Zoology of heterotic supercurrent supermultiplets in d=2

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.