Superstring Field Theory Research Articles

Construction of action for heterotic string field theory including the Ramond sector

Extending the formulation for open superstring field theory given in arXiv:1508.00366, we attempt to construct a complete action for heterotic string field theory. The action is non-polynomial in the Ramond string field Psi, and we construct it order by order in Psi. Using a dual formulation in which the role of eta and Q is exchanged, the action is explicitly obtained at the quadratic and quartic order in Psi with the gauge transformations.

Comments on complete actions for open superstring field theory

We clarify a Wess-Zumino-Wtten-like structure including Ramond fields and propose one systematic way to construct gauge invariant actions: Wess-Zumino-Witten-like complete action $S_{\rm WZW}$. We show that Kunitomo-Okawa's action proposed in arXiv:1508.00366 can obtain a topological parameter dependence of Ramond fields and belongs to our WZW-like framework. In this framework, once a WZW-like functional $\mathcal{A}_{\eta } = \mathcal{A}_{\eta } [\Psi ]$ of a dynamical string field $\Psi $ is constructed, we obtain one realization of $S_{\rm WZW}$ parametrized by $\Psi $. On the basis of this way, we construct an action $\widetilde{S}$ whose on-shell condition is equivalent to the Ramond equations of motion proposed in arXiv:1506.05774. Using these results, we provide the equivalence of two these theories: arXiv:1508.00366 and arXiv:1506.05774.

Reality of superstring field theory action

We determine the reality conditions on the string fields that make the action for heterotic and type II string field theories real.

Cutkosky rules for superstring field theory

Superstring field theory expresses the perturbative S-matrix of superstring theory as a sum of Feynman diagrams each of which is manifestly free from ultraviolet divergences. The interaction vertices fall off exponentially for large space-like external momenta making the ultraviolet finiteness property manifest, but blow up exponentially for large time-like external momenta making it impossible to take the integration contours for loop energies to lie along the real axis. This forces us to carry out the integrals over the loop energies by choosing appropriate contours in the complex plane whose ends go to infinity along the imaginary axis but which take complicated form in the interior navigating around the various poles of the propagators. We consider the general class of quantum field theories with this property and prove Cutkosky rules for the amplitudes to all orders in perturbation theory. Besides having applications to string field theory, these results also give an alternative derivation of Cutkosky rules in ordinary quantum field theories.

Complete action for open superstring field theory with cyclic A ∞ structure

We construct a gauge invariant action for the Neveu-Schwarz and Ramond sectors of open superstring field theory realizing a cyclic $A_\infty$ structure, providing the first complete and fully explicit solution to the classical Batalin-Vilkovisky master equation in superstring field theory. We also demonstrate the equivalence of our action to the Wess-Zumino-Witten-based construction of Kunitomo and one of the authors.

A singular one-parameter family of solutions in cubic superstring field theory

Performing a gauge transformation of a simple identity-like solution of superstring field theory, we construct a one-parameter family of solutions, and by evaluating the energy associated to this family, we show that for most of the values of the parameter the solution represents the tachyon vacuum, except for two isolated singular points where the solution becomes the perturbative vacuum and the half brane solution.

Open superstring field theory on the restricted Hilbert space

Recently an action for open superstring field theory was proposed where the Neveu-Schwarz sector is formulated in the large Hilbert space while the Ramond sector lives in a restriction of the small Hilbert space. The purpose of this note is to clarify the relation of the restricted Hilbert space with other approaches and to formulate open superstring field theory entirely in the small Hilbert space.

20pAK-4 Complete action of open superstring field theory with cyclic A_∞ structure

20pAK-4 Complete action of open superstring field theory with cyclic A_∞ structure

Relating Berkovits and A ∞ superstring field theories; large Hilbert space perspective

We lift the dynamical field of the A ∞ superstring field theory to the large Hilbert space by introducing a gauge invariance associated with the eta zero mode. We then provide a field redefinition which relates the lifted field to the dynamical field of Berkovits’ superstring field theory in the large Hilbert space. This generalizes the field redefinition in the small Hilbert space described in earlier works, and gives some understanding of the relation between the gauge symmetries of the theories. It also provides a new perspective on the algebraic structure underlying gauge invariance of the Wess-Zumino-Witten-like action.

Complete action for open superstring field theory: Table 1.

