Open Bosonic String Field Theory Research Articles

On the spectrum around numerical solutions in Siegel gauge in open string field theory

Abstract In bosonic open string field theory, the spectrum around the numerical tachyon vacuum solution in Siegel gauge was investigated by Giusto and Imbimbo. Using their numerical method, we study the mass spectrum around two other solutions, which are “double brane” and “single brane” solutions in Siegel gauge constructed by the level truncation approximation. The “double brane” solution was constructed by Kudrna and Schnabl and its energy might correspond to a double brane. On the other hand, the “single brane” solution was constructed by Takahashi and the author in the theory around the identity-based solution for the tachyon vacuum and its energy corresponds to the perturbative vacuum, namely, a single brane. From the eigenvalues of the matrix for the kinetic term in Siegel gauge, we find a tachyon state and a massless vector state in the ghost number g = 1 sector around the “single brane” solution, which is consistent with the perturbative vacuum, although the mass spectrum around the “double brane” solution is obscure up to truncation level L = 10 and within scalar and vector states.

Higher-spin states of the superstring in an electromagnetic background

Constructing a consistent four-dimensional Lagrangian for charged massive higher-spin fields propagating in an electromagnetic background is an open problem. In 1989, Argyres and Nappi used bosonic open string field theory to construct a Lagrangian for charged massive spin-2 fields in a constant electromagnetic background. In this paper, we use the four-dimensional hybrid formalism for open superstring field theory to construct a supersymmetric Lagrangian for charged massive spin-2 and spin-3/2 fields in a constant electromagnetic background. The hybrid formalism has the advantage over the RNS formalism of manifest mathcal{N} = 1 d=4 spacetime supersymmetry so that the spin-2 and spin-3/2 fields are combined into a single superfield and there is no need for picture-changing or spin fields.

Mapping between Witten and lightcone string field theories

We propose a transformation between the off-shell field variables of Witten’s open bosonic string field theory and the traditional lightcone string field theory of Kaku and Kikkawa, based on Mandelstam’s interacting string picture. This is accomplished by deforming the Witten vertex into lightcone cubic and quartic vertices, followed by integrating out the ghost and lightcone oscillator excitations from the string field. Surprisingly, the last step does not alter the cubic and quartic interactions and does not generate effective vertices, and leads precisely to Kaku and Kikkawa’s lightcone string field theory.

Numerical universal solutions in a-gauge in open string field theory

Abstract In bosonic open string field theory, we construct numerical universal solutions in a-gauge corresponding to “double brane” and “ghost brane” solutions in Siegel gauge in addition to the tachyon vacuum solution, and evaluate their gauge invariants, which are energy- and gauge-invariant observables. The a-gauge condition, which contains a real parameter a, was introduced by Asano and Kato. In earlier works it has been applied to find the tachyon vacuum solution with the level truncation method up to level 14. The “double brane” and “ghost brane” solutions were constructed by Kudrna and Schnabl in Siegel gauge, which corresponds to (a = 0)-gauge, up to level 28. Starting from these solutions, by varying a little by little, we have constructed numerical solutions in a-gauge for various values of a including a = ∞ up to level 20. Contrary to naive expectation, the gauge invariants of “double brane” and “ghost brane” solutions in a-gauge seem to be non-constant for a. In particular, although the normalized energy E of the “double brane” solution in a-gauge is approximately two for a ∼ 0, we find that E becomes almost one for 0.5 < a < 1. The gauge-invariant observable behaves similarly. This might imply that the “double brane” solution varies to a single brane solution in such a-gauges.

Numerical twist-even SU(1,1)-singlet solutions in open string field theory around the identity-based solution

Using the level truncation method, we construct numerical solutions, which are twist even and SU(1) singlet, in the theory around the Takahashi-Tanimoto identity-based solution (TT solution) with a real parameter a in the framework of bosonic open string field theory. We find solutions corresponding to “double brane” and “ghost brane” solutions which were constructed by Kudrna and Schnabl in the conventional theory around the perturbative vacuum. Our solutions show somewhat similar a-dependence to tachyon vacuum and single brane solutions, which we found in the earlier works. In this sense, we might be able to expect that they are consistent with the conventional interpretation of a-dependence of the TT solution. We observe that numerical complex solutions at low levels become real ones at higher levels for some region of the parameter a. However, these real solutions do not so improve interpretation for double brane.

