Can one restore Lorentz invariance in quantum N=2 string?

Abstract

We consider quantum N=2 string embedded into the N=4 topological framework from the perspective of the old covariant quantisation. Making use of the causality and cyclic symmetry of tree amplitudes we argue that no Lorentz covariant boson emission vertex can be constructed within the N=4 topological formalism.Comment: 12 pages, LaTe

Making the hyper-Kähler structure ofN=2quantum string manifest

“…[11]. Alternatively, working within the framework of the old covariant quantization, one discovers that the Lorentz invariance of the boson emission vertex proves to be incompatible with the causality and cyclic symmetry of tree level scattering amplitudes [23], thus reproducing, once again, the result of Ooguri and Vafa [11].…”

“…Taking into account commutation relations characterizing the N = 4 superconformal algebra (we use the notation in Ref. [23]) it suffices to fix G, Ḡ and the R-symmetry generators J, J (1) , J (2) .…”

Exact solutions of Berkovits' string field theory

“…Realization in terms of N = 2 matter multiplets. For later use, we also discuss the representation in terms of N = 2 multiplets [26,29,30]: From the world-sheet point of view, critical N = 2 strings in flat Kleinian space R 2,2 ∼ = C 1,1 are described by a theory of N = 2 supergravity on a (1+1)-dimensional (pseudo)Riemann surface, coupled to two chiral N = 2 massless matter multiplets (Z, ψ). The components of these multiplets are complex scalars (the four string coordinates) and so(1, 1) Dirac spinors (their four NSR partners).…”