Restoring Reality for the Self-Dual N=2 String

Abstract

It is known that the critical N=(2,2) string describes 2+2 dimensional self-dual gravity in a non-covariant form, since it requires the choice of a complex structure in the target, which leaves only U(1,1) Lorentz symmetry. We briefly review picture-changing and spectral flow and show that the world-sheet Maxwell instantons individually break the Lorentz group further to SU(1,1). However, their contributions conspire to restore full SO(2,2) global symmetry if dilaton and axion fields are assembled in a null anti-self-dual two-form, denying them the status of Lorentz scalars. We present the fully SO(2,2) invariant tree-level three-point amplitude and the corresponding extension of the Plebanski action for self-dual gravity.

13 pages + 1 figure, 44 kb, plain LaTeX

References in corpus (8)

• N=4 Topological Strings
• All Loop N=2 String Amplitudes
• Gso Projection, BRST Cohomology and Picture-Changing in N=2 String Theory
• A tour through N=2 strings
• The String Measure and Spectral Flow of Critical N=2 Strings
• Vanishing Theorems for the Self-Dual N=2 String
• Twisting the N=2 String
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Cited by in corpus (13)

• Path-Integral Quantization of the (2,2) String
• Extended Self-Dual Yang-Mills from the N=2 String
• N=2 Worldsheet Instantons Yield Cubic Self-Dual Yang-Mills
• Non-local symmetries of the closed N=2 string
• Self-Dual Supergravity from N=2 Strings
• Closed N=2 Strings: Picture-Changing, Hidden Symmetries and SDG Hierarchy
• Large N WZW Field Theory Of N=2 Strings
• Large N Field Theory of N=2 Strings and Self-Dual Gravity
• Can one restore Lorentz invariance in quantum N=2 string?
• String-induced Yang-Mills coupling to self-dual gravity
• Self-duality and F theory
• $A_{\infty }$ Action of Open $\mathcal{N}=2$ Superstring Field Theory
• Hidden Symmetries of the Open N=2 String