arXiv subjects

Hiroaki Matsunaga

Publications and source records attributed to Hiroaki Matsunaga.

14 recordsLinked to original sources

arXiv2026

A Non-local "Boundary'' Term for Two-Point Amplitudes in String Field Theory

We propose a new ``boundary'' term in free bosonic string field theory. Here, the term ``boundary'' refers to a contribution introduced to restore the cyclicity broken by the insertion of a stringy step-function operator, although it is not strictly localized as it involves an operator that selects positive-energy modes. We construct this term as a bilinear form involving the commutator of the BRST operator with the step-function operator. The resulting action has a well-defined variational principle. When evaluated on on-shell string fields, the proposed term reproduces the correct tree-level two-point amplitude for both open and closed strings. We verify this explicitly in the tachyon and massless sectors.

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arXiv2022

Perturbative path-integral of string field and the $A_{\infty }$ structure of the BV master equation

The perturbative path-integral gives a morphism of the (quantum) $A_{\infty }$ structure intrinsic to each quantum field theory, which we show explicitly on the basis of the homological perturbation. As is known, in the BV formalism, any effective action also solves the BV master equation, which implies that the path-integral can be understood as a morphism of the BV differential. Since each solution of the BV master equation is in one-to-one correspondence with a (quantum) $A_{\infty }$ structure, the path-integral preserves this intrinsic $A_{\infty }$ structure of quantum field theory, where $A_{\infty }$ reduces to $L_{\infty }$ whenever multiplications of space-time fields are graded commutative. We apply these ideas to string field theory and (re-)derive some quantities based on the perturbative path-integral, such as effective theories with finite $α^{\prime }$, reduction of gauge and unphysical degrees, $S$-matrix and gauge invariant observables.

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arXiv2021

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.

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arXiv2021

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)

We study relation between the gauge invariant quantity obtained in [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 in [arXiv:2003.05021 [hep-th]] reproduces the onshell disc amplitudes correctly by using the same combinatorial identities.

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arXiv2019

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

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 show that these gauge invariant quantities compute on shell tree-level scattering amplitudes around the correspondent D-brane configuration.

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arXiv2019

Light-cone reduction of Witten's open string field theory

We elucidate some exact relations between light-cone and covariant string field theories on the basis of the homological perturbation lemma for $A_{\infty }$. The covariant string field splits into the light-cone string field and trivial excitations of BRST quartets: The latter generates the gauge symmetry and covariance. We first show that the reduction of gauge degrees can be performed by applying the lemma, which gives a refined version of the no-ghost theorem of covariant strings. Then, we demonstrate that after the reduction, gauge-fixed theory can be regarded as a kind of effective field theory and it provides an exact gauge-fixing procedure taking into account interactions. As a result, a novel light-cone string field theory is obtained from Witten's open string field theory.

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arXiv2018

$A_\infty / L_\infty$ structure and alternative action for WZW-like superstring field theory

We propose new gauge invariant actions for open NS, heterotic NS, and closed NS-NS superstring field theories. They are based on the large Hilbert space, and have Wess-Zumino-Witten-like expressions which are the $\mathbb{Z}_{2}$-reversed versions of the conventional WZW-like actions. On the basis of the procedure proposed in arXiv:1505.01659, we show that our new WZW-like actions are completely equivalent to $A_{\infty }/L_{\infty }$ actions proposed in arXiv:1403.0940 respectively.

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arXiv2018

Notes on the Wess-Zumino-Witten-like structure: $L_{\infty }$ triplet and NS-NS superstring field theory

In the NS-NS sector of superstring field theory, there potentially exist three nilpotent generators of gauge transformations and two constraint equations: It makes the gauge algebra of type II theory somewhat complicated. In this paper, we show that every NS-NS actions have their WZW-like forms, and that a triplet of mutually commutative $L_{\infty }$ products completely determines the gauge structure of NS-NS superstring field theory via its WZW-like structure. We give detailed analysis about it and present its characteristic properties by focusing on two NS-NS actions proposed by arXiv:1512.03379 and arXiv:1403.0940.

