Deep learning and holographic QCD

Abstract

We apply the relation between deep learning (DL) and the AdS/CFT correspondence to a holographic model of QCD. Using a lattice QCD data of the chiral condensate at a finite temperature as our training data, the deep learning procedure holographically determines an emergent bulk metric as neural network weights. The emergent bulk metric is found to have both a black hole horizon and a finite-height IR wall, so shares both the confining and deconfining phases, signaling the cross-over thermal phase transition of QCD. In fact, a quark antiquark potential holographically calculated by the emergent bulk metric turns out to possess both the linear confining part and the Debye screening part, as is often observed in lattice QCD. From this we argue the discrepancy between the chiral symmetry breaking and the quark confinement in the holographic QCD. The DL method is shown to provide a novel data-driven holographic modeling of QCD, and sheds light on the mechanism of emergence of the bulk geometries in the AdS/CFT correspondence.

Branes with brains: exploring string vacua with deep reinforcement learning

“…In this case data is not labelled, but the algorithm attempts to learn features that describe correlations between data points. Strikingly, in [21] QCD observables were utilized to learn bulk metrics that give the first predictions of the qq potential in holographic QCD. The results match lattice data well, including the existence of the Coulomb, linear confining, and Debye screening phases.…”

AdS/CFTcorrespondence as a deep Boltzmann machine

“…This means that the saddle point of the deep Boltzmann machine brings it to a folded feed-forward type deep neural network. The AdS/CFT interpretation of a feed-forward neural network was studied in [15,16] and the trained weights exhibit an interesting physical picture.…”

“…In [15,16], a deep neural network employs J and O as the input at the initial layer while the black hole horizon boundary condition is used as an output at the final layer. Another natural implementation is to use J (the non-normalizable mode of the AdS scalar field) as an input and O (normalizable mode) as the output data.…”

“…where ≡ g(η) −2 d−1 i=1 ∂ 2 i is a covariant Laplacian. As opposed to the case in [15,16], here we included the spatial (x) dependence of the external field and the response. According to the holographic renormalization group [38] the equation (A2) can be rewritten as…”

“…In [14], entanglement feature of a free fermion chain was trained at a random tensor network as a deep Boltzmann machine. The holographic interpretation for feed-foward deep neural networks was proposed and studied in [15,16] for training QFT and QCD linear response functions, and the obtained emergent bulk spacetime for large N c QCD exhibits interesting physical properties and computes other observables as predictions. While our work here naturally relates to these work, in this paper we concentrate on deep Boltzmann machines as an AdS/CFT correspondence.…”