arXiv subjects

Machiko Hatsuda

Publications and source records attributed to Machiko Hatsuda.

At least 19 recordsLinked to original sources

arXiv2026

Mega-Space Current Algebra and Green-Schwarz Geometry in Heterotic String Theory

We study the Lorentz and gauge connections in heterotic string theories within a framework of manifest T-duality. A central motivation is the Bergshoeff--de Roo (BdR) type parallelism between the torsionful Lorentz and Yang-Mills connections in heterotic $\alpha'$-corrections. We formulate worldsheet current algebras in a mega-space that incorporates the Lorentz and gauge sectors simultaneously. By generalizing the Pol\'a\v{c}ek-Siegel scheme, we evaluate the commutators of the extended generators and determine the generalized connections. We show that this mega-space current algebra geometrically embeds the heterotic Chern--Simons structures into the generalized vielbeins and curvatures. We also show that the Green-Schwarz anomaly cancellation condition follows from the Jacobi identity for the algebra of stringy covariant derivatives, the ``nachos'' operators $\triangleright_{\mathcal{M}}$.

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arXiv2026

Gauss law constraint in A-theory branes

A-theory realizes U-duality symmetry by extending the string worldsheet to a higher dimensional brane worldvolume, in which the worldvolume and the spacetime belong to different representations of the exceptional group. The closure of the brane Virasoro algebra requires the Gauss law constraint. The Gauss law constraint promotes spacetime coordinates to gauge fields and extends the string worldsheet into the brane worldvolume. While the Virasoro constraint is used to reduce the spacetime coordinate, the Gauss law constraint is used to reduce both the worldvolume and the spacetime coordinates. As in conventional gauge theories, the treatment of the Gauss law constraint is a technically important aspect of the quantization of A-theory. We show that the string solution is only consistent solution of the Gauss law dimensional reduction condition for D=3 and 4 cases. This result implies that the physical symmetry of the theory is two-dimensional conformal symmetry, suggesting that the theory admits a string-like quantization. We further construct a string solution that is covariant under the exceptional group symmetry. The relation between this solution and the constant charge parameter appearing in the exceptional {\sigma}-model is also discussed.

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arXiv2025

Strings and membranes from $\mathcal{A}$-theory five brane

The $\mathcal{A}$-theory takes U-duality symmetry as a guiding principle, with the SL(5) U-duality symmetry being described as the world-volume theory of a 5-brane. Furthermore, by unifying the 6-dimensional world-volume Lorentz symmetry with the SL(5) spacetime symmetry, it extends to SL(6) U-duality symmetry. The SL(5) spacetime vielbein fields and the 5-brane world-volume vielbein fields are mixed under the SL(6) U-duality transformation. We demonstrate that consistent sectionings of the SL(6) $\mathcal{A}$5-brane world-volume Lagrangian yield Lagrangians of the ${\cal T}$-string with O(D,D) T-duality symmetry, the conventional string, the $\mathcal{M}$5-brane with GL(4) duality symmetry, and the non-perturbative M2-brane in supergravity theory. The GL(4) covariant Lagrangian of the $\mathcal{M}$5-brane derived in this manner is a new, perturbatively quantizable theory.

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arXiv2023

$\mathcal{A}$-theory: A brane world-volume theory with manifest U-duality

In this paper, the ${\cal A}$-theory, an extension of F-theory, is described as a fully U-duality covariant brane theory. This theory has some distinguishing features not known from world-sheet models. In particular, seen as a sigma model, both world-volume and target space coordinates are specific representations of the same group (the U-duality group). The U-duality group in question is an exceptional group (a split form of the $E_d$ series). The structure of this group allows it to encompass both the T-duality group of string theory as well as the general linear symmetry group of ${\cal M}$-theory. ${\cal A}$-theory is defined by the current algebras in Hamiltonian formalism, or by world-volume actions in Lagrangian formalism. The spacetime coordinates are selfdual gauge fields on the world-volume, requiring the Gauss law constraints tying the world-volume to spacetime. Solving the Gauss law constraints/the Virasoro constraints gives the world-volume/spacetime sectioning from ${\cal A}$-theory to ${\cal T}$-theory/ ${\cal M}$-theory respectively. The ${\cal A}$-theory Lagrangian admits extended symmetry which has not been observed previously in the literature, where the background fields include both the spacetime and the world-volume gravitational fields. We also constructed the four-point amplitude of ${\cal A}$-theory in the low energy limit. The amplitude is written in a way that the U-duality symmetry is manifest, but after solving the section condition, it reduces to the usual four-graviton amplitude. In the previous papers, we have referred to this model as F-theory, however, F-theory initiated by Vafa is now a big branch of string theory as the study of elliptic fibrations, so we refer to these constructions as generalized models of theory for all dimensions with all duality symmetries as ${\cal A}$-theory.

