In the large N limit, quantum field theories organise themselves into string theories. The AdS/CFT correspondence is an important class of gauge/string dualities. In this paper, we provide a...Show moreIn the large N limit, quantum field theories organise themselves into string theories. The AdS/CFT correspondence is an important class of gauge/string dualities. In this paper, we provide a literature review of a precise AdS_3/CFT_2 duality. We calculate the spectrum for the symmetric product orbifold of T^4 and show that is matches with that of the superstring theory on AdS_3 X S^3 X T^4 with one unit of NS-NS flux. Further support for the duality is obtained by matching the correlation functions at genus 0. Our analysis sheds light on why the two theories are so intimately related; it requires interpreting the worldsheet as the covering space over the boundary CFT. This is captured in a `delta function localization' property of the vertex operator correlation function. When integrated over in worldsheet moduli space, it localizes onto points that holomorphically covers the boundary sphere thus reproducing features of the dual CFT.Show less
The field of deep learning has seen dramatic developments over the last decade. Improved fundamental understanding of deep learning can enhance our ability to train deeper and more advanced...Show moreThe field of deep learning has seen dramatic developments over the last decade. Improved fundamental understanding of deep learning can enhance our ability to train deeper and more advanced networks. We have explored random neural networks. These networks exhibit two phases depending on the weight variances used to initialise them. Through numerical simulations, we are able to confirm the existence of these two phases and the associated emerging depth scales. Furthermore, we characterise the edge of chaos that separates these two phases. We find that significant differences between activation layer distributions on this edge of chaos exist. This raises the question as to whether some points on this edge show improved training performance over others.Show less
