Supersymmetric Localization in GLSMs for Supermanifolds

In this paper we apply supersymmetric localization to study gauged linear sigma models (GLSMs) describing supermanifold target spaces. We use the localization method to show that A-twisted GLSM correlation functions for certain supermanifolds are equivalent to A-twisted GLSM correlation functions for hypersurfaces in ordinary spaces under certain conditions. We also argue that physical two-sphere partition functions are the same for these two types of target spaces. Therefore, we reproduce the claim of arXiv:hep-th/9404186, arXiv:hep-th/9506070. Furthermore, we explore elliptic genera and (0,2) deformations and find similar phenomena.Comment: 31 pages, no figure

Limits on luminosity and mass accretion rate of a radiation pressure dominated accretion disc

There is a maximum for the gravity of a black hole in the vertical direction in the accretion disc. Outflows may probably be driven from the disc if the radiation flux of the disc is greater than a critical value corresponding to the maximal vertical gravity. We find that outflows are driven by the radiation force from the disc if the accretion rate is greater than the Eddington rate. The radiation of the disc is therefore limited by such outflows. The disc luminosity, L=L_Edd\propto ln mdot, at large-mdot cases. The Eddington ratio of the disc is ~3 for mdot~100, which is significantly lower than that of a conventional slim disc without outflows. This implies that the emission from some ultra-luminous X-ray sources with highly super Eddington luminosity should be Doppler beamed, or intermediate mass black holes are in these sources instead of stellar mass black holes. The spectra of the discs with outflows are saturated in the high frequency end provided mdot>2. We suggest that the saturated emission can be observed to estimate the masses of the black holes accreting at high rates, such as the narrow-line Seyfert galaxies, with the model calculations. The rate of the mass accreted by the black hole is always around the Eddington rate even if the mass accretion rate at the outer radius is very high, because most of the gas is removed into the outflows. This implies that the luminous quasars at high redshifts z>6 should have grown up through persistent accretion at a rate close to the Eddington rate.Comment: 8 pages, accepted by MNRA

Source Coding for a Multihop Network

Summary form only given. In this paper, we bound the rate-distortion region for a four-node network. The results are the first known expansion of rate-distortion theory from single-hop networks (every source has a direct connection to each of its destinations), to multihop networks, which allow intermediate nodes. While single-hop network source coding solutions may be applied in multihop networks, such applications require explicit rate allocation for each source-destination pair, and the resulting solutions may be suboptimal. We therefore tackle the multihop network source coding problem directly using a diamond network

Topological and differentiable rigidity of submanifolds in space forms

Let $F^{n+p}(c)$ be an $(n+p)$-dimensional simply connected space form with nonnegative constant curvature $c$. We prove that if $M^n(n\geq4)$ is a compact submanifold in $F^{n+p}(c)$, and if $Ric_M>(n-2)(c+H^2),$ where $H$ is the mean curvature of $M$, then $M$ is homeomorphic to a sphere. We also show that the pinching condition above is sharp. Moreover, we obtain a new differentiable sphere theorem for submanifolds with positive Ricci curvature.Comment: 12 page