8.2 As BPS SUGRA solitons

^[1]

\subsubsection{Dictionary} All the elements of the dictionary are, in principle, extractable from the first one because they contain all the correlations and, therefore, all the information.

\begin{tabular}{||c | c | c ||} \hline $AdS_{d+1}$ & $CFT_d$ & Ref\ [0.5ex] \hline\hline $Z_{AdS}$ & $Z_{CFT}$ &
\hline $\mathcal{H}{AdS}$ & $\mathcal{H}{CFT}$ &
Asymptotically AdS geometry & Quantum state &
Ex: Pure AdS & Vacuum State &
Ex: 2-sided Schwarzschild AdS BH & Thermofield Double State &
\hline Scalar fields & Scalar primary operators & Correlation
$m^2L^2=\Delta(\Delta-d)$ & $\Delta$ &
\hline Dirac fermion & $d=\text{even}\Rightarrow$ chiral fermion & ^[2]
$|m|L=\Delta-\frac{d} {2}$ & $d=\text{odd}\Rightarrow$ Dirac fermion & Correlation
\hline Gauge fields $A_\mu$ & Conserved currents $j_\mu$ $\Delta=d-1$ & ^[3]
Gauge symmetry & Global symmetry & Correlation
\hline $p$ form higher gauge fields $A_{\mu_1\cdots \mu_p}$ & Conserved currents $j_{\mu_1\cdots \mu_p}$ & ^[4]
$m^2L^2=(\Delta-p)(\Delta+p-d)$ & & Correlation
\hline $h_{\mu\nu}$ (perturbed $g_{\mu\nu}$) & $T_{\mu\nu}$ & ^[5]
$m^2L^2=\Delta(\Delta-d)=0$ & $\Delta =d$ & Correlation
\hline Single string excitations & Single trace operators &
\hline Wrapped branes & Baryonic vertex &
\hline $Z_{AdS}$ with a string worldsheet & Wilson loops &
ending at the boundary loop $C$ & &
\hline IR divergence & UV divergences & HolographicRenormalisation
Radial direction & Energy scale &
\hline Branes & Solitons &
D(-1)-instanton & instanton VEV &
\hline RT or QES & von Neumann entropy & HEE
Einstein’s equations & (\delta S_A = \delta \langle K_A \rangle) & gravityfromentanglement
Entanglement wedge & $\rho$ of a subregion& ^[6]
Cosmic Brane & R´enyi entropies & ^[7]
\hline Action & Complexity &
\hline \end{tabular}

\subsubsection{Correlation functions} \subsubsection{Finite temperature} \subsubsection{Solitons} Chapter 13 of ^[8] \& ^[9] \subsubsection{The pp wave correspondence} \subsubsection{Different dimensions} \paragraph{$A d S_{3}$ compactifications}~
^[10] \subsubsection{Orbifolds and orientifolds} \subsubsection{Integrability} ^[11] and ^[12] and chapter 7 of ^[13]. \subsubsection{Holographic renormalisation group} \subsubsection{Supersymmetric localization} ^[14] \subsubsection{Higher spin holography (tensionless limit)} ^[15] and for arbitrary D ^[16]. See also HigherSpinTheory. \subsubsection{Fluid/gravity correspondence} ^[17] \subsubsection{Holographic QCD} ^[18] \paragraph{Bottom-up} \paragraph{Top-down} \subsubsection{Nonrelativistic limit} ^[19] and section nonrelativistic

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