Pole-skipping and chaos in hot$$\mathcal{M}{\text{QCD}}$$

Abstract

Abstract We address the question of whether thermal QCD at high temperature is chaotic from the $$\mathcal{M}$$ theory dual of QCD-like theories at intermediate coupling as constructed in [1]. The equations of motion of the gauge-invariant combination Zs(r) of scalar metric perturbations is shown to possess an irregular singular point at the horizon radius rh. Very interestingly, at a specific value of the imaginary frequency and momentum used to read off the analogs of the “Lyapunov exponent” λL and “butterfly velocity” vb not only does rh become a regular singular point, but truncating the incoming mode solution of Zs(r) as a power series around rh, yields a “missing pole”, i.e., Cn,n+1 = 0, det M(n) = 0, n ∈ $${\mathbb{Z}}^{+}$$ is satisfied for a single n ≥ 3 depending on the values of the string coupling gs, number of (fractional) D3 branes (M)N and flavor D7-branes Nf in the parent type IIB set [2], e.g., for the QCD(EW-scale)-inspired N = 100, M = Nf = 3, gs = 0.1, one finds a missing pole at n = 3. For integral n > 3, truncating Zs(r) at $$\mathcal{O}\left({\left(r-{r}_{h}\right)}^{n}\right)$$, yields Cn,n+1 = 0 at order n, ∀n ≥ 3. Incredibly, (assuming preservation of isotropy in $${\mathbb{R}}^{3}$$ even with the inclusion of higher derivative corrections) the aforementioned gauge-invariant combination of scalar metric perturbations receives no $$\mathcal{O}\left({R}^{4}\right)$$ corrections. Hence, (the aforementioned analogs of) λL, vb are unrenormalized up to $$\mathcal{O}\left({R}^{4}\right)$$ in $$\mathcal{M}$$ theory.