arXiv subjects

Yuji Okawa

Publications and source records attributed to Yuji Okawa.

At least 19 recordsLinked to original sources

arXiv2025

The LSZ reduction formula from homotopy algebras

When we describe string field theory or quantum field theory in terms of homotopy algebras, on-shell scattering amplitudes at the tree level are obtained by the formula based on the minimal model. While this formula can be extended to loop amplitudes and it generates the correct set of Feynman diagrams, the evaluation of each Feynman diagram may fail to be well defined because of mass renormalization. Furthermore, this formula does not explain why we use Feynman propagators in loops. In this paper we first present the LSZ reduction formula in terms of quantum $A_\infty$ algebras, which provides a well-defined prescription for loop amplitudes. We then present a formula for connected correlation functions based on quantum $A_\infty$ algebras, and we use it to discuss the relation between the LSZ reduction formula and the extension of the minimal model to loop amplitudes.

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arXiv2024

Nonperturbative correlation functions from homotopy algebras

The formula for correlation functions based on quantum $A_\infty$ algebras in arXiv:2203.05366, arXiv:2305.11634, and arXiv:2305.13103 requires us to divide the action into the free part and the interaction part. We present a new form of the formula which does not involve such division. The new formula requires us to choose a solution to the equations of motion which does not have to be real, and we claim that the formula gives correlation functions evaluated on the Lefschetz thimble associated with the solution we chose. Our formula correctly reproduces correlation functions in perturbation theory, but it can be valid nonperturbatively, and we present numerical evidence for scalar field theories in zero dimensions both in the Euclidean case and the Lorentzian case that correlation functions for finite coupling constants can be reproduced. When the theory consists of a single Lefschetz thimble, our formula gives correlation functions of the theory by choosing the solution corresponding to the thimble. When the theory consists of multiple Lefschetz thimbles, we need to evaluate the ratios of the partition functions for those thimbles and we describe a method of such evaluations based on quantum $A_\infty$ algebras in a forthcoming paper.

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arXiv2023

Correlation Functions Involving Dirac Fields from Homotopy Algebras I: The Free Theory

We extend the formula for correlation functions of scalar field theories in terms of quantum $A_{\infty}$ algebras, presented in arXiv:2203.05366, to incorporate Dirac fields. We use a description that is analogous to string field theory, and the formula for correlation functions takes the same form for both scalar fields and Dirac fields. We prove that correlation functions from our formula satisfy the Schwinger-Dyson equations in the free theory. The proof for interacting theories is presented in the companion paper arXiv:2305.13103 by one of the authors. We also explain the relation of our formula to the definition of correlation functions in the approach by Costello and Gwilliam based on factorization algebras.

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arXiv2022

Closed string field theory without the level-matching condition

In formulating covariant closed string field theories, we have always used closed string fields with the level-matching condition. Recently, open superstring field theories including the Ramond sector were constructed, and one approach was to use open superstring fields with a constraint analogous to the level-matching condition for closed string fields. There is another approach developed by Sen, where no constraints are imposed on open superstring fields but additional free string fields are introduced so that covariant kinetic terms for the Ramond sector were constructed. Motivated by this development, we construct closed string field theory without imposing the level-matching condition on the closed string field, while we introduce an additional free string field. This is the first implementation of general covariance in the context of string theory without using the level-matching condition. We explicitly expand the string fields up to the level relevant to massless fields, and we confirm the equivalence to the theory with the level-matching condition up to decoupled free fields.

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arXiv2022

Correlation functions of scalar field theories from homotopy algebras

We present expressions for correlation functions of scalar field theories in perturbation theory using quantum $A_\infty$ algebras. Our expressions are highly explicit and can be used for theories both in Euclidean space and in Minkowski space including quantum mechanics. Correlation functions at a given order of perturbation theory can be calculated algebraically without using canonical quantization or the path integral, and we demonstrate it explicitly for $\varphi^3$ theory. We show that the Schwinger-Dyson equations are satisfied as an immediate consequence of the form of the expressions based on quantum $A_\infty$ algebras.

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arXiv2020

Nonperturbative definition of closed string theory via open string field theory

In typical examples of the AdS/CFT correspondence, the world-sheet theory with holes in the presence of D-branes is assumed to be equivalent in a low-energy limit to a world-sheet theory without holes for a different background such as $AdS_5 \times S^5$. In the case of the bosonic string, we claim under the assumption of this equivalence that open string field theory on $N$ coincident D-branes can be used to provide a nonperturbative definition of closed string theory based on the fact that the $1/N$ expansion of correlation functions of gauge-invariant operators reproduces the world-sheet theory with holes where the moduli space of Riemann surfaces is precisely covered.

