  We study the capability of the James Webb Space Telescope (JWST) to detect
Supermassive Dark Stars (SMDS). If the first stars are powered by dark matter
heating in triaxial dark matter haloes, they may grow to be very large and very
bright, visible in deep imaging with JWST and even Hubble Space Telescope
(HST). We use HST surveys to place bounds on the numbers of SMDSs that may be
detected in future JWST imaging surveys. We showed that SMDS in the mass range
$10^6-10^7 M_\odot$ are bright enough to be detected in all the wavelength
bands of the NIRCam on JWST . If SMDSs exist at z ~10, 12, and 14, they will be
detectable as J-band, H-band, or K-band dropouts, respectively. With a total
survey area of 150 arcmin^2 (assuming a multi-year deep parallel survey with
JWST), we find that typically the number of $10^6 M_\odot$ SMDSs found as H or
K-band dropouts is ~10^5\fsmds, where the fraction of early DM haloes hosting
DS is likely to be small, \fsmds<<1. If the SDMS survive down to z=10 where HST
bounds apply, then the observable number of SMDSs as H or K-band dropouts with
JWST is ~1-30. While individual SMDS are bright enough to be detected by JWST,
standard PopIII stars are not, and would only be detected in first galaxies
with total stellar masses of ~$10^6-10^8 M_\odot$. Differentiating first
galaxies at z>10 from SMDSs would be possible with spectroscopy: the SMDS
(which are too cool produce significant nebular emission) will have only
absorption lines while the galaxies are likely to produce emission lines as
well. Of particular interest would be the 1640 HeII emission line as well as
H{\alpha} lines which would be signatures of early galaxies rather than SMDSs.
The detection of SMDSs would not only provide alternative evidence for WIMPs
but would also provide possible seeds for the formation of supermassive black
holes that power QSOs at z~6.
