Covariant currents in N = 2 super-Liouville theory

Abstract

Based on a path integral prescription for anomaly calculation, we analyze an effective theory of the two-dimensional N = 2 supergravity, i.e., N = 2 superLiouville theory. We calculate the anomalies associated with the BRST supercurrent and the ghost number supercurrent. From those expressions of anomalies, we construct covariant BRST and ghost number supercurrents in the effective theory.We then show that the (super-)coordinate BRST current algebra forms a superfield extension of the topological conformal algebra for an arbitrary type of conformal matter or, in terms of the string theory, for an arbitrary number of space-time dimensions. This fact is very contrast with N = 0 and N = 1 (super-)Liouville theory, where the topological algebra singles out a particular value of dimensions.Our observation suggests a topological nature of the two-dimensional N = 2 supergravity as a quantum theory. * Electronic address: quim@ebubecm1.bitnet † JSPS Junior Scientist Fellow. Also

N = 2 super-Weyl symmetry, super-Liouville theory and super-Riemannian surfaces

“…[29]. Namely, the BRST super-current algebra in these theories appears to be the particular N = 2 supersymmetric extension of the topological conformal algebra [29] for an arbitrary conformal matter [28]. As was noticed in ref.…”

“…As was noticed in ref. [28] for both critical and non-critical N = 2 fermionic string theories, the vanishing of the ghost-number anomaly associated with the total divergence term in the full BRST anomaly is crucial for the apparently topological properties of these theories. There are also many reasons to believe that the two-dimensional N = 2 supergravity itself is a topological quantum field theory [21,28].…”

“…The current algebra of the N = 2 super-Liouville theory in the N = 2 superconformal gauge was recently discussed in refs. [27,28].…”

“…The effective theory of the quantised N = 2 supergravity in two dimensions is given by the N = 2 super-Liouville theory, as it should have been expected from a consistency with the component approach. The current algebra of the N = 2 super-Liouville theory in the N = 2 superconformal gauge was recently discussed in refs [27,28]…”

Super-Liouville Theory from Superstring Theory in the Presence of Gauge Worldsheet Fields

“…Gauge superstring theories have been studied in different points of view [1,2]. They are obtained by introducing the worldsheet abelian gauge fields in superstring action [3][4][5]. The action of the gauged superstring allows us to build two worldsheet fields from elements of the gauge field.…”