The zero modes of closed strings on a torus –the torus coordinates plus dual coordinates conjugate to winding number– parameterize a doubled torus. In closed string field theory, the string field depends on all zero-modes and so can be expanded to give an infinite set of fields on the doubled torus. We use string field theory to construct a theory of massless fields on the doubled torus. Key to...

governments around the worlds especially in developing countries face with tremendous challenges.  high or moderate rate of corruption can be named as one of the most important of these challenges.  corruption and its inefficiency can deviate resources allocation to unproductive sectors of economy. trust in social networks or within the society has two antithetic effects in deployment of corrup...

Abstract Achieving localization with molecular precision has been of great interest for extending fluorescence microscopy to nanoscopy. MINFLUX pioneers this transition through point spread function (PSF) engineering, yet its performance is primarily limited by the signal-to-background ratio. Here we demonstrate theoretically that two-photon (2p-MINFLUX) could double PSF engineering nonlinear e...