Open String Field Theory Research Articles

Open String Renormalization Group Flow as a Field Theory

AbstractThis article shows that the integral flow‐lines of the RG‐flow of open string theory can be interpreted as the solitons of a Hořova–Lifshitz sigma‐model of open membranes. The authors argue that the effective background description of this model implies the g‐theorem of open string theory. Its close connection to boundary string field theory is described. Additionally, the study endows the Hilbert space of the open membrane with a graded non‐commutative, associative, cyclic algebra and construct an open membrane field theory, whose action measures the energy difference between different backgrounds in open string field theory. The authors use an identity‐based membrane field to proof Sen's conjecture. Finally, the ideas are applied to the topological string and it is shown that the membrane action is quantized in equivariant K‐theory of the moduli space of framed instantons.

Open string stub as an auxiliary string field

Witten’s open string field theory with a generalized version of stubs is reformulated as a cubic string field theory using an auxiliary string field. The gauge symmetries and equations of motion as well as the associative algebra of the resulting theory are investigated. Integrating out either the original or auxiliary field is shown to recover the conventional cubic theory. Our analysis demonstrates that deformations due to the stubs can be described as a homotopy transfer purely in the context of strong deformation retract. We also discuss to what extent the vertex regions resulting from stubs provide a model for the elementary interactions of closed string field theory.

On democratic string field theories

We reexamine democratic open string field theories, namely, theories in which string fields are not constrained to a single picture number and picture changing is obtained as a gauge transformation. We describe several possibilities for regular free theories and attempt to construct the lowest order interaction term and identify the lowest order gauge transformation for some of these theories. We also discuss projections over string field spaces that might be needed for a consistent off-shell implementation of picture changing.

A stringy effect on Hawking radiation

In string theories, interactions are exponentially suppressed for trans-Planckian space-like external momenta. We study a class of quantum field theories that exhibit this feature modeled after Witten’s bosonic open string field theory, and discover a Lorentz-invariant UV/IR relation that leads to the spacetime uncertainty principle proposed by Yoneya. Application to a dynamical black hole background suggests that Hawking radiation is turned off around the scrambling time.

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.

Open string field theory with stubs

There are various reasons why adding stubs to the vertices of open string field theory (OSFT) is interesting: the stubs can not only tame certain singularities and make the theory more well-behaved, but also the new theory shares a lot of similarities with closed string field theory, which helps to improve our understanding of its structure and possible solutions. In this paper we explore two natural ways of implementing stubs into the framework of OSFT, resulting in an A∞-algebra giving rise to infinitely many vertices. We find two distinct consistent actions, both generated by a field redefinition, interestingly sharing the same equations of motion. In the last section we illustrate their relationship and physical meaning by applying our construction to nearly marginal solutions.

Boundary states in the SU(2)k WZW model from open string field theory

We analyze boundary states in the SU(2)k WZW model using open string field theory in the level truncation approximation. We develop algorithms that allow effective calculation of the action in this model and we search for classical solutions of the equations of motion, which are conjectured to describe boundary states. We find three types of solutions. First, there are real solutions that represent maximally symmetric Cardy boundary states and we show that they satisfy certain selection rules regarding their parameters. Next, we find complex solutions that go beyond the SU(2) model and describe maximally symmetric SL(2, ℂ) boundary conditions. Finally, we find exotic solutions that correspond to symmetry-breaking boundary states. Most of real exotic solutions describe the so-called B-brane boundary states, but some may represent yet unknown boundary states.

Generating string field theory solutions with matter operators from KBc algebra

Abstract The KBc algebra is a subalgebra that has been used to construct classical solutions in Witten’s open string field theory, such as the tachyon vacuum solution. The main purpose of this paper is to give various operator sets that satisfy the KBc algebra. In addition, since those sets can contain matter operators arbitrarily, we can reproduce the solution of Kiermaier, Okawa, and Soler, and that of Erler and Maccaferri. Starting with a single D-brane solution on the tachyon vacuum, we replace the original KBc in it with an appropriate set to generate each of the above solutions. Thus, it is expected that the KBc algebra, combined with the single D-brane solution, leads to a more unified description of classical solutions.

Large N phenomena and quantization of the Loday-Quillen-Tsygan theorem

We offer a new approach to large N limits using the Batalin-Vilkovisky formalism, both commutative and noncommutative, and we exhibit how the Loday-Quillen-Tsygan Theorem admits BV quantizations in that setting. Matrix integrals offer a key example: we demonstrate how this formalism leads to a recurrence relation that in principle allows us to compute all multi-trace correlation functions. We also explain how the Harer-Zagier relations may be expressed in terms of this noncommutative geometry derived from the BV formalism.As another application, we consider the problem of quantization in the large N limit and demonstrate how the Loday-Quillen-Tsygan Theorem leads us to a solution in terms of noncommutative geometry. These constructions are relevant to open topological field theories and string field theory, providing a mechanism that relates moduli of categories of branes to moduli of brane gauge theories.

