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We study six luminous Lyman-alpha emitters (LAEs) with very blue rest-frameUV continua at $5.7\le z \le 6.6$. These LAEs have previous HST and SpitzerIRAC observations. Combining our newly acquired HST images, we find that theirUV-continuum slopes $\beta$ are in a range of $-3.4\le \beta \le -2.6$. Unlikeprevious, tentative detections of $\beta \simeq -3$ in photometricallyselected, low-luminosity galaxies, our LAEs are spectroscopically confirmed andluminous ($M_{\rm UV}<-20$ mag). We model their broadband spectral energydistributions (SEDs), and find that two $\beta\simeq-2.6\pm0.2$ galaxies can bewell fitted with young and dust-free stellar populations. However, it becomesincreasingly difficult to fit bluer galaxies. We explore furtherinterpretations by including non-zero LyC escape fraction $f_{\rm esc}$, verylow metallicities, and/or AGN contributions. Assuming $f_{\rm esc}\simeq0.2$,we achieve the bluest slopes $\beta\simeq-2.7$ when nebular emission isconsidered. This can nearly explain the SEDs of two galaxies with$\beta\simeq-2.8$ and --2.9 ($\sigma_{\beta}=0.15$). Larger $f_{\rm esc}$values and very low metallicities are not favored by the strong nebular lineemission (evidenced by the IRAC flux) or the observed (IRAC 1 - IRAC 2) color.Finally, we find that the $\beta\simeq-2.9$ galaxy can potentially be wellexplained by the combination of a very young population with a high $f_{\rmesc}$ ($\ge0.5$) and an old, dusty population. We are not able to produce two$\beta \simeq -3.4 \pm0.4$ galaxies. Future deep spectroscopic observations areneeded to fully understand these galaxies.

Luminous Lyman-alpha Emitters with Very Blue UV-continuum Slopes at Redshift 5.7 <= z <= 6.6