On String Integrability: A Journey through the Two-Dimensional Hidden Symmetries in the AdS/CFT Dualities

<table>Example of a spin chain. The “up” arrow represents the field <svg height="11.45125" id="M305" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 13.31125 11.45125" width="13.31125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.45125)">
<text transform="matrix(1,0,0,-1,0.498,0.498)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑍</tspan>
</text>
</g>
</svg>, while the down spin is represented by the field <svg height="11.70125" id="M306" style="vertical-align:-0.20064pt" version="1.1" viewbox="0 0 15.56125 11.70125" width="15.56125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.70125)">
<text transform="matrix(1,0,0,-1,0.498,0.698)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑊</tspan>
</text>
</g>
</svg>.</table>

Advances in High Energy Physics

fig2

Figure 2

Figure 2: On String Integrability: A Journey through the Two-Dimensional Hidden Symmetries in the AdS/CFT Dualities 