We also investigate the limits to GUE and chGUE and confirm our conjecture that the non-uniformity of the GUE limit would carry over to the hard edge limit.