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arXiv2020

Gauge-invariant operators of open bosonic string field theory in the low-energy limit

In the AdS/CFT correspondence we consider correlation functions of gauge-invariant operators on the gauge theory side, which we obtain in the low-energy limit of the open string sector. To investigate this low-energy limit we consider the action of open bosonic string field theory including source terms for gauge-invariant operators and classically integrate out massive fields to obtain the effective action for massless fields. While the gauge-invariant operators depend linearly on the open string field and do not resemble the corresponding operators such as the energy-momentum tensor in the low-energy limit, we find that nonlinear dependence is generated in the process of integrating out massive fields. We also find that the gauge transformation is modified in such a way that the effective action and the modified gauge transformation can be written in terms of the same set of multi-string products which satisfy weak $A_\infty$ relations, and we present explicit expressions for the multi-string products.

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arXiv2018

Open superstring field theory based on the supermoduli space

We present a new approach to formulating open superstring field theory based on the covering of the supermoduli space of super-Riemann surfaces and explicitly construct a gauge-invariant action in the Neveu-Schwarz sector up to quartic interactions. The cubic interaction takes a form of an integral over an odd modulus of disks with three punctures and the associated ghost is inserted. The quartic interaction takes a form of an integral over one even modulus and two odd moduli, and it can be interpreted as the integral over the region of the supermoduli space of disks with four punctures which is not covered by Feynman diagrams with two cubic vertices and one propagator. As our approach is based on the covering of the supermoduli space, the resulting theory naturally realizes an $A_\infty$ structure, and the two-string product and the three-string product used in defining the cubic and quartic interactions are constructed to satisfy the $A_\infty$ relations to this order.

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arXiv2016

Fermion scattering amplitudes from gauge-invariant actions for open superstring field theory

We calculate on-shell scattering amplitudes involving fermions at the tree level in open superstring field theory. We confirm that four-point and five-point amplitudes in the world-sheet path integral with the standard prescription using picture-changing operators are reproduced. For the four-point amplitudes, we find that the quartic interaction required by gauge invariance adjusts the different assignment of picture-changing operators in the $s$-channel and in the $t$-channel of Feynman diagrams with two cubic vertices. For the five-point amplitudes, the correct amplitudes are reproduced in a more intricate way via the quartic and quintic interactions. Our calculations can be interpreted as those for a complete action with a constraint on the Ramond sector or as those for the covariant formulation developed by Sen with spurious free fields.

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arXiv2016

Complete Action for Open Superstring Field Theory with Cyclic $A_\infty$ Structure

We construct a gauge invariant action for the Neveu-Schwarz and Ramond sectors of open superstring field theory realizing a cyclic $A_\infty$ structure, providing the first complete and fully explicit solution to the classical Batalin-Vilkovisky master equation in superstring field theory. We also demonstrate the equivalence of our action to the Wess-Zumino-Witten-based construction of Kunitomo and one of the authors.

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arXiv2016

Complete action for open superstring field theory

We construct a complete action for open superstring field theory that includes the Neveu-Schwarz sector and the Ramond sector. For the Neveu-Schwarz sector, we use the string field in the large Hilbert space of the superconformal ghost sector, and the action in the Neveu-Schwarz sector is the same as the Wess-Zumino-Witten-like action of the Berkovits formulation. For the Ramond sector, it is known that the BRST cohomology on an appropriate subspace of the small Hilbert space reproduces the correct spectrum, and we use the string field projected to this subspace. We show that the action is invariant under gauge transformations that are consistent with the projection for the string field in the Ramond sector.

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arXiv2015

$A_\infty$ structure from the Berkovits formulation of open superstring field theory

By formulating open superstring field theory based on the small Hilbert space of the superconformal ghost sector, an action for the Neveu-Schwarz sector with an $A_\infty$ structure has recently been constructed. We transform this action to the Wess-Zumino-Witten-like form and show that this theory is related to the Berkovits formulation of open superstring field theory based on the large Hilbert space by partial gauge fixing and field redefinition.

