We study, for the first time, the Casimir effect in non-Abelian gauge theory using first-principles numerical simulations. Working in two spatial dimensions at zero temperature, we find that closely ...spaced perfect chromoelectric conductors attract each other with a small anomalous scaling dimension. At large separation between the conductors, the attraction is exponentially suppressed by a new massive quantity, the Casimir mass, which is surprisingly different from the lowest glueball mass. The apparent emergence of the new massive scale may be a result of the backreaction of the vacuum to the presence of the plates as sufficiently close chromoelectric conductors induce, in a space between them, a smooth crossover transition to a color deconfinement phase.
We show that the Casimir effect may lead to a deconfinement phase transition induced by the presence of boundaries in confining gauge theories. Using first-principle numerical simulations we ...demonstrate this phenomenon in the simplest case of the compact lattice electrodynamics in two spatial dimensions. We find that the critical temperature of the deconfinement transition in the vacuum between two parallel dielectric/metallic wires is a monotonically increasing function of the separation between the wires. At infinite separation the wires do not affect the critical temperature while at small separations the vacuum between the wires loses the confinement property due to modification of vacuum fluctuations of virtual monopoles.
Using first-principle lattice simulations, we demonstrate that in the background of a strong magnetic field (around 10^{20} T), the electroweak sector of the vacuum experiences two consecutive ...crossover transitions associated with dramatic changes in the zero-temperature dynamics of the vector W bosons and the scalar Higgs particles, respectively. Above the first crossover, we observe the appearance of large, inhomogeneous structures consistent with a classical picture of the formation of W and Z condensates pierced by vortices. The presence of the W and Z condensates supports the emergence of the exotic superconducting and superfluid properties induced by a strong magnetic field in the vacuum. We find evidence that the vortices form a disordered solid or a liquid rather than a crystal. The second transition restores the electroweak symmetry. Such conditions can be realized in the near-horizon region of the magnetized black holes.
We study the machine learning techniques applied to the lattice gauge theory's critical behavior, particularly to the confinement/deconfinement phase transition in the SU(2) and SU(3) gauge theories. ...We find that the neural network, trained on lattice configurations of gauge fields at an unphysical value of the lattice parameters as an input, builds up a gauge-invariant function, and finds correlations with the target observable that is valid in the physical region of the parameter space. In particular, we show that the algorithm may be trained to build up the Polyakov loop which serves an order parameter of the deconfining phase transition. The machine learning techniques can thus be used as a numerical analog of the analytical continuation from easily accessible but physically uninteresting regions of the coupling space to the interesting but potentially not accessible regions.
We investigate the advantages of machine learning techniques to recognize the dynamics of topological objects in quantum field theories. We consider the compact U(1) gauge theory in three spacetime ...dimensions as the simplest example of a theory that exhibits confinement and mass gap phenomena generated by monopoles. We train a neural network with a generated set of monopole configurations to distinguish between confinement and deconfinement phases, from which it is possible to determine the deconfinement transition point, and to predict several observables. The model uses a supervised learning approach and treats the monopole configurations as three-dimensional images (holograms). We show that the model can determine the transition temperature with accuracy, which depends on the criteria implemented in the algorithm. More importantly, we train the neural network with configurations from a single lattice size before making predictions for configurations from other lattice sizes, from which a reliable estimation of the critical temperatures is obtained.
We demonstrate that Casimir forces associated with zero-point fluctuations of quantum vacuum may be substantially affected by the presence of dynamical topological defects. In order to illustrate ...this nonperturbative effect we study the Casimir interactions between dielectric wires in a compact formulation of Abelian gauge theory in two spatial dimensions. The model possesses topological defects, instantonlike monopoles, which are known to be responsible for nonperturbative generation of a mass gap and for a linear confinement of electrically charged probes. Despite the fact the model has no matter fields, the Casimir energy depends on the value of the gauge coupling constant. We show, both analytically and numerically, that in the strong coupling regime the Abelian monopoles make the Casimir forces short ranged. Simultaneously, their presence increases the interaction strength between the wires at short distances for a certain range of values of the gauge coupling. The wires suppress monopole density in the space between them compared to the density outside the wires. In the weak coupling regime the monopoles become dilute and the Casimir potential reduces to a known theoretical result that does not depend on the gauge coupling.
We propose a general numerical method to study the Casimir effect in lattice gauge theories. We illustrate the method by calculating the energy density of zero-point fluctuations around two parallel ...wires of finite static permittivity in Abelian gauge theory in two spatial dimensions. We discuss various subtle issues related to the lattice formulation of the problem and show how they can successfully be resolved. Finally, we calculate the Casimir potential between the wires of a fixed permittivity, extrapolate our results to the limit of ideally conducting wires and demonstrate excellent agreement with a known theoretical result.
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