Can neutrino-cooled accretion disk be an origin of gamma-ray bursts?

It is often considered that a massive torus with solar mass or so surrounding a stellar-mass black hole may be a central engine of a gamma-ray burst. We study the properties of such massive accretion tori (or disks) based on the $\alpha$ viscosity model. For surface density exceeding about $10^{20}$ g cm$^{-2}$, which realizes when about a solar-mass material is contained within a disk with a size of $\sim 5 \times 10^6$ cm, we find that (1) luminosity of photons is practically zero due to significant photon trapping, (2) neutrino cooling dominates over advective cooling, (3) pressure of degenerate electrons dominates over pressure of gas and photons, and (4) magnetic field strength exceeds the critical value of about $4 \times 10^{13}$ G, even if we take 0.1 % of the equi-partition value. The possible observable quantum electrodynamical (QED) effects arising from super-critical fields are discussed. Most interestingly, photon splitting may occur, producing significant number of photons of energy below $\sim 511$ keV, thereby possibly suppressing e$^\pm$ pair creation.