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arXiv2018

On the BV formalism of open superstring field theory in the large Hilbert space

We construct several BV master actions for open superstring field theory in the large Hilbert space. First, we show that a naive use of the conventional BV approach breaks down at the third order of the antifield number expansion, although it enables us to define a simple "string antibracket" taking the Darboux form as space-time antibrackets. This fact implies that in the large Hilbert space, "string fields-antifields" should be reassembled to obtain master actions in a simple manner. We determine the assembly of the string antifields on the basis of Berkovits' constrained BV approach, and give solutions to the master equation defined by Dirac antibrackets on the constrained string field-antifield space. It is expected that partially gauge-fixing enables us to relate superstring field theories based on the large and small Hilbert spaces directly: Reassembling string fields-antifields is rather natural from this point of view. Finally, inspired by these results, we revisit the conventional BV approach and construct a BV master action based on the minimal set of string fields-antifields.

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arXiv2018

Nonlinear gauge invariance and WZW-like action for NS-NS superstring field theory

We complete the construction of a gauge-invariant action for NS-NS superstring field theory in the large Hilbert space begun in arXiv:1305.3893 by giving a closed-form expression for the action and nonlinear gauge transformations. The action has the WZW-like form and vertices are given by a pure-gauge solution of heterotic string field theory in the small Hilbert space.

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arXiv2018

Comments on complete actions for open superstring field theory

We clarify a Wess-Zumino-Wtten-like structure including Ramond fields and propose one systematic way to construct gauge invariant actions: Wess-Zumino-Witten-like complete action $S_{\rm WZW}$. We show that Kunitomo-Okawa's action proposed in arXiv:1508.00366 can obtain a topological parameter dependence of Ramond fields and belongs to our WZW-like framework. In this framework, once a WZW-like functional $\mathcal{A}_{η} = \mathcal{A}_{η} [Ψ]$ of a dynamical string field $Ψ$ is constructed, we obtain one realization of $S_{\rm WZW}$ parametrized by $Ψ$. On the basis of this way, we construct an action $\widetilde{S}$ whose on-shell condition is equivalent to the Ramond equations of motion proposed in arXiv:1506.05774. Using these results, we provide the equivalence of two these theories: arXiv:1508.00366 and arXiv:1506.05774.

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arXiv2018

Hidden gauge reducibility of superstring field theory and Batalin-Vilkovisky master action

In this paper, we show that there exists a hidden gauge reducibility in superstring field theory based on the small dynamical string field $Ψ\in \mathcal{H}_{βγ}$ whose gauge variation is also small $δΨ\in \mathcal{H}_{βγ}$. It requires additional ghost-antighost fields in the gauge fixed or quantum gauge theory, and thus changes the Batalin-Vilkovisky master action, which implies that additional propagating degrees of freedom appear in the loop superstring amplitudes via the gauge choice of the field theory. We present that the resultant master action can take a different and enlarged form, and that there exist canonical transformations getting it back to the canonical form. On the basis of the Batalin-Vilkovisky formalism, we obtain several exact results and clarify this underlying gauge structure of superstring field theory.

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arXiv2015

On-shell equivalence of two formulations for superstring field theory

In this paper we derive the condition providing the on-shell equivalence of $L_{\infty}$-type and WZW-like formulations for superstring field theory. We construct the NS string products $L= \{L_{n}\}_{n=1}^{\infty}$ of $L_{\infty}$-type formulation and the shifted BRST operator $Q_{\mathcal{G}}$ in WZW-like formulation by the similarity transformations of the BRST operator $Q$. Utilizing the similarity transformations, we can consider a morphism connecting the $L_{\infty}$-algebras on both sides. It naturally induces the field redefinitions and guarantees the equivalence of the on-shell conditions in two formulations. In addition, we have confirmed up to quartic order that the on-shell equivalence condition also provides the off-shell equivalence. Then partial-gauge-fixing conditions giving $L_{\infty}$-relations in WZW-like formulation naturally appear.

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arXiv2013

Construction of a Gauge-Invariant Action for Type II Superstring Field Theory

We construct a gauge-invariant action for covariant type II string field theory in the NS-NS sector. Our construction is based on the large Hilbert space description and Zwiebach's string products are used. First, we rewrite the action for bosonic string field theory into a new form where a state in the kernel of the generator of the gauge transformation appears explicitly. Then we use the same strategy and write down our type II action, where a projector onto the small Hilbert space plays an important role. We present lower-order terms up to quartic order and show that three-point amplitudes are reproduced correctly.

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