Abstract
We complete the construction of a gauge-invariant action for NS-NS superstring field theory in the large Hilbert space begun in arXiv:1305.3893 by giving a closed-form expression for the action and nonlinear gauge transformations. The action has the WZW-like form and vertices are given by a pure-gauge solution of heterotic string field theory in the small Hilbert space.
Highlights
The cancellation of singularities can occur in the small Hilbert space
We find that using the elegant technique of [31], one can construct the WZW-like action for NS-NS superstring field theory in the large Hilbert space
A pure-gauge solution of small-space theory is the key concept of WZW-like formulation of NS superstring field theory in the large Hilbert space, which determines the vertices of theory, and we expect that it goes in the case of the NS-NS sector
Summary
We derive the equation of motion and the closed form expression of nonlinear gauge transformations. For example, GL(t = 0) = 0, GL(t = 1) = GL, Ψδ(t = 0) = 0, and Ψδ(t = 1) = Ψδ hold For this purpose, we prove that the variation δS does not includes t and is given by δS = Ψδ, η GL. The equation of motion is, given by (4.24) and it is independent of t-parametrization of fields. Since η GL is a QGL-, η-, and η-exact state, we find that the action is invariant under the following nonlinear Q- and η-gauge transformations and linear η-gauge transformation. An explicit expression for Q-gauge transformation δΛΨ and η-gauge transformation δΩΨ are given by δΛΨ. The action has three generators of gauge transformations, since one of these gauge invariances reduces to trivial, the resulting theory is Wess-Zumino-Wittenlikely formulated with two nonlinear gauge invariances
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