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arXiv2023

Gauged Double Field Theory, Current Algebras and Heterotic Sigma Models

We study the $O(D,D+n)$ generalized metric and the gauge symmetries in the gauged double field theory (DFT) in view of current algebras and sigma models. We show that the $O(D,D+n)$ generalized metric in the gauged DFT is consistent with the heterotic sigma models at the leading order in the $α'$-corrections. We then study the non-Abelian gauge symmetries and current algebras of heterotic string theories. We show that the algebras exhibit the correct diffeomorphism, the $B$-field gauge transformations of the background fields together with the non-Abelian gauge transformations possibly with the appropriate local Lorentz transformations.

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arXiv2022

Open F-branes

We include in F-theory, through open Type I F-theory branes (F-branes), string theories with N = 1 supersymmetry, both Type I and heterotic. Type I branes are distinguished from Type II by worldvolume parity projection. The same open Type I branes describe both open Type I superstrings and closed heterotic upon different sectionings from F-branes to worldsheets, while closed Type I superstrings arise from closed Type I branes. (Type II superstrings come from closed Type II branes, as described previously.) F-theory manifests the exceptional-group U-duality symmetry, with all massless bosonic fields in a single gauge coset. This coset branches to the usual bosonic supergravity fields upon sectioning. We examine in detail the simple case of D = 3 F-theory: Parity projection reduces the Type II coset SL(5)/SO(3,2) to the Type I coset SO(3,3)/SO(2,1)2 = SL(4)/SO(2,2).

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arXiv2021

Perturbative F-theory 10-brane and M-theory 5-brane

The exceptional symmetry is realized perturbatively in F-theory which is the manifest U-duality theory. The SO(5,5) U-duality symmetry acts on both the 16 spacetime coordinates and the 10 worldvolume coordinates. Closure of the Virasoro algebra requires the Gauss law constraints on the worldvolume. This set of current algebras describes a F-theory 10-brane. The SO(5,5) duality symmetry is enlarged to the SO(6,6) in the Lagrangian formulation. We propose actions of the F-theory 10-brane with SO(5,5) and SO(6,6) symmetries. The gauge fields of the latter action is coset elements of SO(6,6)/SO(6;C) which includes both the SO(5,5)/SO(5;C) spacetime backgrounds and the worldvolume backgrounds. The SO(5,5) current algebra obtained from the Pasti-Sorokin-Tonin M5-brane Lagrangian leads to the theory behind M-theory, namely F-theory. We also propose an action of the perturbative M-theory 5-brane obtained by sectioning the worldvolume of the F-theory 10-brane.

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arXiv2021

Five-brane Current Algebras in Type II String Theories

We study the current algebras of the NS5-branes, the Kaluza-Klein (KK) five-branes and the exotic $5^2_2$-branes in type IIA/IIB superstring theories. Their worldvolume theories are governed by the six-dimensional $\mathcal{N}= (2,0)$ tensor and the $\mathcal{N} = (1,1)$ vector multiplets. We show that the current algebras are determined through the S- and T-dualities. The algebras of the $\mathcal{N} = (2,0)$ theories are characterized by the Dirac bracket caused by the self-dual gauge field in the five-brane worldvolumes, while those of the $\mathcal{N} = (1,1)$ theories are given by the Poisson bracket. By the use of these algebras, we examine extended spaces in terms of tensor coordinates which are the representation of ten-dimensional supersymmetry. We also examine the transition rules of the currents in the type IIA/IIB supersymmetry algebras in ten dimensions. Based on the algebras, we write down the section conditions in the extended spaces and gauge transformations of the supergravity fields.

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arXiv2020

T-dual Superstring Lagrangian with double zweibeins

We present superstring Lagrangians with manifest T-duality. The Lagrangian version of the section conditions are necessary to make Lagrangians to be general coordinate invariant. We show the general solution of section conditions. The D-dimensional left and right moving currents are the 2D-dimensional chiral current which causes the chiral boson problem. We solve the problem by adding the unphysical 2D-dimensional anti-selfdual current with the selfduality constraints. The Lagrange multipliers of the selfduality constraints play the role of the worldsheet zweibein allowing the Weyl invariant and Lorentz symmetric worldsheet. Doubling the zweibein makes the type II kappa-symmetry splitting into two sets of the type I kappa-symmetries.

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arXiv2019

O(D,D) gauge fields in the T-dual string Lagrangian

We present the string Lagrangian with manifest T-duality. Not only zero-modes but also all string modes are doubled. The gravitational field is an O(D,D) gauge field. We give a Lagrangian version of the section condition for the gauge invariance which compensates the O(D,D) transformation from the gravitational field and the GL(2D) coordinate transformation. We also show the gauge invariance of the line element of the manifest T-duality space and the O(D,D) condition on the background. Different sections describe dual spaces.

