arXiv subjects

Tomohiko Takahashi

Publications and source records attributed to Tomohiko Takahashi.

At least 19 recordsLinked to original sources

arXiv2026

Graviton vertex operators in the de Donder gauge and BRST descent

We revisit the role of the trace sector of the graviton in covariant string amplitudes by constructing the ghost-number-three graviton vertex operator via BRST descent, imposing only the de Donder gauge condition without requiring tracelessness. The resulting operator is well defined even at zero momentum, while for nonzero momentum the trace-dependent sector of the descent chain forms a trivial BRST descent chain. Evaluating its disk one-point function in the presence of a D$p$-brane, we show that the trace-dependent term is essential for reproducing the correct graviton-brane coupling, canceling the Dirichlet-direction contributions and leaving the expected coupling to the world-volume components.

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arXiv2026

Vertex Operators in Superstring Theory from Integral Forms and Descent Equations

We develop a geometric formulation of vertex operators in superstring theory based on integral forms on super Riemann surfaces. Starting from the integrated NS-NS vertex operator, we derive descent equations that relate operators with different ghost and picture numbers. A key result is a correspondence between supergeometric objects and ghost superfields, in which the one-form $dz-θdθ$ and the even differential $dθ$ are identified with the ghost superfield and its superderivative. This provides a geometric realization of the superghost structure. We further extend the construction by incorporating inverse picture-changing operators, which generate new descent sequences across different picture sectors. We also introduce a superfield construction of higher-ghost-number operators, for which additional terms are required compared to the bosonic case. All operators are organized into a universal descent structure and are well-defined in BRST cohomology.

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arXiv2024

Closed string vertex operators with various ghost number

We construct closed string vertex operators with various ghost numbers in addition to the conventional ones, using the Faddeev-Popov procedure for the gauge fixing of the conformal Killing group, from matter primary fields. We find that these operators give solutions to the descent equations in the framework of the BRST formalism. Similarly, we also construct solutions to the descent equations for the dilaton vertex operator with the Lorentz covariant form. Using the unintegrated vertex operator of the dilaton with the ghost number three, we obtain the correct result of the tadpole amplitude on the disk, including a non-zero contribution from a BRST exact term which comes from a conformal transformation.

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arXiv2024

Two-point closed string amplitudes in the BRST formalism

Two-point tree-level amplitudes in bosonic closed string theory are described by a correlation function within the BRST formalism, which respects manifest Lorentz and conformal invariance. In the derivation of the two-point amplitudes, we use the mostly BRST exact operator, which has been introduced for two-point open string amplitudes, and a closed string vertex with ghost number three, which has been explored in our recent work, in addition to the conventional one.

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arXiv2021

The Veneziano Amplitude via Mostly BRST Exact Operator

The Veneziano amplitude is derived from fixing one degree of freedom of $PSL(2,\mathbb{R})$ symmetry by the insertion of a mostly BRST exact operator. Evaluating the five-point function which consists of four open string tachyons and this gauge fixing operator, we find it equals the Veneziano amplitude up to a sign factor. The sign factor is interpreted as a signed intersection number.The result implies that the mostly BRST exact operator, which is originally used to provide two-point string amplitudes, correctly fixes the $PSL(2,\mathbb{R})$ gauge symmetry for general amplitudes. We conjecture an expression for general $n$-point tree amplitudes with an insertion of this gauge fixing operator.

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arXiv2021

Reduction of Open String Amplitudes by Mostly BRST Exact Operators

We study two and three-point tree-level amplitudes of open strings. These amplitudes are reduced from higher-point correlation functions by using mostly BRST exact operators for gauge fixing. For simplicity, we focus on an open string tachyon. The two-point amplitude of open string tachyons is reduced from a three-point function of two tachyon vertex operators and one mostly BRST exact operator. Similarly the three-point amplitude is from a four-point function of three tachyon vertex operators and one mostly BRST exact operator. One can also obtain the two-point amplitude from the four-point function of two tachyon vertex operators and two mostly BRST exact operators. In these derivation from four-point functions, moduli integrals are significant. We discuss the overall signs of amplitudes which are indefinite in this formalism.

