12.4 Spacetime Emerging from QCD
191
• In the middle region, h(η) is negative. This is a behavior not found in any solution
of the ordinary vacuum Einstein equation.
In this way, an asymptotically AdS emergent spacetime metric that consistently
reproduces the chiral condensate data of QCD was obtained. A method of solving
the inverse problem and obtaining a gravity model was made possible by machine
learning.
Then, does the metric gained from this learning make any interesting new
predictions? The strange aspect about the resulting metric is that h is negative,
as mentioned in the third point above. This means that the black hole spacetime
actually shows a confinement behavior. The confinement spacetime is a spacetime
in which the value of the metric increases at a certain spacetime location, so when
going from the asymptotic AdS region to the depth of the spacetime, one reaches
the bottom and cannot proceed further. Since h is with a differentiation by η, the
reversal of its sign indicates the behavior of such a metric. Therefore, although our
spacetime has a black hole horizon (deconfinement), at the same time the metric
shows the confinement.
In fact, with this metric, using the AdS/CFT dictionary we can calculate the
vacuum expectation value of an operator called the Wilson loop. Then we can
see both the properties of Debye screening coming from the event horizon and the
linear potential coming from confining spacetime. They qualitatively match well the
predictions of lattice QCD. Surprisingly, the spacetime that emerged from QCD data
using deep learning had both properties. In this way, when the inverse problem is
specifically solved using deep learning, it has become possible to construct a model
that gives a concept that goes beyond the conventional holographic model.
It is very interesting that the network itself can be interpreted as a smooth
spacetime, beyond the construction of such a practical model. As mentioned in
the column of the Ising model, Hopfield models regard the neural network itself
as a spin system, and the weight of the network corresponded to the strength of
interaction between spins. In the model introduced in this chapter, the network
weights directly include the metric. Therefore, the distance between the nodes of
the network is defined by the weights, and the whole network is interpreted as a
space. Such an idea is especially reminiscent of quantum gravity theory based on
dynamical triangulation. How far can the idea of a network becoming spacetime be
generalized?
Holographic models based on deep learning are classical gravity theories, but
in the future, we may be able to understand how quantum effects and essential
effects of gravity appear, and how this modeling is related to other quantum gravity
concepts.
191
• In the middle region, h(η) is negative. This is a behavior not found in any solution
of the ordinary vacuum Einstein equation.
In this way, an asymptotically AdS emergent spacetime metric that consistently
reproduces the chiral condensate data of QCD was obtained. A method of solving
the inverse problem and obtaining a gravity model was made possible by machine
learning.
Then, does the metric gained from this learning make any interesting new
predictions? The strange aspect about the resulting metric is that h is negative,
as mentioned in the third point above. This means that the black hole spacetime
actually shows a confinement behavior. The confinement spacetime is a spacetime
in which the value of the metric increases at a certain spacetime location, so when
going from the asymptotic AdS region to the depth of the spacetime, one reaches
the bottom and cannot proceed further. Since h is with a differentiation by η, the
reversal of its sign indicates the behavior of such a metric. Therefore, although our
spacetime has a black hole horizon (deconfinement), at the same time the metric
shows the confinement.
In fact, with this metric, using the AdS/CFT dictionary we can calculate the
vacuum expectation value of an operator called the Wilson loop. Then we can
see both the properties of Debye screening coming from the event horizon and the
linear potential coming from confining spacetime. They qualitatively match well the
predictions of lattice QCD. Surprisingly, the spacetime that emerged from QCD data
using deep learning had both properties. In this way, when the inverse problem is
specifically solved using deep learning, it has become possible to construct a model
that gives a concept that goes beyond the conventional holographic model.
It is very interesting that the network itself can be interpreted as a smooth
spacetime, beyond the construction of such a practical model. As mentioned in
the column of the Ising model, Hopfield models regard the neural network itself
as a spin system, and the weight of the network corresponded to the strength of
interaction between spins. In the model introduced in this chapter, the network
weights directly include the metric. Therefore, the distance between the nodes of
the network is defined by the weights, and the whole network is interpreted as a
space. Such an idea is especially reminiscent of quantum gravity theory based on
dynamical triangulation. How far can the idea of a network becoming spacetime be
generalized?
Holographic models based on deep learning are classical gravity theories, but
in the future, we may be able to understand how quantum effects and essential
effects of gravity appear, and how this modeling is related to other quantum gravity
concepts.