arXiv subjects

Yuho Sakatani

Publications and source records attributed to Yuho Sakatani.

At least 19 recordsLinked to original sources

arXiv2025

Consistent truncation and generalized duality based on exceptional generalized cosets

We present a systematic framework for constructing consistent truncations of supergravity based on exceptional generalized cosets of the form $\GS \backslash G/H$. This approach generalizes the well-established generalized Scherk-Schwarz reductions on generalized parallelizable spaces $G/H$, which preserve maximal supersymmetry, to scenarios with reduced supersymmetry by introducing a non-trivial generalized structure group $\GS$. The double coset structure plays two distinct roles: for a given $G$, the choice of subgroup $\GS$ determines the (constant) generalized torsion/curvature and the pattern of supersymmetry breaking, while $H$ parameterizes inequivalent supergravity backgrounds that share the same truncated theory. The entire construction proceeds algebraically, systematically building $\GS$-invariant tensors from generalized frame fields, with the intrinsic torsion automatically constant and a $\GS$-singlet. Different choices of $H$ lead to distinct higher-dimensional backgrounds that truncate to the same lower-dimensional theory, thereby realizing U-duality. We illustrate the framework through explicit examples in double field theory and exceptional field theory.

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arXiv2024

Duality covariant curvatures for the heterotic string

Duality covariant curvature and torsion tensors in double field theory/generalized geometry are central in analyzing consistent truncations, generalized dualities, and related integrable $σ$-models. They are constructed systematically with the help of a larger, auxiliary space in a procedure inspired by Cartan geometry originally proposed by Poláček and Siegel for bosonic strings. It pivots around a maximally isotropic group that captures the generalized structure group of the physical space. We show how dropping the isotropy condition on this group allows us to describe heterotic/type I strings. As an immediate application, we construct a new family of heterotic backgrounds that interpolates between the two-dimensional cigar and trumpet backgrounds.

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arXiv2024

Generalized Dualities for Heterotic and Type I Strings

We define generalized dualities for heterotic and type I strings based on consistent truncations to half-maximal gauged supergravities in more than three dimensions. The latter are constructed from a generalized Scherk-Schwarz ansatz in heterotic double field theory that satisfies the strong constraint. Necessary and sufficient conditions on the resulting embedding tensor are discussed, showing that only certain gaugings, called geometric, can arise from this procedure. For all of them, we explicitly construct the internal geometry and gauge potentials. In general, this construction is not unique and permits different uplifts which are used to define generalized T-duality. Two examples are worked out underlying the utility of our approach to explore new dualities and uplifts of half-maximal gauged supergravities.

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arXiv2024

All maximal gauged supergravities with uplift

Generalised parallelisable spaces permit to uplift many maximal gauged supergravities to ten or eleven dimensions. While some of the former are explicitly known, the literature is still lacking a systematic construction and a complete classification. We resolve this issue and present an explicit construction, and with it a full classification, of generalised parallelisable spaces for maximal gauged supergravities in four or more dimensions. All embedding tensors that can be realised without breaking the section condition of exceptional field theory are identified and the corresponding generalised frame fields are constructed. This finally resolved the old question: "Which maximal gauged supergravities have uplifts to 10/11d?". Furthermore, it provides the basis to explore solution generating techniques based on generalised dualities.

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arXiv2024

On quantum Poisson-Lie T-duality of WZNW models

We study Poisson-Lie T-duality of the Wess-Zumino-Novikov-Witten (WZNW) models which are obtained from a class of Drinfel'd doubles and its generalization. In this case, the resultant WZNW models are known to be classically self-dual under Poisson-Lie T-duality. We describe an explicit construction of the associated currents, and discuss the conformal invariance under this duality. In a concrete example of the SU(2) WZNW model, we find that the self-duality is represented as a chiral automorphism of the $\widehat{\mathfrak{su}}(2)$ affine Lie algebra, though the transformation of the currents is non-local and non-linear. This classical automorphism can be promoted to the quantum one through the parafermionic formulation of $\widehat{\mathfrak{su}}(2)$, which in turn induces an isomorphism of the WZNW model. We thus find a full quantum equivalence of the dual pair under Poisson-Lie T-duality. The isomorphism is represented by a sign-change of a chiral boson or the order-disorder duality of the parafermionic conformal field theory as in Abelian T-duality on tori or in the mirror symmetry of the Gepner model.

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arXiv2023

O$(D,D)$-covariant formulation of perfect and imperfect fluids in the double geometry

We study generic matter coupled to a $D$-dimensional supergravity using a formulation of Double Field Theory (DFT), where all the fields are encoded in O$(D,D)$ multiplets. We study both the case when the matter comes from a variational principle, as well as the case where the matter comes from a statistical or thermodynamic approach. For the latter, we construct the distribution function for the perfect fluid and its entropy current, which is a conserved quantity. We then include general viscous and elastic terms in the generalized energy-momentum tensor which, in the general case, lead to entropy production. We consistently deform the conservation law of the generalized entropy current and identify a particular non-dissipative deformation. Using the generalized fluid model, we revisit the issue of non-covariance of perfect fluids under T-dualities and we show how to resolve it in our DFT model with matter.

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arXiv2023

The Hierarchy of Curvatures in Exceptional Geometry

Despite remarkable success in describing supergravity reductions and backgrounds, generalized geometry and the closely related exceptional field theory are still lacking a fundamental object of differential geometry, the Riemann tensor. We explain that to construct such a tensor, an as of yet overlooked hierarchy of connections is required. They complement the spin connection with higher representations known from the tensor hierarchy of gauged supergravities. In addition to solving an important conceptual problem, this idea allows to define and explicitly construct generalized homogeneous spaces. They are the underlying structures of generalized U-duality, admit consistent truncations and provide a huge class of new backgrounds for flux compactifications with non-trivial generalized structure groups.

