Pole-skipping and chaos in hotMQCD

A bstract We address the question of whether thermal QCD at high temperature is chaotic from the M theory dual of QCD-like theories at intermediate coupling as constructed in [1]. The equations of motion of the gauge-invariant combination Z s ( r ) of scalar metric perturbations is shown to possess an irregular singular point at the horizon radius r h . Very interestingly, at a specific value of the imaginary frequency and momentum used to read off the analogs of the “Lyapunov exponent” λ L and “butterfly velocity” v b not only does r h become a regular singular point, but truncating the incoming mode solution of Z s ( r ) as a power series around r h , yields a “missing pole”, i.e., C n , n +1 = 0, det M ( n ) = 0, n ∈ Z⁺ is satisfied for a single n ≥ 3 depending on the values of the string coupling g s , number of (fractional) D 3 branes ( M ) N and flavor D 7-branes N f in the parent type IIB set [2], e.g., for the QCD(EW-scale)-inspired N = 100, M = N f = 3, g s = 0.1, one finds a missing pole at n = 3. For integral n > 3, truncating Z s ( r ) at O((r-rₕ)ⁿ) , yields C n , n +1 = 0 at order n , ∀ n ≥ 3. Incredibly, (assuming preservation of isotropy in R³ even with the inclusion of higher derivative corrections) the aforementioned gauge-invariant combination of scalar metric perturbations receives no O(R⁴) corrections. Hence, (the aforementioned analogs of) λ L , v b are unrenormalized up to O(R⁴) in M theory.