Journal of High Energy Physics (Oct 2023)

Fuzzballs and random matrices

  • Suman Das,
  • Sumit K. Garg,
  • Chethan Krishnan,
  • Arnab Kundu

DOI
https://doi.org/10.1007/JHEP10(2023)031
Journal volume & issue
Vol. 2023, no. 10
pp. 1 – 27

Abstract

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Abstract Black holes are believed to have the fast scrambling properties of random matrices. If the fuzzball proposal is to be a viable model for quantum black holes, it should reproduce this expectation. This is considered challenging, because it is natural for the modes on a fuzzball microstate to follow Poisson statistics. In a previous paper, we noted a potential loophole here, thanks to the modes depending not just on the n-quantum number, but also on the J-quantum numbers of the compact dimensions. For a free scalar field ϕ, by imposing a Dirichlet boundary condition ϕ = 0 at the stretched horizon, we showed that this J-dependence leads to a linear ramp in the Spectral Form Factor (SFF). Despite this, the status of level repulsion remained mysterious. In this letter, motivated by the profile functions of BPS fuzzballs, we consider a generic profile ϕ = ϕ 0(θ) instead of ϕ = 0 at the stretched horizon. For various notions of genericity (eg. when the Fourier coefficients of ϕ 0(θ) are suitably Gaussian distributed), we find that the J-dependence of the spectrum exhibits striking evidence of level repulsion, along with the linear ramp. We also find that varying the profile leads to natural interpolations between Poisson and Wigner-Dyson(WD)-like spectra. The linear ramp in our previous work can be understood as arising via an extreme version of level repulsion in such a limiting spectrum. We also explain how the stretched horizon/fuzzball is different in these aspects from simply putting a cut-off in flat space or AdS (i.e., without a horizon).

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