Free String Field Research Articles

On the spectrum and spacetime supersymmetry of heterotic ambitwistor string

We analyse the BRST cohomology of the Ramond sector of heterotic ambitwistor theory. We also write the free string field theory action and compute the supersymmetry transformations.

Field theory actions for ambitwistor string and superstring

We analyze the free ambitwistor string field theory action for the bosonic string, heterotic string and both GSO sectors of the Type II string. The spectrum contains non-unitary states and provides an interesting consistency test for one-loop ambitwistor string computations.

Remarks on entanglement entropy in string theory

Entanglement entropy for spatial subregions is difficult to define in string theory because of the extended nature of strings. Here we propose a definition for Bosonic open strings using the framework of string field theory. The key difference (compared to ordinary quantum field theory) is that the subregion is chosen inside a Cauchy surface in the "space of open string configurations". We first present a simple calculation of this entanglement entropy in free light-cone string field theory, ignoring subtleties related to the factorization of the Hilbert space. We reproduce the answer expected from an effective field theory point of view, namely a sum over the one-loop entanglement entropies corresponding to all the particle-excitations of the string, and further show that the full string theory regulates the ultraviolet divergences in the entanglement entropy. We then revisit the question of factorization of the Hilbert space by analyzing the covariant phase-space associated with a subregion in Witten's covariant string field theory. We show that the pure gauge (i.e., BRST exact) modes in the string field become dynamical at the entanglement cut. Thus, a proper definition of the entropy must involve an extended Hilbert space, with new stringy edge modes localized at the entanglement cut.

Gauge invariant and gauge fixed actions for various higher-spin fields from string field theory

We propose a systematic procedure for extracting gauge invariant and gauge fixed actions for various higher-spin gauge field theories from covariant bosonic open string field theory. By identifying minimal gauge invariant part for the original free string field theory action, we explicitly construct a class of covariantly gauge fixed actions with BRST and anti-BRST invariance. By expanding the actions with respect to the level N of string states, the actions for various massive fields including higher-spin fields are systematically obtained. As illustrating examples, we explicitly investigate the level N⩽3 part and obtain the consistent actions for massive graviton field, massive 3rd rank symmetric tensor field, or anti-symmetric field. We also investigate the tensionless limit of the actions and explicitly derive the gauge invariant and gauge fixed actions for general rank n symmetric and anti-symmetric tensor fields.

PP-wave light-cone free string field theory at finite temperature

In this paper, a real-time formulation of light-cone pp-wave string field theory at finite temperature is presented. This is achieved by developing the thermo field dynamics (TFD) formalism in a second quantized string scenario. The equilibrirum thermodynamic quantities for a pp-wave ideal string gas are derived directly from expectation values on the second quantized string thermal vacuum. Also, we derive the real-time thermal pp-wave closed string propagator. In the flat space limit it is shown that this propagator can be written in terms of Theta functions, exactly as the zero temperature one. At the end, we show how supestrings interactions can be introduced, making this approach suitable to study the BMN dictionary at finite temperature.

On the geometry of higher-spin gauge fields

We review a recent construction of the free-field equations for totally symmetric tensors and tensor-spinors that exhibits the corresponding linearized geometry. These equations are not local for all spins >2, involve unconstrained fields and gauge parameters, rest on the curvatures introduced long ago by de Wit and Freedman and reduce to the local (Fang–)Fronsdal form upon partial gauge fixing. We also describe how the higher-spin geometry is realized in free string field theory, and how the gauge fixing to the light cone can be effected.

Locality in Free String Field Theory - II

We study the covariant free bosonic string field theory and explore its locality (causality) properties. We find covariant string fields which are strictly local and covariant, but act on an unconstrained Hilbert space with an indefinite inner product. From these we also define observable fields which act on the physical Hilbert space with an definite inner product. These are shown to be approximately local.

Locality in free string field theory

Free string field operators are constructed for the open bosonic string in the light cone gauge in any dimension. These are naturally localized by the center of mass coordinate. Relative to this localization they are shown to have a causal commutator provided there are no tachyons. For the critical string in d=26 the result still holds if the tachyon is suppressed. We also show a causal commutator relative to the “string light cone.”

Causality in covariant string field theory

Causality is studied in the covariant formulation of free string field theory (SFT). We find that, though the string field in the covariant formulation is a functional of the ghost coordinates as well as the space-time coordinate and the latter contains the time-like oscillators with negative norm, the condition for the commutator of two open string fields to vanish is simply given by ∫ O τ dδ(ΔX μ(δ)) 2<O , which is the same condition as in the light-cone gauge SFT. For closed SFT, the corresponding condition is given in a form which is manifestly invariant under the rigid shifts of the σ parameters of the two string fields.

Complex world-sheets from N = 2 strings

We study some properties of target space strings constructed from (2,1) heterotic strings. We argue that world-sheet complexification is a general property of the bosonic sector of such target world-sheets. We give a target space interpretation of this fact and relate it to the non-gaussian nature of free String Field Theory. We provide several one-loop calculations supporting the stringy construction of critical world-sheets in terms of (2,1) models. Using finite-temperature boundary conditions in the underlying (2,1) string we obtain non-chiral target space spin structures, and point out some of the problems arising for chiral spin structures, such as the heterotic world-sheet. To this end, we study the torus partition function of the corresponding asymmetric orbifold of the (2,1) string.

