The IceCube Collaboration recently reported a stringent upper limit on the
high energy neutrino flux from GRBs, which provides a meaningful constraint on
the standard internal shock model. Recent broad band electromagnetic
observations of GRBs also challenge the internal shock paradigm for GRBs, and
some competing models for gamma-ray prompt emission have been proposed. We
describe a general scheme for calculating the GRB neutrino flux, and compare
the predicted neutrino flux levels for different models. We point out that the
current neutrino flux upper limit starts to constrain the standard internal
shock model. The dissipative photosphere models are also challenged if the
cosmic ray luminosity from GRBs is at least 10 times larger than the gamma-ray
luminosity. If the neutrino flux upper limit continues to go down in the next
few years, then it would suggest the following possibilities: 1. the
photon-to-proton luminosity ratio in GRBs is anomalously high for shocks, which
may be achieved in some dissipative photosphere models and magnetic dissipation
models; or 2. the GRB emission site is at a larger radius than the internal
shock radius, as expected in some magnetic dissipation models such as the
ICMART model.Comment: 5 pages, 1 figure, PRL, in pres