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arXiv2014

From the Berkovits formulation to the Witten formulation in open superstring field theory

The Berkovits formulation of open superstring field theory is based on the large Hilbert space of the superconformal ghost sector. We discuss its relation to the Witten formulation based on the small Hilbert space. We introduce a one-parameter family of conditions for partial gauge fixing of the Berkovits formulation such that the cubic interaction of the theory under the partial gauge fixing reduces to that of the Witten formulation in a singular limit. The local picture-changing operator at the open-string midpoint in the Witten formulation is regularized in our approach, and the divergence in on-shell four-point amplitudes coming from collision of picture-changing operators is resolved. The quartic interaction inherited from the Berkovits formulation plays a role of adjusting different behaviors of the picture-changing operators in the $s$ channel and in the $t$ channel of Feynman diagrams with two cubic vertices, and correct amplitudes in the world-sheet theory are reproduced. While gauge invariance at the second order in the coupling constant is obscured in the Witten formulation by collision of picture-changing operators, it is well defined in our approach and is recovered by including the quartic interaction inherited from the Berkovits formulation.

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arXiv2013

Gauge-invariant observables and marginal deformations in open string field theory

The level-truncation analysis of open string field theory for a class of periodic marginal deformations indicates that a branch of solutions in Siegel gauge exists only for a finite range of values of the marginal field. The periodicity in the deformation parameter is thus obscure. We use the relation between gauge-invariant observables and the closed string tadpole on a disk conjectured by Ellwood to construct a map between the deformation parameter of the boundary conformal field theory and the parameter labeling classical solutions of open string field theory. We evaluate the gauge-invariant observables for the numerical solutions in Siegel gauge up to level 12 and find that our results qualitatively agree with the analysis by Sen using the energy-momentum tensor and are consistent with the picture that the finite range of the branch covers one fundamental domain of the periodic moduli space.

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arXiv2012

Open superstring field theory I: gauge fixing, ghost structure, and propagator

The WZW form of open superstring field theory has linearized gauge invariances associated with the BRST operator Q and the zero mode eta_0 of the picture minus-one fermionic superconformal ghost. We discuss gauge fixing of the free theory in a simple class of gauges using the Faddeev-Popov method. We find that the world-sheet ghost number of ghost and antighost string fields ranges over all integers, except one, and at any fixed ghost number, only a finite number of picture numbers appear. We calculate the propagators in a variety of gauges and determine the field-antifield content and the free master action in the Batalin-Vilkovisky formalism. Unlike the case of bosonic string field theory, the resulting master action is not simply related to the original gauge-invariant action by relaxing the constraint on the ghost and picture numbers.

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arXiv2011

Solutions from boundary condition changing operators in open superstring field theory

We construct analytic solutions of open superstring field theory in the Berkovits formulation using boundary condition changing operators under some regularity conditions, extending the previous construction in the bosonic string. We also consider the gauge-invariant observables corresponding to closed string one-point functions on the disk. We analytically calculate the gauge-invariant observables for the solutions both in the bosonic string and in the superstring and find the expected change of boundary conditions of the disk.

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arXiv2011

Solutions from boundary condition changing operators in open string field theory

We construct analytic solutions of open string field theory using boundary condition changing (bcc) operators. We focus on bcc operators with vanishing conformal weight such as those for regular marginal deformations of the background. For any Fock space state phi, the component string field of the solution Psi exhibits a remarkable factorization property: it is given by the matter three-point function of phi with a pair of bcc operators, multiplied by a universal function that only depends on the conformal weight of phi. This universal function is given by a simple integral expression that can be computed once and for all. The three-point functions with bcc operators are thus the only needed physical input of the particular open string background described by the solution. We illustrate our solution with the example of the rolling tachyon profile, for which we prove convergence analytically. The form of our solution, which involves bcc operators instead of explicit insertions of the marginal operator, can be a natural starting point for the construction of analytic solutions for arbitrary backgrounds.

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arXiv2008

The boundary state from open string fields

We construct a class of BRST-invariant closed string states for any classical solution of open string field theory. The closed string state is a nonlinear functional of the open string field and changes by a BRST-exact term under a gauge transformation of the solution. As a result, its contraction with an on-shell closed string state provides a gauge-invariant observable of open string field theory. Unlike previously known observables, however, the contraction with off-shell closed string states in the Fock space is well defined and regular. Moreover, we claim that the BRST-invariant closed string state coincides, up to a possible BRST-exact term, with the boundary state of the boundary conformal field theory which the solution is expected to describe. Our construction requires a choice of a propagator strip. If we choose the Schnabl propagator strip, the BRST-invariant state becomes explicitly calculable. We calculate it for various known analytic solutions of open string field theory and, remarkably, we find that it precisely coincides with the boundary state without any additional BRST-exact term. Our results imply, in particular, that the wildly oscillatory rolling tachyon solution of open string field theory actually describes the regular closed string physics studied by Sen using the boundary state.

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