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Extension of the HKLL bulk reconstruction for small increment

Aoki, Sinya Balog, János 京都大学 DOI:10.1007/JHEP05(2023)034

2023.05.05

概要

We re-analyse the bulk reconstruction for a scalar field in Lorentzian AdS spacetime, both for the case of even and odd dimensions, for an extended range of conformal dimensions where the original HKLL reconstruction has to be modified. We also discuss the use of space-like Green’s functions in the bulk reconstruction. We demonstrate that in the extended range also the singular part of the Green’s function, omitted in the original papers, has be included. The results are particularly simple and physically interesting for integer conformal dimensions below the range considered in the original HKLL papers.

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参考文献

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• From the recursion (G.24) and (G.25), we can calculate the value of the coefficients

− 1)(−1)a π

Γ(∆)(−1)a π

−d Γ(∆

−d

f0 = 2

πc = 2

(I.7)

2π d/2 Γ(D/2)Γ(ν + 1)

Γ d−1

Γ(ν + 2)π d/2

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