Supersymmetry in Open Superstring Field Theory

We realize the 16 unbroken supersymmetries on a BPS D-brane as invariances of the action of the corresponding open superstring field theory. We work in the small Hilbert space approach, where a symmetry of the action translates into a symmetry of the associated cyclic $A_\infty$ structure. We compute the supersymmetry algebra, being careful to disentangle the components which produce a translation, a gauge transformation, and a symmetry transformation which vanishes on-shell. Via the minimal model theorem, we illustrate how supersymmetry of the action implies supersymmetry of the tree level open string scattering amplitudes.Comment: 37 page

Superstring Field Theory and the Wess-Zumino-Witten Action

We describe a notion of "higher" Wess-Zumino-Witten-like action which is natural in the context of superstring field theories formulated in the large Hilbert space. For the open string, the action is characterized by a pair of commuting cyclic $A_\infty$ structures together with a hierarchy of higher-form potentials analogous to the Maurer-Cartan elements which appear in the conventional Wess-Zumino-Witten action. We apply this formalism to get a better understanding of symmetries of open superstring field theory and the structure of interactions in the Ramond sector, describing an interesting connection between Ramond vertices and Feynman diagrams.Comment: v2: 63 pages, 4 figures. Minor corrections, references adde

A fresh look at midpoint singularities in the algebra of string fields

In this paper we study the midpoint structure of the algebra of open strings from the standpoint of the operator/Moyal formalism. We construct a split string description for the continuous Moyal product of hep-th/0202087, study the breakdown of associativity in the star algebra, and identify in infinite sequence of new (anti)commutative coordinates for the star product in in the complex plane. We also explain how poles in the open string non(anti)commutativity parameter correspond to certain ``null'' operators which annihilate the vertex, implying that states proportional to such operators tend to have vanishing star product with other string fields. The existence of such poles, we argue, presents an obstruction to realizing a well-defined formulation of the theory in terms of a Moyal product. We also comment on the interesting, but singular, representation $L_0$ which has appeared prominently in the recent studies of Bars {\it et al}.Comment: 40 pages, 5 figures. Version to be submitted to JHEP. Some interesting and previouusly unpublished results are included here. These include both an interpretation of poles in the open string noncommutativity parameter as corresponding to null operators in the algebra, and an identification of an infinite sequence of new commutative and null coordinates in the complex $\kappa$ plan

Level Truncation and Rolling the Tachyon in the Lightcone Basis for Open String Field Theory

A recent paper by Gross and Erler (hep-th/0406199) showed that by making a certain well-defined, unitary transformation on the mode basis for the open bosonic string--one that identifies the lightcone component of position with the string midpoint--it is possible to render the action for cubic string field theory local in lightcone time. In this basis, then, cubic string field theory possesses a well-defined initial value formulation and a conserved Hamiltonian. With this new understanding it seems natural to study time dependent solutions representing the the decay of an unstable D-branes. In this paper we study such solutions using level truncation of mode oscillators in the lightcone basis, finding both homogenous solutions by perturbatively expanding the string field in modes $e^{nt}$, and inhomogenous solutions by integrating the equations of motion on a lattice. Truncating the theory to level $(\tilde{2},\tilde{4})$ in $\alpha^+$ oscillators, we find time dependent solutions whose behavior seems to converge to that of earlier solutions constructed in the center of mass basis, where the cubic action contains an infinite number of time derivatives. We further construct time-dependent inhomogeneous solutions including all fields up to level $(\tilde{2},\tilde{4})$. These solutions at the outset display rather erratic behavior due to an unphysical instability introduced by truncating the theory at the linear level. However upon truncating away the field responsible for the instability, we find more reasonable solutions which may possibly represent an approximation to tachyon matter. We conclude with some discussion of future directions.Comment: 29 pages, 21 figure

String Field Theory Solution for Any Open String Background

We present an exact solution of open bosonic string field theory which can be used to describe any time-independent open string background. The solution generalizes an earlier construction of Kiermaier, Okawa, and Soler, and assumes the existence of boundary condition changing operators with nonsingular OPEs and vanishing conformal dimension. Our main observation is that boundary condition changing operators of this kind can describe nearly any open string background provided the background shift is accompanied by a timelike Wilson line of sufficient strength. As an application we analyze the tachyon lump describing the formation of a D$(p-1)$-brane in the string field theory of a D$p$-brane, for generic compactification radius. This not only provides a proof of Sen's second conjecture, but also gives explicit examples of higher energy solutions, confirming analytically that string field theory can "reverse" the direction of the worldsheet RG flow. We also find multiple D-brane solutions, demonstrating that string field theory can add Chan-Paton factors and change the rank of the gauge group. Finally, we show how the solution provides a remarkably simple and nonperturbative proof of the background independence of open bosonic string field theory.Comment: V2: 42 pages, 11 figures, typos correcte

Vertical Integration from the Large Hilbert Space

We develop an alternative description of the procedure of vertical integration based on the observation that amplitudes can be written in BRST exact form in the large Hilbert space. We relate this approach to the description of vertical integration given by Sen and Witten.Comment: V2: 28 pages, 5 figures. Minor correction

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.Comment: 43 pages, 5 figure

One Loop Tadpole in Heterotic String Field Theory

We compute the off-shell 1-loop tadpole amplitude in heterotic string field theory. With a special choice of cubic vertex, we show that this amplitude can be computed exactly. We obtain explicit and elementary expressions for the Feynman graph decomposition of the moduli space, the local coordinate map at the puncture as a function of the modulus, and the $b$-ghost insertions needed for the integration measure. Recently developed homotopy algebra methods provide a consistent configuration of picture changing operators. We discuss the consequences of spurious poles for the choice of picture changing operators.Comment: v3: 36 pages, 8 figures. Figure 8 correcte