Nonlinear gauge invariance and WZW-like action for NS-NS superstring field theory

Journal of High Energy Physics, Sep 2015

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 closedform 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 NS heterotic string field theory in the small Hilbert space of right movers.

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Nonlinear gauge invariance and WZW-like action for NS-NS superstring field theory

JHE Open Access 0 1 c The Authors. 0 1 0 Komaba , Meguro-ku, Tokyo 153-8902 , Japan 1 Institute of Physics, University of Tokyo 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 closedform 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 NS heterotic string field theory in the small Hilbert space of right movers. String Field Theory; Superstrings and Heterotic Strings; Gauge Symmetry - Nonlinear gauge invariance and WZW-like action for NS-NS superstring field theory 1 Introduction Nonlinear gauge invariance Quartic vertex WZW-like expression Coalgebraic description of vertices Gauge-invariant insertions NS string products Wess-Zumino-Witten-like action Nonlinear gauge invariance Gauge-invariant insertions of picture-changing operators B Some identities A Heterotic theory in the small Hilbert space Introduction While bosonic string field theories have been well-understood [1–8], superstring field theories remain mysterious. A formulation of supersymmetric theories in the early days [9], which is a natural extension of bosonic theory, has some disadvantages caused by picturechanging operators inserted into string products: singularities and broken gauge invariances [10]. To remedy these, various approaches have been proposed within the same There exists an alternative formulation of superstring field theory: large space theory [18–26]. Large space theories are formulated by utilizing the extended Hilbert space of operators. One can check the variation of the action, the equation of motion, and gauge invariance without taking account of these operators. Of course, the action implicitly includes picture-changing operators, which appear when we concretely compute scattering amplitudes after gauge fixing. The singular behaivor of them is, however, completely regulated and there is no divergence [28, 29]. The cancellation of singularities can also occur in the small Hilbert space. Recently, by the brilliant works of [30, 31], it is revealed how to obtain gauge-invariant insertions of picture-changing operators into (super-) string products in the small Hilbert space: the NS and NS-NS sectors of superstring field theories in the small Hilbert space is completely formulated. In this paper, 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. There is an attempt to construct non-vanishing interaction terms of NS-NS string fields utilizing a pure-gauge solution GB of bosonic closed string field theory [22]. However, the construction is not complete: the nonlinear gauge invariance is not clear and the defining equation of GB is ambiguous. To obtain nonlinear gauge invariances, we have to add appropriate terms to these interaction terms defined by GB at each order. Then, the ambiguities of vertices are removed and we obtain the defining equation of a suitable pure-gauge solution GL, which we explain in the following sections. In this paper, we complete this construction begun in [22] by determining these additional terms which are necessitated for the nonlinear gauge invariance and by giving closed-form expressions for the action and nonlinear gauge transformations in the NS-NS sector of closed superstring field theory. We propose the action S = the NS heterotic string equation of motion in the small Hilbert space of right movers. The action has the WZW-like form and the almost same algebraic properties as the large-space action for NS open and NS closed (heterotic) string field theory [20, 21]. This paper is organized as follows. In section 2 we show that cubic and quartic actions can be determined by adding appropriate terms and imposing gauge invariance. In section 3, we briefly review the method of gauge-invariant insertions of picture-changing operaIn section 4, first, we give the defining equation of GL and associated fields which are necessitated to construct the NS-NS action. Then, we derive the WZW-like expression for the string equation of motion just as other large-space theories. We end with some conclusions. Nonlinear gauge invariance string field theory in powers of κ: S = α2′ P number 0, and right-mover picture number 0 state. The free action S2 is given by S2 = use the symbol (G|p, p˜) which denotes that the total ghost number is G, the left-mover picture number is p, and the right-mover picture number is p˜. Then, ghost-and-picture that the inner product hA, Bi gives a nonzero value if and only if the sum of A’s and B’s S2 is invariant under the (...truncated)


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Hiroaki Matsunaga. Nonlinear gauge invariance and WZW-like action for NS-NS superstring field theory, Journal of High Energy Physics, 2015, pp. 11, Volume 2015, Issue 9, DOI: 10.1007/JHEP09(2015)011