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Pole-Skipping and Chaos in Too ${\cal M}$UCH Hot QCD

Gopal YadavShivam Singh KushwahAalok Misra
Nov 2023
We address the question of whether thermal QCD at high temperature is chaotic from the ${\cal M}$ theory dual of QCD-like theories at intermediate coupling as constructed in arXiv: 2004.07259, and find the dual to be unusually chaotic-like - hence the title ${\cal M}$-theoretic (too) Unusually Chaotic Holographic (${\cal M}$UCH) QCD. The EOM 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" $\lambda_L$ 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., "$C_{n, n+1}=0,\ {\rm det}\ M^{(n)}=0", n\in\mathbb{Z}^+$ is satisfied for a single $n\geq3$ depending on the values of the string coupling $g_s$, number of (fractional) $D3$ branes $(M)N$ and flavor $D7$-branes $N_f$ in the parent type IIB set (arXiv:hep-th/0902.1540), 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 ${\cal O}((r-r_h)^n)$, yields $C_{n, n+1}=0$ at order $n,\ \forall n\geq3$. Incredibly, (assuming preservation of isotropy in $\mathbb{R}^3$ even with the inclusion of HD corrections) the aforementioned gauge-invariant combination of scalar metric perturbations receives no ${\cal O}(R^4)$ corrections. Hence, (the aforementioned analogs of) $\lambda_L, v_b$ are unrenormalized up to ${\cal O}(R^4)$ in ${\cal M}$ theory.
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