  As applications of arXiv:2004.07259, the first part of the thesis is based on
(i) arXiv:2011.04660 wherein we computed the low energy coupling constants of
SU(3) chiral perturbation theory at NLO in the chiral expansion in the chiral
limit, from the type IIA string dual inclusive of ${\cal O}(R^4)$ corrections
and found a novel HD-large-$N$ connection; (ii) arXiv:2108.05372,
arXiv:2203.11959 wherein we discussed confinement-deconfinement phase
transition in thermal QCD-like theories at intermediate coupling in the
absence/presence of rotation and observed (a) a novel "UV-IR" mixing, (b)
"Flavor Memory" effect, (c) M$\chi$PT compatibility,(d) non-renormalization of
deconfinement temperature $T_c$ beyond one loop in the zero instanton sector,
and (e) found that the $T_c$ of rotating QGP decreases when angular velocity of
rotating cylindrical black hole increases and vice-versa. In the second part of
thesis, we obtained Page curves of Reissner-Nordstr\"{o}m black holes in the
presence of ${\cal O}(R^2)$ terms and black holes with multiple horizons in
arXiv:2204.11882 and arXiv:2210.00331 respectively. In arXiv:2207.04048, we
constructed a doubly holographic setup for a non-conformal bath (thermal QCD)
in ${\cal M}$-theory background with the inclusion of ${\cal O}(R^4)$ terms and
obtained the Page curve of an eternal neutral black hole for massless graviton
localized on an ETW-"brane"/(Fluxed) hypersurface. Multiverse is described as
the setup of 2n anti de-Sitter (AdS) or de-Sitter branes embedded in the
corresponding bulk (arXiv:2301.06151). Since all the universes can communicate
with each other due to transparent boundary conditions at the defect, therefore
one could exchange information between any universes. This setup is also used
to obtain the Page curve of the Schwarzschild de-Sitter black hole, which has
two horizons.
