$\mathcal{M}$cTEQ ($\mathcal{M}$ $\mathbf{c}$hiral perturbation theory-compatible deconfinement $\mathbf{T}$emperature and $\mathbf{E}$ntanglement Entropy up to terms $\mathbf{Q}$uartic in curvature) and FM ($\mathbf{F}$lavor $\mathbf{M}$emory)

Abstract

A holographic computation of $T_c$ at $intermediatecoupling$ from M-theory dual of thermal QCD-like theories, has been missing in the literature. Filling this gap, we demonstrate a novel UV-IR mixing, (conjecture and provide evidence for) a non-renormalization beyond 1 loop of $\mathbf{M}-\mathbf{c}$hiral perturbation theory arXiv:2011.04660[hep-th]-compatible deconfinement $\mathbf{T}$emperature, and show equivalence with an $\mathbf{E}$ntanglement (as well as Wald) entropy arXiv:0709.2140[hep-th] computation, up to terms $\mathbf{Q}$uartic in curvature. We demonstrate a $\mathbf{F}$lavor-$\mathbf{M}$emory (FM) effect in the M-theory uplifts of the gravity duals, wherein the no-braner M-theory uplift retains the "memory" of the flavor D7-branes of the parent type IIB dual in the sense that a specific combination of the aforementioned quartic corrections to the metric components precisely along the compact part of the non-compact four-cycle "wrapped" by the flavor D7-branes, is what determines, e.g., the Einstein-Hilbert action at O$(R^4)$. The same linear combination of O$(R^4)$ metric corrections, upon matching the phenomenological value of the coupling constant of one of the SU(3) NLO ChPT Lagrangian, is required to have a definite sign. Interestingly, in the decompactification limit of the spatial circle, we $derive$ this, and obtain the values of the relevant O$(R^4)$ metric corrections. Further, equivalence with Wald entropy for the black hole at $\mathcal{O}(R^4)$ imposes a linear constraint on the same linear combination of metric corrections. Remarkably, when evaluating $T_c$ from an entanglement entropy computation in the thermal gravity dual, due to a delicate cancelation between the $\mathcal{O}(R^4)$ corrections from a subset of the abovementioned metric components, one sees that there are no corrections to $T_c$ at quartic order supporting the conjecture referred to above.

Comments: v2, 1+64 pages, 2 figures, LaTeX; a reference added, the title decrypted/expanded and minor changes made; Published in JHEP, Some typos corrected