  We present various (0,2) heterotic supercurrent supermultiplets in (1+1)
dimensional quantum field theories. From the minimal supercurrent
supermultiplets, we deduce conditions on symmetry enhancement such as Lorentz
invariance, (chiral) dilatation invariance, R-invariance, (chiral) conformal
invariance and their various combinations. Our construction covers many
interesting and/or exotic possibilities such as Lifshitz supersymmetry and
warped superconformal algebra. We also discuss the corresponding supergravity
by gauging the supercurrent supermultiplet. In particular, we propose a novel
class of heterotic supergravity based on the virial supercurrent.