We construct a complete action for open superstring field theory that includes the Neveu-Schwarz sector and the Ramond sector. For the Neveu-Schwarz sector, we use the string field in the large Hilbert space of the superconformal ghost sector, and the action in the Neveu-Schwarz sector is the same as the Wess-Zumino-Witten-like action of the Berkovits formulation. For the Ramond sector, it is known that the BRST cohomology on an appropriate subspace of the small Hilbert space reproduces the correct spectrum, and we use the string field projected to this subspace. We show that the action is invariant under gauge transformations that are consistent with the projection for the string field in the Ramond sector.

The S-matrix of superstring field theory

We show that the classical S-matrix calculated from the recently proposed superstring field theories give the correct perturbative S-matrix. In the proof we exploit the fact that the vertices are obtained by a field redefinition in the large Hilbert space. The result extends to include the NS-NS subsector of type II superstring field theory and the recently found equations of motions for the Ramond fields. In addition, our proof implies that the S-matrix obtained from Berkovits' WZW-like string field theory then agrees with the perturbative S-matrix to all orders.

Ramond equations of motion in superstring field theory

We extend the recently constructed NS superstring field theories in the small Hilbert space to give classical field equations for all superstring theories, including Ramond sectors. We also comment on the realization of supersymmetry in this framework.

Relating Berkovits and A ∞ superstring field theories; small Hilbert space perspective

In a previous paper it was shown that the recently constructed action for open superstring field theory based on A ∞ algebras can be re-written in Wess-Zumino-Witten-like form, thus establishing its relation to Berkovits’ open superstring field theory. In this paper we explain the relation between these two theories from a different perspective which emphasizes the small Hilbert space, and in particular the relation between the A ∞ structures on both sides.

Relation between the reducibility structures and between the master actions in the Witten formulation and the Berkovits formulation of open superstring field theory

Developing the analysis in JHEP 03 (2014) 044 [ arXiv:1312.1677 ] by the present authors et al., we clarify the relation between the Witten formulation and the Berkovits formulation of open superstring field theory at the level of the master action, namely the solution to the classical master equation in the Batalin-Vilkovisky formalism, which is the key for the path-integral quantization. We first scrutinize the reducibility structure, a detailed gauge structure containing the information about ghost string fields. Then, extending the condition for partial gauge fixing introduced in the above-mentioned paper to the sector of ghost string fields, we investigate the master action. We show that the reducibility structure and the master action under partial gauge fixing of the Berkovits formulation can be regarded as the regularized versions of those in the Witten formulation.

Symmetries and Feynman rules for the Ramond sector in heterotic string field theory

Examining the symmetries of the pseudo-action, we propose a prescription for the new Feynman rules for the Ramond sector of the WZW-like heterotic string field theory. The new rules are an analog of that recently proposed for the open superstring field theory and respect all the gauge symmetries including those provided we impose the constraint after transformation. It is shown that the new rules reproduce the well-known on-shell tree-level amplitudes for four and five external strings including fermions.

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

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.

Symmetries and Feynman rules for the Ramond sector in open superstring field theory

We examine the symmetries of the action suppelemented by the constraint in the WZW-type open superstring field theory. It is found that this pseudo-action has additional symmetries provided we impose the constraint after the transformation. Respecting these additional symmetries, we propose a prescription for the new Feynman rules for the Ramond sector. It is shown that the new rules reproduce the well-known on-shell four- and five-point amplitudes with external fermions.

Level truncation analysis of a simple tachyon vacuum solution in cubic superstring field theory

We evaluate the vacuum energy of a simple tachyon vacuum solution using the level truncation scheme in cubic superstring field theory. By truncating the standard Virasoro $L_0$ level expansion of the solution, we obtain a value of the vacuum energy in agreement with Sen's first conjecture.

New analytic solutions in string field theory: Towards a collective higher spin vacuum

We construct analytic solutions in cubic open superstring field theory at higher superconformal ghost numbers.The solutions are the pure ghost ones and are given by combinations of Bell polynomials of bosonized superconformal ghost fields multiplied by exponents of the bosonized ghosts. Based on the structure of the solutions, we conjecture them to describe the ghost part of collective vacuum for higher spin modes in open string theory.

NS-NS sector of closed superstring field theory

We give a construction for a general class of vertices in superstring field theory which include integration over bosonic moduli as well as the required picture changing insertions. We apply this procedure to find a covariant action for the NS-NS sector of Type II closed superstring field theory.