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arXiv2020

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(1,1) 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.

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arXiv2020

Supersymmetric nonlinear sigma models as anomalous gauge theories

We revisit supersymmetric nonlinear sigma models on the target manifold $CP^{N-1}$ and $SO(N)/SO(N-2)\times U(1)$ in four dimensions. These models are formulated as gauged linear models, but it is indicated that the Wess-Zumino term should be added to the linear model since the hidden local symmetry is anomalous. Applying a procedure used for quantization of anomalous gauge theories to the nonlinear models, we determine the form of the Wess-Zumino term, by which a global symmetry in the linear model becomes smaller in the action than the conventional one. Moreover, we analyze the resulting linear model in the $1/N$ leading order. Consequently, we find that the model has a critical coupling constant similar to bosonic models. In the weak coupling regime, the $U(1)$ local symmetry is broken but supersymmetry is never broken. In contrast to the bosonic case, it is impossible to find stable vacua in the strong coupling regime as far as in the $1/N$ leading order. These results are straightforwardly generalized to the case of the hermitian symmetric space.

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arXiv2019

Two-point String Amplitudes Revisited by Operator Formalism

So far we have considered that a two-point string amplitude vanishes due to the infinite volume of residual gauge symmetry. However recently Erbin-Maldacena-Skliros have suggested that the two-point amplitude can have non-zero value, because one can cancel the infinite volume by the infinity coming from on-shell energy conservation. They derived the two-point function by Fadeev-Popov method. In this paper we revisit this two-point string amplitude in the operator formalism. We find the mostly BRST exact operator which yields non-zero two-point amplitudes.

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arXiv2019

Vector profile and gauge invariant observables of string field theory solutions for constant magnetic field background

We study profiles and gauge invariant observables of classical solutions corresponding to a constant magnetic field on a torus in open string field theory. We numerically find that the profile is not discontinuous on the torus, although the solution describes topologically nontrivial configurations in the context of low energy effective theory. From the gauge invariant observables, we show that the solution provide correct couplings of closed strings to a D-brane with constant magnetic field.

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arXiv2019

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.

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arXiv2017

String field theory solution corresponding to constant background magnetic field

Following the method recently proposed by Erler and Maccaferri, we construct solutions to the equation of motion of Witten's cubic string field theory, which describe constant magnetic field background. We study the boundary condition changing operators relevant to such background and calculate the operator product expansions of them. We obtain solutions whose classical action coincide with the Born-Infeld action.

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arXiv2015

Open String Fields as Matrices

We show that the action expanded around Erler-Maccaferri's N D-brane solution describes the N+1 D-brane system where one D-brane disappears due to tachyon condensation. String fields on multi-branes can be regarded as block matrices of a string field on a single D-brane in the same way as matrix theories.

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arXiv2014

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.

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arXiv2014

Comments on Observables for Identity-Based Marginal Solutions in Berkovits' Superstring Field Theory

We construct an analytic solution for tachyon condensation around identity-based marginal solutions in Berkovits' WZW-like open superstring field theory. Using this, which is a kind of wedge-based solution, the gauge invariant overlaps for the identity-based marginal solutions can be calculated analytically. This is a straightforward extension of a method in bosonic string field theory, which has been elaborated by the authors, to superstring. We also comment on a gauge equivalence relation between the tachyon vacuum solution and its marginally deformed one. From this viewpoint, we can find the vacuum energy of the identity-based marginal solutions to be zero, which agrees with the previous result as a consequence of $ξ$ zero mode counting.

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arXiv2013

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.

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arXiv2013

Gauge Invariant Overlaps for Identity-Based Marginal Solutions

We investigate identity-based solutions associated with marginal deformations in open string field theory. We find that the identity-based marginal solutions can be represented as a difference of wedge-based solutions plus an integration of a deformed BRST exact state. Using this expression, the gauge invariant overlap can be calculated analytically for the identity-based solutions. Moreover, we show that, by gauge transformation, the overlap is transformed into a disk correlation function with the integrations of currents at the boundary.

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arXiv2013

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.

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