Superstrings from theories with N > 1 world-sheet supersymmetry

Abstract

String theories with (N, N ′ ) local world-sheet supersymmetries are related to each other by marginal deformations. This connects N = 1 and N = 0 theories in which the target-spaces are interpreted as space-times, N = 2 theories in which the target spaces can be interpreted as world-volumes, and theories with N ≥ 3, in which the central charge vanishes -theories with zero target-space dimensions. *

M-Theory from Worldsheet Defects in Liouville String

“…To understand the relation of n = 2 world-sheet supersymmetric models to n = 1, we note that this n = 2 string has been shown recently to be connected by world-sheet marginal deformations to strings with less world-sheet local supersymmetry, such as (1,1) or (1,0) superstrings [14]. This was achieved by adding suitable topological packages to the critical fields of the (2, 2) n = 2 world-sheet theory, whose action was described by a BRST -exact form.…”

“…We also discuss how the theories with n = 1 world-sheet supersymmetry that we discuss may be described as marginal deformations of theories with n = 2 world-sheet supersymmetry [14], thereby making more direct contact with string models with N = 1 space-time supersymmetry. Finally, we conjecture that the extra dimension provided by the Liouville field with non-trivial dynamics may be interpreted as a world-sheet description of F theory [3].…”

Topological Gravity versus Supergravity on Manifolds with Special Holonomy

“…Indeed, all types of superstring theories can be obtained by suitable anomaly free untwisting of topological sigma-models, which are quite easy to derive, at least in a formal way [8]. Then, we can rely on the fact that supergravities arise as low energy limits of superstrings in order to predict a link between supergravities and topological gravities.…”

Covariant map between Ramond-Neveu-Schwarz and pure spinor formalisms for the superstring

“…This "twisting" by the γ ghost was earlier used in the Calabi-Yau fermions of the d=4 hybrid formalism [9] and also appeared in the topological twisting papers of Baulieu et al [10][11][12][13]. Although (1.4) breaks SO(10) covariance to U(5), one can recover the full SO(10) covariance by using the pure spinor λ α and its complex conjugate λ α to "dynamically" choose the U(5) direction of the twisting so that…”

“…Although q α does not anticommute with the BRST operator of (2.10), one can perform the further similarity transformation O → e −R Oe R where 12) under which the BRST operator of (2.10) transforms into the manifestly spacetime supersymmetric operator…”