String field theory solution for any open string background. Part II

Generalizing previous work, we give a new analytic solution in Witten’s open bosonic string field theory which can describe any open string background. The central idea is to use Riemann surface degenerations as a mechanism for taming OPE singularities. This requires leaving the familiar subalgebra of wedge states with insertions, but the payoff is that the solution makes no assumptions about the reference and target D-brane systems, and is therefore truly general. For example, unlike in previous work, the solution can describe time dependent backgrounds and multiple copies of the reference D-brane within the universal sector. The construction also resolves some subtle issues resulting from associativity anomalies, giving a more complete understanding of the relation between the degrees of freedom of different D-brane systems, and a nonperturbative proof of background independence in classical open bosonic string field theory.

Closed string symmetries in open string field theory: tachyon vacuum as sine-square deformation

We revisit the identity-based solutions for tachyon condensation in open bosonic string field theory (SFT) from the viewpoint of the sine-square deformation (SSD). The string Hamiltonian derived from the simplest solution includes the sine-square factor, which is the same as that of an open system with SSD in the context of condensed matter physics. We show that the open string system with SSD or its generalization exhibits decoupling of the left and right moving modes and so it behaves like a system with a periodic boundary condition. With a method developed by Ishibashi and Tada, we construct pairs of Virasoro generators in this system, which represent symmetries for a closed string system. Moreover, we find that the modified BRST operator in the open SFT at the identity-based tachyon vacuum decomposes to holomorphic and antiholomorphic parts, and these reflect closed string symmetries in the open SFT. On the basis of SSD and these decomposed operators, we construct holomorphic and antiholomorphic continuous Virasoro algebras at the tachyon vacuum. These results imply that it is possible to formulate a pure closed string theory in terms of the open SFT at the identity-based tachyon vacuum.

Numerical solution of open string field theory in Schnabl gauge

Using traditional Virasoro L0 level-truncation computations, we evaluate the open bosonic string field theory action up to level (10, 30). Extremizing this level-truncated potential, we construct a numerical solution for tachyon condensation in Schnabl gauge. We find that the energy associated to the numerical solution overshoots the expected value −1 at level L = 6. Extrapolating the level-truncation data for L ≤ 10 to estimate the vacuum energies for L > 10, we predict that the energy reaches a minimum value at L ∼ 12, and then turns back to approach −1 asymptotically as L → ∞. Furthermore, we analyze the tachyon vacuum expectation value (vev), for which by extrapolating its corresponding level-truncation data, we predict that the tachyon vev reaches a minimum value at L ∼ 26, and then turns back to approach the expected analytical result as L → ∞.

Comments on real tachyon vacuum solution without square roots

We analyze the consistency of a recently proposed real tachyon vacuum solution without square roots in open bosonic string field theory. We show that the equation of motion contracted with the solution itself is satisfied. Additionally, by expanding the solution in the basis of the curly ℒ0 and the traditional L0 eigenstates, we evaluate numerically the vacuum energy and obtain a result in agreement with Sen’s conjecture.

Covariant open bosonic string field theory on multiple D-branes in the proper-time gauge

We construct a covariant open bosonic string field theory on multiple D-branes, which reduces to a non-Abelian group Yang-Mills gauge theory in the zero-slope limit. Making use of the first quantized open bosonic string in the proper time gauge, we convert the string amplitudes given by the Polyakov path integrals on string world sheets into those of the second quantized theory. The world sheet diagrams generated by the constructed open string field theory are planar in contrast to those of the Witten's cubic string field theory. However, the constructed string field theory is yet equivalent to the Witten's cubic string field theory. Having obtained planar diagrams, we may adopt the light-cone string field theory technique to calculate the multi-string scattering amplitudes with an arbitrary number of external strings. We examine in detail the three-string vertex diagram and the effective four-string vertex diagrams generated perturbatively by the three-string vertex at tree level. In the zero-slope limit, the string scattering amplitudes are identified precisely as those of non-Abelian Yang-Mills gauge theory if the external states are chosen to be massless vector particles.

