Super-Liouville Theory as a Two-Dimensional, Superconformal Supergravity Theory

Abstract

In this paper we extend our previous results on the bosonic Liouville theory, to the supersymmetric case. As in the bosonic case, we find that the quantization of the N=1 theory is limited to the region D≤1. We compute the exact critical exponents and the analogue of the Hausdorff dimension of super random surfaces. Our procedure is manifestly covariant and our results hold for the surface of arbitrary topology. We also examine the N=2, O(2) string theory and find that it appears to be well-defined for all D.

Super-Virasoro Anomaly, Super-Weyl Anomaly, and the Super-Liouville Action for 2D Supergravity

“…This can also be regarded as a canonical verification of the the functional measure ansatz of refs. [7,8,16]. We have also noted the subtlety concerning the cosmological term, which is not seen for the bosonic case [2].…”

“…Since the (super)conformal invariance is equivalent to the BRST invariance in (super)conformal gauge, our approach naturally reproduces the basic resutls of refs. [7,8,16] as argued in refs. [22,23].…”

“…In refs. [7,8,16] the key observation leading to the (super-)Liouville action is that the resulting effective theory should be (super)conformally invariant. Since the (super)conformal invariance is equivalent to the BRST invariance in (super)conformal gauge, our approach naturally reproduces the basic resutls of refs.…”

“…In this case the stress tensor and the supercurrent become those of free field with coupling to background charge as in refs. [8,16].…”

On the amplitudes for non-critical N=2 superstrings

“…The amplitude vanishes for any other kinematic region, where at least two momenta satisfy Rek > α 0 and are therefore "on shell" (k ·k = 0) in the critical sense. It should be stressed that the amplitude A 3 in the critical case = 0 and z 1 = ∞ , z 2 = 1 , z 3 = z , z 4 = 0 we have , after using (22), basically the same expression as in the critical case:…”