The BRST Symmetry of Affine Lie Superalgebras and Noncritical Strings

Abstract

The topological eld theories associated with ane Lie superalgebras are constructed. Their BRST symmetry is characterised by a Kazama algebra containing spin 1, 2 and 3 operators and closes linearly. Under this symmetry all operators are grouped into BRST doublets. The relation between the models constructed and non-critical string theories is explored.

One-instanton predictions for non-hyperelliptic curves derived from M-theory

“…Thus, the techniques of section two of this paper generalizes the methods described in refs. [10] and [11].…”

“…Asymptotic freedom restricts N f to be less than N −2. (In previous work [11], we obtained the one-instanton prediction for N f = 0.) The Seiberg-Witten curve for this theory, constructed by Landsteiner, Lopez, and Lowe [15], is…”

“…which takes a different value on each of the Riemann sheets. The perturbative expansion in ǫ, (11), induces a comparable expansion for the SW differential. For example, on sheet one…”

“…Methods required to extract explicit predictions for the prepotentials associated to non-hyperelliptic curves are just beginning to be developed. In particular, in two previous papers [10,11], we provided a construction for the instanton expansion for SU(N) gauge theory, with matter in the antisymmetric or symmetric representations, with explicit results for the one-instanton contribution to the prepotential. (These two cases involve non-hyperelliptic cubic curves.)…”

“…. (10) As in our previous work [10,11], we will solve the prepotential for this problem by means of a systematic expansion in powers of ǫ, with the zeroth-order term being a hyperelliptic curve. The solutions to (9), correct to O(ǫ), are…”