Singular gauge transformation and the Erler–Maccaferri solution in bosonic open string field theory

We study candidates of the multiple-brane solutions of bosonic open string field theory. They are constructed by performing a singular gauge transformation $n$ times for the Erler-Maccaferri solution. We check the EOM in the strong sense, and find that it is satisfied only when we perform the gauge transformation once. We calculate the energy for that case and obtain a support that the solution is a multiple-brane solution. We also check the tachyon profile for a specific solution which we interpret as describing a D24-brane placed on a D25-brane.

String field representation of the Virasoro algebra

We construct a representation of the zero central charge Virasoro algebra using string fields in Witten's open bosonic string field theory. This construction is used to explore extensions of the KBc algebra and find novel algebraic solutions of open string field theory.

Solutions in bosonic string field theory and higher spin algebras in AdS

We find a class of analytic solutions in open bosonic string field theory, parametrized by the chiral copy of higher spin algebra in $AdS_3$. The solutions are expressed in terms of the generating function for the products of Bell polynomials in derivatives of bosonic space-time coordinates $X^m(z)$ of the open string, which form is determined in this work. The products of these polynomials form a natural operator algebra realizations of $W_\infty$ (area-preserving diffeomorphisms), enveloping algebra of SU(2) and higher spin algebra in $AdS_3$. The class of SFT solutions found can, in turn, be interpreted as the "enveloping of enveloping", or the enveloping of $AdS_3$ higher spin algebra. We also discuss the extensions of this class of solutions to superstring theory and their relations to higher spin algebras in higher space-time dimensions.

Comments on Takahashi-Tanimoto’s scalar solution

We study the identity-based solution of Witten's cubic bosonic open string field theory constructed by Takahashi and Tanimoto, which is claimed to describe the tachyon vacuum. We argue that the observables of the solution coincide with those of the tachyon vacuum using the method proposed by Kishimoto and Takahashi. We also discuss how to treat the kinetic term of the string field theory expanded around it.

Observables for identity-based tachyon vacuum solutions

We consider a modified KBc algebra in bosonic open string field theory expanded around identity-based scalar solutions. By use of the algebra, classical solutions on the background are constructed and observables for them, including energy densities and gauge invariant overlaps, are calculable. These results are applied to evaluate observables analytically for both of the identity-based trivial pure gauge solution and the identity-based tachyon vacuum solution.

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.

Numerical solutions of open string field theory in marginally deformed backgrounds

We investigate numerical solutions of bosonic open string field theory in some marginally deformed backgrounds, which are obtained by expanding the action around an identity-based marginal solution with one parameter. We construct numerical solutions in the Siegel gauge and the Landau gauge corresponding to the tachyon vacuum. Their vacuum energy approximately cancels the D-brane tension for larger intervals of the parameter with increasing truncation level. The result is consistent with the previous expectation that the identity-based marginal solution has vanishing energy regardless of the values of the parameter. We also study the marginal branch (M-branch) and the vacuum branch (V-branch) and evaluate not only the vacuum energy but also the gauge invariant overlaps with the graviton and the closed tachyon. We observe that there is a finite bound for the value of the massless field of numerical solutions even in the marginally deformed background.

Tachyon vacuum of bosonic open string field theory in marginally deformed backgrounds

We consider bosonic open string field theory in marginally deformed backgrounds, which is obtained by expanding the string field around the identity-based solutions associated with marginal deformations. We find a new set of string fields which satisfies the KBc algebra, but the nilpotent kinetic operator is that of the theory expanded around the identity-based marginal solution. By use of these string fields, we construct the tachyon vaccum solution in marginally deformed backgrounds. The vacuum energy density is equivalent to that of the tachyon vacuum without marginal deformations. The gauge invariant overlap is changed according to the effect of marginal deformations, as expected from known results in CFT. These results suggest that the vacuum energy is zero for the identity-based marginal solutions in the original theory.

ONE-LOOP VACUUM ENERGY AT THE TACHYON VACUUM

We consider one-loop vacuum energy at the tachyon vacuum in cubic bosonic open string field theory. The BRST operator Ql in the theory around an identity-based solution is believed to represent a kinetic operator at the tachyon vacuum. Using homotopy operators for Ql, we find that one-loop vacuum energy at the tachyon vacuum is independent of moduli such as interbrane distances. This result can be interpreted as support for the annihilation of D-branes at the tachyon vacuum even in the quantum theory.

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.