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arXiv2017

Manifestly T-dual formulation of AdS space

We present a manifestly T-dual formulation of curved spaces such as an AdS space. For group manifolds related by the orthogonal vielbein fields the three form H=dB in the doubled space is universal at least locally. We construct an affine nondegenerate doubled bosonic AdS algebra to define the AdS space with the Ramond-Ramond flux. The non-zero commutator of the left and right momenta leads to that the left momentum is in an AdS space while the right momentum is in a dS space. Dimensional reduction constraints and the physical AdS algebra are shown to preserve all the doubled coordinates.

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arXiv2015

Type II chiral affine Lie algebras and string actions in doubled space

We present affine Lie algebras generated by the supercovariant derivatives and the supersymmetry generators for the left and right moving modes in the doubled space. Chirality is manifest in our doubled space as well as the T-duality symmetry. We present gauge invariant bosonic and superstring actions preserving the two-dimensional diffeomorphism invariance and the kappa-symmetry where doubled spacetime coordinates are chiral fields. The doubled space becomes the usual space by dimensional reduction constraints.

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arXiv2015

Ramond-Ramond gauge fields in superspace with manifest T-duality

A superspace with manifest T-duality including Ramond-Ramond gauge fields is presented. The superspace is defined by the double nondegenerate super-Poincare algebras where Ramond-Ramond charges are introduced by central extension. This formalism allows a simple treatment that all the supergravity multiplets are in a vielbein superfield and all torsions with dimension 1 and less are trivial. A Green-Schwarz superstring action is also presented where the Wess-Zumino term is given in a bilinear form of local currents. Equations of motion are separated into left and right modes in a suitable gauge.

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arXiv2014

Superspace with manifest T-duality from type II superstring

A superspace formulation of type II superstring background with manifest T-duality symmetry is presented. This manifestly T-dual formulation is constructed in a space spanned by two sets of nondegenerate super-Poincare algebra. Supertorsion constraints are obtained from consistency of the kappa-symmetric Virasoro constraints. All superconnections and vielbein fields are solved in terms of a prepotential which is one of the vielbein components. AdS5xS5 background is explained in this formulation.

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arXiv2013

M5 algebra and SO(5,5) duality

We present "M5 algebra" to derive Courant brackets of the generalized geometry of $T\oplus Λ^2T^\ast \oplus Λ^5T^\ast$: The Courant bracket generates the generalized diffeomorphism including gauge transformations of three and six form gauge fields. The Dirac bracket between selfdual gauge fields on a M5-brane gives a $C^{[3]}$-twisted contribution to the Courant brackets. For M-theory compactified on a five dimensional torus the U-duality symmetry is SO(5,5) and the M5 algebra basis is in the 16-dimensional spinor representation. The M5 worldvolume diffeomorphism constraints can be written as bilinear forms of the basis and transform as a SO(5,5) vector. We also present an extended space spanned by the 16-dimensional coordinates with section conditions determined from the M5 worldvolume diffeomorphism constraints.

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arXiv2012

SL(5) duality from canonical M2-brane

We show how the SL(5) duality in M-theory is explained from a canonical analysis of M2-brane mechanics. Diffeomorphism constraints for a M2-brane coupled to supergravity background in d=4 are reformulated in a SL(5) covariant form, in which spatial diffeomorphism constraints are recast into a SL(5) vector and the generalized metric in the Hamiltonian constraint is quartic in the SL(5) generalized vielbein. The Hamiltonian for a M2 brane has the SL(5) duality symmetry in a background dependent gauge.

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arXiv2012

Canonical approach to Courant brackets for D-branes

We present an extension of the Courant bracket to the ones for Dp-branes by analyzing Hamiltonians and local superalgebras. Contrast to the basis of the bracket for a fundamental string which consists of the momentum and the winding modes, the ones for Dp-branes contain higher rank R-R coupling tensors. We show that the R-R gauge transformation rules are obtained by these Courant brackets for Dp-branes where the Dirac-Born-Infeld gauge field and the "two-vierbein field" play an essential role. Canonical analysis of the worldvolume theories naturally gives the basis of the brackets and the target space backgrounds keeping T-duality manifest at least for NS-NS sector. In a D3-brane analysis S-duality is manifest as a symmetry of interchanging the NS-NS coupling and the R-R coupling.

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arXiv2011

Super Yangian of superstring on AdS5xS5 revisited

We construct infinite number of conserved nonlocal charges for type IIB superstring on the AdS5xS5 space in the conformal gauge without assuming any kappa gauge fixing, and show that they satisfy the super Yangian algebra. The resultant algebra is the same as our previous work, where a special gauge was assumed in such a way that the Noether current satisfies a flatness condition. However the flatness condition for the Noether current of a superstring on the AdS space is broken in general. We show that the anomalous contribution is absorbed into the current where fermionic constraints play an essential role, and a resultant conserved nonlocal charge has different expression satisfying the same super Yangian algebra.

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