Closed N=2 Strings: Picture-Changing, Hidden Symmetries and SDG Hierarchy

Abstract

We study the action of picture-changing and spectral flow operators on a ground ring of ghost number zero operators in the chiral BRST cohomology of the closed N=2 string and describe an infinite set of symmetry charges acting on physical states. The transformations of physical string states are compared with symmetries of self-dual gravity which is the effective field theory of the closed N=2 string. We derive all infinitesimal symmetries of the self-dual gravity equations in 2+2 dimensional spacetime and introduce an infinite hierarchy of commuting flows on the moduli space of self-dual metrics. The dependence on moduli parameters can be recovered by solving the equations of the SDG hierarchy associated with an infinite set of abelian symmetries generated recursively from translations. These non-local abelian symmetries are shown to coincide with the hidden abelian string symmetries responsible for the vanishing of most scattering amplitudes. Therefore, N=2 string theory "predicts" not only self-dual gravity but also the SDG hierarchy.

41 pages, no figures

References in corpus (7)

• Extended Self-Dual Yang-Mills from the N=2 String
• Holomorphic Chern-Simons-Witten Theory: from 2D to 4D Conformal Field Theories
• On the Picture Dependence of Ramond-Ramond Cohomology
• N=2 Worldsheet Instantons Yield Cubic Self-Dual Yang-Mills
• Non-local symmetries of the closed N=2 string
• Chiral BRST Cohomology of N=2 Strings at Arbitrary Ghost and Picture Number
• String-induced Yang-Mills coupling to self-dual gravity

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• Supertwistors and Cubic String Field Theory for Open N=2 Strings
• On the Connection between N=2 Minimal String and (1,n) Bosonic Minimal String
• The Ground Ring of N=2 Minimal String Theory
• N=2 String Geometry and the Heavenly Equations