International Journal of Modern Physics A

We review a recent model of a fuzzy BTZ black hole. The fuzzy black hole is a quantum space defined in terms of an operator algebra together with a covariant differential calculus. It satisfies vacuum Einstein’s equations with a negative cosmological constant. Black hole interior and exterior are identified with discrete and continuous parts of the radius coordinate spectrum, respectively.

In this contribution, we summarize our recent studies of the phase structure of the Grosse–Wulkenhaar model and its connection to renormalizability. Its action contains a special term that couples the field to the curvature of the noncommutative background space. We first analyze the numerically obtained phase diagram of the model and its three phases: the ordered, the disordered, and the noncommutative stripe phase. Afterward, we discuss the analytical derivation of the effective action and the ordered-to-stripe transition line, and how the obtained expression successfully explains the curvature-induced shift of the triple point compared to the model without curvature. This shift also causes the removal of the stripe phase and makes the model renormalizable.

We study inflation in a model with constant second slow-roll parameter $\eta$. In this case, the Hubble expansion rate equation has analytical solutions describing four possible, nontrivial inflation scenarios. The evolution of the inflaton governed by a tachyon field is studied in the framework of the standard and Randall–Sundrum II cosmology. The attractor behavior of the solution is briefly demonstrated. Finally, the calculated values of the parameters $n_{\mathrm{\text{s}}}$ and $r$ are compared with observational data.

We study a noncommutative (NC) deformation of a charged scalar field, minimally coupled to a classical (commutative) Reissner–Nordström-like background. The deformation is performed via a particularly chosen Killing twist to ensure that the geometry remains undeformed (commutative). An action describing a NC scalar field minimally coupled to the RN geometry is manifestly invariant under the deformed $U{(1)}_{\star }$ gauge symmetry. We find the equation of motion and conclude that the same equation is obtained from the commutative theory in a modified geometrical background described by an effective metric. This correspondence we call “duality between formal and effective approach”. We also show that a NC deformation via semi-Killing twist operator cannot be rewritten in terms of an effective metric. There is dual description for those particular deformations.

This is a short review of our recent work [B. Bajc and A. R. Lugo, arXiv:2212.13639 [hep-th]] with some new original results. We numerically calculate the conformal two point correlation function of operators with arbitrary scale dimension up to order $T^{2d}$ in the low temperature expansion. We analytically compute its large scale dimension limit up to the same order.

The NA61/SHINE collaboration measured the production of $K_S^0$ in $p+p$ interactions at two beam momenta: 80 and 158GeV/c. The ${\pi }^{+}+{\pi }^{-}$ decay of $K_S^0$ (branching ratio of 69.2%) was measured via the invariant mass method. The rapidity and transverse momentum distributions of $K_S^0$ are presented and compared to transport model predictions. The measured mean multiplicities of $K_S^0$ mesons equal to $〈K_S^0〉=0.120\pm 0.001(\mathrm{\text{stat.}})\pm 0.005(\mathrm{\text{sys.}})$ (80GeV/c) and $〈K_S^0〉=0.162\pm 0.001(\mathrm{\text{stat.}})\pm 0.011(\mathrm{\text{sys}}.)$ (158GeV/c) are compared with the available data in the energy range $\sqrt{s_{NN}}=3$–32GeV.

I give a geometric construction of certain first-order natural dynamical observables in multifield cosmological models with arbitrary target space topology and discuss a system of related dynamical approximations and regimes for such models.

We review recent developments on Fayet–Iliopoulos terms in four-dimensional supergravity and discuss their applications to natural models of inflation driven by supersymmetry breaking with the superpartner of the goldstino (sgoldstino) playing the role of the inflaton.

In this study, we adopt an algebraic method to find the spectrum of quasinormal modes for the three-dimensional regular rotating Chern–Simons black hole solution. The latter is a solution to topologically massive gravitoelectrodynamics (TMGE). Due to the fact that the Chern–Simons black hole metric admits four local Killing vectors generating the $𝔰𝔩(2,ℝ)\times ℝ$ Lie algebra, the solutions to the equations of motion for the fields can be classified by the representations of this algebra. Subsequently, the quasinormal spectrum can be extracted as the infinite tower of descendants of the highest weight mode of $𝔰𝔩(2,ℝ)$.

We will review the non-Lorentzian (nonrelativistic and ultrarelativistic) Jackiw–Teitelboim supergravity theories, which are the limits of relativistic Jackiw–Teitelboim supergravity. The construction is based on BF theory formalism and also the extended Newton–Hooke and extended AdS Carroll superalgebras in two space–time dimensions. It is also shown that nonrelativistic and ultrarelativistic supergravity actions are related to each other by a map which is shown explicitly in this review. This is supersymmetric version of Galilei/Carroll duality in two dimensions.

It was shown recently that a very simple nonlocal de Sitter gravity model contains exact vacuum cosmological solution which mimics dark energy and dark matter in flat space. Some other interesting solutions have been also found. In this paper, we proceed with finding several new exact cosmological solutions which belong to Bianchi I space. These solutions are simple generalizations of solutions previously found in the FLRW case of the same nonlocal de Sitter gravity model. Obtained results are discussed.