Emptiness formation in polytropic quantum liquids

We study large deviations in interacting quantum liquids with the polytropic equation of state P (ρ) ∼ ργ, where ρ is density and P is pressure. By solving hydrodynamic equations in imaginary time we evaluate the instanton action and calculate the emptiness formation probability (EFP), the probability that no particle resides in a macroscopic interval of a given size. Analytic solutions are found for a certain infinite sequence of rational polytropic indexes γ and the result can be analytically continued to any value of γ ≥ 1. Our findings agree with (and significantly expand on) previously known analytical and numerical results for EFP in quantum liquids. We also discuss interesting universal spacetime features of the instanton solution.

Multi-instantons in quantum mechanics (QM)

In general, a linear combination of instanton solutions is not a solution of the imaginary-time equations of motion, because the equations not linear. Moreover, in quantum mechanics (QM), all solutions of the classical equations can depend only on one time collective coordinate (in this respect, in field theory, the situation is different). However, a linear combination of largely separated instantons (a multi-instanton configuration) renders the action almost stationary, because each instanton solution differs, at large distances, from a constant solution by only exponentially small corrections (in field theory this is only true if the theory is massive). A situation where multi-instantons play a role is provided by large order behaviour estimates of perturbation theory for potentials with degenerate minima. When one starts from a situation in which the minima are almost degenerate, one obtains, in the degenerate limit, a contribution of the superposition of two, infinitely separated, instantons, but with an infinite multiplicative coefficient. Indeed, in this limit, the fluctuations which tend to change the distance between the instanton and the anti-instanton induce a vanishingly small variation of the action. To correctly determine the limit, one has to introduce a second collective coordinate which describes these fluctuations. The determination, at leading order, of all many-instanton contributions has led to conjecture the exact form of the semi-classical expansion for potentials with degenerate minima, generalizing the exact Bohr-Sommerfeld quantization condition.

Giant gravitons in the Schrödinger holography

We construct and study new giant graviton configurations in the framework of the non-supersymmetric Schrödinger holography. We confirm in the original Schrödinger spacetime, the picture discovered previously in the pp-wave limit of the geometry, namely that it is the giant graviton that becomes the energetically favored stable configuration compared to the point graviton one. Furthermore, there is a critical value of the deformation above which the point graviton disappears from the spectrum. The former fact leads also to the possibility of tunnelling from the point graviton to the giant graviton configuration. We calculate, explicitly, the instanton solution and its corresponding action which gives a measure of the tunnelling probability. Finally, we evaluate holographically the three-point correlation function of two giant gravitons and one dilaton mode as a function of the Schrödinger invariant.

Hartle-Hawking wave function and large-scale power suppression of CMB

In this presentation, we first describe the Hartle-Hawking wave function in the Euclidean path integral approach. After we introduce perturbations to the background instanton solution, following the formalism developed by Halliwell-Hawking and Laflamme, one can obtain the scale-invariant power spectrum for small-scales. We further emphasize that the Hartle-Hawking wave function can explain the large-scale power suppression by choosing suitable potential parameters, where this will be a possible window to confirm or falsify models of quantum cosmology. Finally, we further comment on possible future applications, e.g., Euclidean wormholes, which can result in distinct signatures to the power spectrum.

MONOPOLE-INSTANTON SOLUTIONS FOR THE MASSIVE SU(2) YANG–MILLS–HIGGS THEORY

Monopole-instanton in topologically massive gauge theories in 2+1 dimensions with a Chern–Simons mass term have been studied by Pisarski some years ago. He investigated the SU(2) Yang–Mills–Higgs model with an additional Chern–Simons mass term in the action. Pisarski argued that there is a monopole-instanton solution that is regular everywhere, but found that it does not possess finite action. There were no exact or numerical solutions being presented by Pisarski. Hence it is our purpose to further investigate this solution in more detail. We obtained numerical regular solutions that smoothly interpolates between the behavior at small and large distances for different values of Chern–Simons term strength and for several fixed values of Higgs field strength. The monopole-instanton's action is real but infinite. The action vanishes for large Chern–Simons term only when the Higgs field expectation value vanishes.