McTEQ (M chiral perturbation theory-compatible deconfinement Temperature and Entanglement Entropy up to terms Quartic in curvature) and FM (Flavor Memory)

A bstract 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 - c hiral perturbation theory [ 1 ]-compatible deconfinement T emperature, and show equivalence with an E ntanglement (as well as Wald) entropy [ 2 ] computation, up to terms Q uartic in curvature ( R ). We demonstrate a F lavor- 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 D 7-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 D 7-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 Mχ PT [ 1 ] with the phenomenological value of the coupling constant of one of the SU(3) NLO χ PT 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 computatio