Quiver Matrix Mechanics for IIB String Theory (I): Wrapping Membranes and Emergent Dimension

In this paper we present a discrete, non-perturbative formulation for type IIB string theory. Being a supersymmetric quiver matrix mechanics model in the framework of M(atrix) theory, it is a generalization of our previous proposal of compactification via orbifolding for deconstructed IIA strings. In the continuum limit, our matrix mechanics becomes a $(2+1)$-dimensional Yang-Mills theory with 16 supercharges. At the discrete level, we are able to construct explicitly the solitonic states that correspond to membranes wrapping on the compactified torus in target space. These states have a manifestly SL(2,\integer)-invariant spectrum with correct membrane tension, and give rise to an emergent flat dimension when the compactified torus shrinks to vanishing size.Comment: LaTeX 2e; 39 pages, 3 eps figures. v2: typos corrected; references added; identification of certain membrane states added. v3: minor corrections on membrane state

Late-Time Optical Afterglow Observations with LBT and MDM

Using the 2.4m MDM and 8.4m Large Binocular Telescope, we observed nine GRB afterglows to systematically probe the late time behaviors of afterglows including jet breaks, flares, and supernova bumps. In particular, the LBT observations have typical flux limits of 25-26 mag in the Sloan r' band, which allows us to extend the temporal baseline for measuring jet breaks by another decade in time scale. We detected four jet breaks (including a "textbook" jet break in GRB070125) and a fifth candidate, all of which are not detectable without deep, late time optical observations. In the other four cases, we do not detect the jet breaks either because of contamination from the host galaxy light, the presence of a supernova bump, or the intrinsic faintness of the optical afterglow. This suggests that the basic picture that GRBs are collimated is still valid and that the apparent lack of Swift jet breaks is due to poorly sampled afterglow light curves, particularly at late times. Besides the jet breaks, we also detected late time flares, which could attribute to late central engine activities, and two supernova bumps.Comment: 5 pages, 5 figures, 2008 NANJING GAMMA-RAY BURST CONFERENCE. AIP Conference Proceedings, Volume 1065, pp. 93-97 (2008), Eds. Y.F. Huang, Z.G. Dai, B. Zhan

Long lived central engines in Gamma Ray Bursts

The central engine of Gamma Ray Bursts may live much longer than the duration of the prompt emission. Some evidence of it comes from the presence of strong precursors, post-cursors, and X-ray flares in a sizable fraction of bursts. Additional evidence comes from the fact that often the X-ray and the optical afterglow light curves do not track one another, suggesting that they are two different emission components. The typical "steep-flat-steep" behavior of the X-ray light curve can be explained if the same central engine responsible for the main prompt emission continues to be active for a long time, but with a decreasing power. The early X-ray "afterglow" emission is then the extension of the prompt emission, originating at approximately the same location, and is not due to forward shocks. If the bulk Lorentz factor Gamma is decreasing in time, the break ending the shallow phase can be explained, since at early times Gamma is large, and we see only a fraction of the emitting area. Later, when Gamma decreases, we see an increasing fraction of the emitting surface up to the time when Gamma ~ 1/theta_j. This time ends the shallow phase of the X-ray light curve. The origin of the late prompt emission can be the accretion of the fall-back material, with an accretion rate dot M proportional to t^(-5/3). The combination of this late prompt emission with the flux produced by the standard forward shock can explain the great diversity of the optical and the X-ray light curves.Comment: 6 pages, 6 figures, To appear in: 2008 Nanjing GRB Conference, AIP, Eds. Y.F. Huang, Z.G. Dai, B. Zhan