| Summary: | Abstract A (semiclassical) holographic computation of the deconfinement temperature at intermediate coupling from (a top-down) ℳ-theory dual of thermal QCD-like theories, has been missing in the literature. In the process of filling this gap, we demonstrate a novel UV-IR connection, (conjecture and provide evidence for) a non-renormalization beyond one loop of ℳ-chiral perturbation theory [1]-compatible deconfinement Temperature, and show equivalence with an Entanglement (as well as Wald) entropy [2] computation, up to terms Quartic in curvature (R). We demonstrate a Flavor-Memory (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 (given by S 3 as an S 1-fibration over the vanishing two-cycle S 2) 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 aforementioned linear combination of 𝒪(R 4) corrections to the ℳ-theory uplift [3, 4] metric, upon matching the holographic result from ℳχPT [1] with the phenomenological value of the coupling constant of one of the SU(3) NLO χPT Lagrangian of [5], is required to have a definite sign. Interestingly, in the decompactification (or “M KK → 0”) limit of the spatial circle in [1] to recover a QCD-like theory in four dimensions after integrating out the compact directions, we not only derive this, but in fact obtain the values of the relevant 𝒪(R 4) metric corrections. Further, equivalence with Wald entropy for the black hole in the high-temperature ℳ-theory dual at 𝒪(R 4) imposes a linear constraint on a similar linear combination of the abovementioned metric corrections. Remarkably, when evaluating the deconfinement temperature from an entanglement entropy computation in the thermal gravity dual, due to a delicate cancellation between the contributions arising from the metric corrections at 𝒪(R 4) in the ℳ theory uplift along the S 1-fiber and an S 2 (which too involves a similar S 1-fibration) resulting in a non-zero contribution only along the vanishing S 2 surviving, one sees that there are consequently no corrections to T c at quartic order in the curvature supporting the conjecture made on the basis of a semiclassical computation.
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