String Field Theory in Rindler Space-Time and String Thermalization

Quantization of free string field theory in the Rindler space-time is studied by using the covariant formulation and taking the center-of-mass value of the Rindler string time-coordinate $\eta(\sigma)$ as the time variable for quantization. We construct the string Rindler modes which vanish in either of the Rindler wedges $\pm$ defined by the Minkowski center-of-mass coordinate of the string. We then evaluate the Bogoliubov coefficients between the Rindler string creation/annihilation operators and the Minkowski ones, and analyze the string thermalization. An approach to the construction of the string Rindler modes corresponding to different definitions of the wedges is also presented toward a thorough understanding of the structure of the Hilbert space of the string field theory on the Rindler space-time.

Causal properties of free string field theory

This paper examines the causal structure of the commutator of two string fields, in free light-cone string field theory. By treating the commutator as a distribution on infinite dimensional loop space, it is shown that the commutator vanishes when ∫d σ( δX( σ)) 2<0. Of more direct physical interest is the commutator of finite mass fields, obtained by smearing the string fields with appropriate wave functions. This is shown to vanish at spacelike separations, reproducing the usual point particle field theory result. The implications of this for the information spreading mechanism proposed by Susskind to solve the black hole information problem are discussed. Finally, it is verified that the above conclusions also hold for the superstring.

A gauge invariant action for the free Neveu-Schwarz string in spacetime of any dimension

Using the idea of gauge invariance based on a nilpotent BRST operator, a local action is constructed for the free Neveu-Schwarz string field in spacetime of any dimension. The gauge-fixing problem in the presence of hidden extra symmetry of an action is considered.

Infinite-dimensional free differential algebras and string field theory

We consider Kac-Moody extensions of free differential algebras, and their BRST quantization. These infinite-dimensional algebras appear in the context of a recently proposed field theory of loops.

Free bosonic string field theory without supplementary fields

A covariant local action for free bosonic string fields is constructed without the use of supplementary fields. The open string case is treated in detail. Up to a mathematical conjecture that is likely to hold it is shown that the Virasoro constraints arise as a special choice of gauge. The kinetic operator turns out to be extremely simple, the gauge transformation law arising rather implicitly. The case of closed strings is briefly discussed.

Bosonic string theory in covariant gauge

We discuss path integral formulations of the first quantization of open and closed bosonic strings in the proper-time gauges which ensure manifest covariance. The string propagators given by path integrals à la Polyakov are evaluated. The evaluated propagators uniquely determine the actions for the free string fields in the second quantized theories. The BRST invariant actions for free bosonic string fields proposed by Siegel are shown to emerge naturally. A geometrical explanation for the proper-time gauge conditions as appropriate gauge fixing conditions is presented. We also evaluate the BRST invariant one loop string path integral.

Gauge fixing in string field theory using the Polyakov path integral

The gauge-fixed off-shell propagator for free closed string field theory is calculated using the Polyakov path integral for a cylinder with boundary conditions that break reparametrization invariance - the result for open strings is given without proof. This explicitly establishes the connection between gauge transformations in free string field theory and world-sheet diffeomorphisms on the boundaries, giving an attractive geometrical picture for the origin of gauge invariance. A decomposition of the two-dimensional metric is used which does not distinguish between changes in the metric g ab which effectively move the boundary, such as Teichmüller variations, and diffeomorphisms M → M which do not move the boundary. This decomposition requires an overcomplete set of parameters which specify coordinate transformations on the boundary. The choice of ghost sources attached to the propagator is determined by the choice of a minimal set of these parameters from the overcomplete set. The parameters representing coordinate transformations of the boundaries can be included as dynamical fields in two dimensions and as new coordinates for string field theory. Zero modes of these new coordinates are modular parameters for the torus when the ends of the cylinder are brought together. The relationship between these new coordinates and those introduced by other groups is discussed.

The string field embedded in a loop space geometry

We study the equations of motion for a loop geometry that we introduced in an earlier paper. These geometrical constraints are necessary in order to satisfy Q 2 = 0, where Q is a BRST charge that encodes the “local” reparametrization invariance related to the loop differential geometry. In the linearized version of these equations, the zeroth order is satisfied by d = 26 and α 0 = = 1, while the first order is satisfied by a string field that essentially obeys the Virasoro constraints, thus reproducing the equations satisfied by free string fields. We are therefore encouraged to speculate that the higher order terms, which are not studied in this paper, correspond to string field interactions.

Equivalence of different formulations of the free Ramond string field theory

We analyze the structure of Witten's formulation of the free Ramond string field theory and show that it is equivalent to other formulations. We establish explicit connections between their string fields. It is shown that the established connections eliminate all terms with mixed mass levels.

BRST quantization in the Siegel gauge

From a formal generalization to N copies of the free open string field theory BRST-quantized in the Siegel gauge we reproduce the BRST quantization of the free closed bosonic string field theory and obtain the one of massless higher spin field theories.