BRST ghost-vertex operator in Witten's cubic open string field theory on multiple Dp-branes

The Becchi–Rouet–Stora–Tyutin (BRST) ghost field is a key element in constructing Witten's cubic open string field theory. However, to date, the ghost sector of the string field theory has not received a great deal of attention. In this study, we address the BRST ghost on multiple Dp-branes, which carries non-Abelian indices and couples to a non-Abelian gauge field. We found that the massless components of the BRST ghost field can play the role of the Faddeev–Popov ghost in the non-Abelian gauge field, such that the string field theory maintains the local non-Abelian gauge invariance.

Witten’s cubic open string field theory on multiple Dp-branes

We study Witten's cubic open string field theory on multiple $Dp$-branes. On multiple $Dp$-branes the string fields carry $U(N)$ group indices. Mapping the string world-sheet onto the upper half complex plane and evaluating the Polyakov string path integral of Witten's cubic open string, we obtain a Fock space representation of one, two and three-string vertex operators. In the low energy region, the system is described by massless gauge fields and massless scalar fields, carrying $U(N)$ group indices. The two-string vertex induces mass terms for the gauge fields and the scalar fields. The cubic interaction reduces correctly to the cubic term of the non-Abelian gauge fields, cubic interaction terms of the gauge fields, and the scalar fields on $(p+1)$ dimensional space. Thus, Witten's string field theory may be a useful tool to study the quantum dynamics of open strings on multiple $Dp$-branes.

The Riemann hypothesis and tachyonic off-shell string scattering amplitudes

The study of the mathbf{4}-tachyon off-shell string scattering amplitude A_4 (s, t, u) , based on Witten’s open string field theory, reveals the existence of poles in the s-channel and associated to a continuum of complex “spins” J. The latter J belong to the Regge trajectories in the t, u channels which are defined by - J (t) = - 1 - { 1over 2 } t = beta (t)= { 1over 2 } + i lambda ; - J (u) = - 1 - { 1over 2 } u = gamma (u) = { 1over 2 } - i lambda , with lambda = real. These values of beta ( t ), gamma (u) given by { 1over 2 } pm i lambda , respectively, coincide precisely with the location of the critical line of nontrivial Riemann zeta zeros zeta (z_n = { 1over 2 } pm i lambda _n) = 0. It is argued that despite assigning angular momentum (spin) values J to the off-shell mass values of the external off-shell tachyons along their Regge trajectories is not physically meaningful, their net zero-spin value J ( k_1 ) + J (k_2) = J ( k_3 ) + J ( k_4 ) = 0 is physically meaningful because the on-shell tachyon exchanged in the s-channel has a physically well defined zero-spin. We proceed to prove that if there were nontrivial zeta zeros (violating the Riemann Hypothesis) outside the critical line Real~ z = 1/2 (but inside the critical strip) these putative zeros don't correspond to any poles of the mathbf{4}-tachyon off-shell string scattering amplitude A_4 (s, t, u) . We finalize with some concluding remarks on the zeros of sinh(z) given by z = 0 + i 2 pi n, continuous spins, non-commutative geometry and other relevant topics.

Erratum to: Proof of new S-matrix formula from classical solutions in open string field theory: Or, deriving on-shell open string field amplitudes without using Feynman rules, Part II

Erratum to: Proof of new S-matrix formula from classical solutions in open string field theory: Or, deriving on-shell open string field amplitudes without using Feynman rules, Part II

Open String Field Theory Beyond Feynman Diagrams

Theoretical physicists propose an alternative way of performing perturbative calculations in an open string field theory that has no analogy in the standard quantum field theory formalism.

Initial value problem in string-inspired nonlocal field theory

We consider a nonlocal scalar field theory inspired by the tachyon action in open string field theory. The Lorentz-covariant action is characterized by a parameter ξ2 that quantifies the amount of nonlocality. Restricting to purely time-dependent configurations, we show that a field redefinition perturbative in ξ2 reduces the action to a local two-derivative theory with a ξ2-dependent potential. This picture is supported by evidence that the redefinition maps the wildly oscillating rolling tachyon solutions of the nonlocal theory to conventional rolling in the new scalar potential. For general field configurations we exhibit an obstruction to a local Lorentz-covariant formulation, but we can still achieve a formulation local in time, as well as a light-cone formulation. These constructions provide an initial value formulation and a Hamiltonian. Their causality is consistent with a lack of superluminal behavior in the nonlocal theory.

Deriving on-shell open string field amplitudes without using Feynman rules

Abstract We present a series of new gauge-invariant quantities in Witten’s open string field theory. They are defined for a given set of open string states which satisfy the physical state condition around a classical solution. For known classical solutions, we demonstrate that these gauge-invariant quantities compute on-shell tree-level scattering amplitudes around the corresponding D-brane configuration.

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.

Proof of new S-matrix formula from classical solutions in open string field theory: Or, deriving on-shell open string field amplitudes without using Feynman rules, Part II

Abstract We study the relation between the gauge-invariant quantity obtained by T. Masuda and H. Matsunaga (arXiv:1908.09784) and the Feynman diagrams in the dressed $\mathcal {B}_0$ gauge in the open cubic string field theory. We derive a set of recurrence relations that hold among the terms of this gauge-invariant quantity. By using these relations, we prove that this gauge-invariant quantity equals the S-matrix at the tree level. We also present a proof that a set of new Feynman rules proposed by T. Masuda and H. Matsunaga (arXiv:2003.05021) reproduces the on-shell disk amplitudes correctly by using the same combinatorial identities.