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We show that the $3d$ Born-Infeld theory can be generated via an irrelevant deformation of the free Maxwell theory. The deforming operator is constructed from the energy-momentum tensor and includes a novel non-analytic contribution that resembles root-$T \ overline{T}$. We find that a similar operator deforms a free scalar into the scalar sector of the Dirac-Born-Infeld action, which describes transverse fluctuations of a D-brane, in any dimension. We also analyse trace flow equations and obtain flows for subtracted models driven by a relevant operator. In $3d$, the irrelevant deformation can be made manifestly supersymmetric by presenting the flow equation in $\mathcal{N} = 1$ superspace, where the deforming operator is built from supercurrents. We demonstrate that two supersymmetric presentations of the D2-brane effective action, the Maxwell-Goldstone multiplet and the tensor-Goldstone multiplet, satisfy superspace flow equations driven by this supercurrent combination. To do this, we derive expressions for the supercurrents in general classes of vector and tensor/scalar models by directly solving the superspace conservation equations and also by coupling to $\mathcal{N} = 1$ supergravity. As both of these multiplets exhibit a second, spontaneously broken supersymmetry, this analysis provides further evidence for a connection between current-squared deformations and nonlinearly realized symmetries.

In this paper, we first give the characterizations of curvature-adapted hypersurfaces in both of the two Kähler surfaces 핊2 × 핊2 and ℍ2 × ℍ2. Then, focusing on two subclasses of the curvature-adapted hypersurfaces in 핊2 × 핊2 and ℍ2 × ℍ2, we classify the Hopf hypersurfaces with two distinct principal curvatures as well as the Hopf hypersurfaces whose Reeb vector field ξ and Reeb function α satisfying ξ(α) = 0. [ABSTRACT FROM AUTHOR]

Measurements of Very-Low-Frequency (VLF) transmitter signals have been widely used to investigate the effects of various space weather events on the D-region ionosphere, including nowcasting solar flares. Previous studies have established a method to nowcast solar flares using VLF measurements, but only using measurements from dayside propagation paths, and there remains limited focus on day–night mixed paths, which are important for method applicability. Between March and May of 2022, the Sun erupted a total of 56 M-class and 6 X-class solar flares, all of which were well captured by our VLF receiver in Antarctica. Using these VLF measurements, we reexamine the capability of the VLF technique to nowcast solar flares by including day–night mixed propagation paths and expanding the path coverage in longitude compared to that in previous studies. The amplitude and phase maximum changes are generally positively correlated with X-ray fluxes, whereas the time delay is negatively correlated. The curve-fitting parameters that we obtain for the X-ray fluxes and VLF signal maximum changes are consistent with those in previous studies for dayside paths, even though different instruments are used, supporting the flare-nowcasting method. Moreover, the present results show that, for day–night mixed paths, the amplitude and phase maximum changes also scale linearly with the logarithm of the flare X-ray fluxes, but the level of change is notably different from that for dayside paths. The coefficients used in the flare-nowcasting method need to be updated for mixed propagation paths. [ABSTRACT FROM AUTHOR]

In this paper, we study real hypersurfaces of the two Kähler surfaces S 2 × S 2 and H 2 × H 2. As the main results, amongst others, we classify all such hypersurfaces whose normal Jacobi operators are parallel with respect to either the Levi-Civita connection or the k-generalized Tanaka–Webster connection. [ABSTRACT FROM AUTHOR]