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arXiv2022

Gauged sigma models and exceptional dressing cosets

The Poisson-Lie (PL) T-duality is a generalized T-duality based on the Lie algebra of the Drinfel'd double. In particular, when we consider the PL T-duality of a coset space, the dual space is found to be a generalized coset space, which is called the dressing coset. In this paper, we investigate an extension of the dressing cosets to the U-duality setup. We propose the gauged actions for various branes in M-theory and type IIB theory, where the generalized metric is constructed by using the Exceptional Drinfel'd Algebra (EDA) and the gauge algebra is a certain isotropic subalgebra of the EDA. By eliminating the gauge fields, the gauged action reduces to the standard brane action on a certain reduced background, which we call the exceptional dressing coset. We also propose an alternative definition of the exceptional dressing cosets based on Sfetsos's approach and reproduce a known example of non-Abelian T-duality in the U-duality-covariant formulation.

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arXiv2022

Poisson-Lie T-plurality for dressing cosets

The Poisson-Lie T-plurality is an equivalence of string theories on various cosets $\mathcal{D}/\tilde{G}$, $\mathcal{D}/\tilde{G}'$, $\cdots$, where $\mathcal{D}$ is a Drinfel'd double and $\tilde{G}$, $\tilde{G}'$, $\cdots$ are maximal isotropic subgroups. This can be extended to the equivalence for dressing cosets, i.e., $F\backslash\mathcal{D}/\tilde{G}$, $F\backslash\mathcal{D}/\tilde{G}'$, $\cdots$, where $F$ is an isotropic subgroup of $\mathcal{D}$. We explore this extended Poisson-Lie T-plurality, clarifying the relation between several previous approaches. We propose a gauged sigma model for a general gauge group $F$ and obtain the formula for the metric and the B-field on the dressing coset. Using this formula and an ansatz for the dilaton, we show that the Poisson-Lie T-plurality for dressing cosets (with spectator fields) is a symmetry of double field theory. The formula for the R-R field strength is also proposed such that the equations of motion for the NS-NS fields are transformed covariantly. In addition, we provide specific examples of the PL T-plurality for dressing cosets.

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arXiv2021

Jacobi-Lie T-plurality

We propose a Leibniz algebra, to be called DD$^+$, which is a generalization of the Drinfel'd double. We find that there is a one-to-one correspondence between a DD$^+$ and a Jacobi--Lie bialgebra, extending the known correspondence between a Lie bialgebra and a Drinfel'd double. We then construct generalized frame fields $E_A{}^M\in\text{O}(D,D)\times\mathbb{R}^+$ satisfying the algebra $\mathcal{L}_{E_A}E_B = - X_{AB}{}^C\,E_C\,$, where $X_{AB}{}^C$ are the structure constants of the DD$^+$ and $\mathcal{L}$ is the generalized Lie derivative in double field theory. Using the generalized frame fields, we propose the Jacobi-Lie T-plurality and show that it is a symmetry of double field theory. We present several examples of the Jacobi-Lie T-plurality with or without Ramond-Ramond fields and the spectator fields.

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arXiv2021

Non-abelian U-duality at work

Non-abelian U-duality originates from the construction of exceptional Drinfel'd algebra (EDA), which extends the constriction of the classical Drinfel'd double. This symmetry is a natural extension of Poisson--Lie T-duality and is believed to be a symmetry of Type II string/M-theory or their low-energy effective theories. In this paper, we consider non-abelian U-dualities of 11- or 10-dimensional backgrounds starting with E${}_{n(n)}$ EDA with $n\leq 6$ with vanishing trombone gauging. The latter guarantees that all dual backgrounds satisfy the standard supergravity equations of motion. In particular, when the duality includes a timelike T-duality, we obtain solutions of M$^*$-theory or Type II$^*$ background equations, as expected. Also starting with coboundary EDA's we provide examples of generalised Yang--Baxter deformations of M-theory and Type IIB backgrounds. The obtained results provide explicit examples when non-abelian U-duality works well as a solution generating transformation.

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arXiv2021

Half-maximal Extended Drinfel'd Algebras

Extended Drinfel'd algebra (ExDA) is the underlying symmetry of non-Abelian duality in the low-energy effective theory of string theory. Non-Abelian U-dualities in maximal supergravities have been studied well, but there has been no study on non-Abelian dualities in half-maximal supergravities. In this paper, we construct the ExDA for half-maximal supergravities in $d\geq 4$. We also find an extension of the homogeneous classical Yang-Baxter equation in these theories.

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arXiv2021

Poisson-Lie T-plurality for WZW backgrounds

Poisson-Lie T-plurality constructs a chain of supergravity solutions from a Poisson-Lie symmetric solution. We study the Poisson-Lie T-plurality for supergravity solutions with $H$-flux, which are not Poisson-Lie symmetric but admit non-Abelian isometries, $\mathcal{L}_{v_a}g_{mn}=0$ and $\mathcal{L}_{v_a}H_3=0$ with $\mathcal{L}_{v_a}B_2\neq 0$. After introducing the general procedure, we study the Poisson-Lie T-plurality for two WZW backgrounds, the AdS$_3$ with $H$-flux and the Nappi-Witten background.

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arXiv2020

Extended Drinfel'd algebras and non-Abelian duality

A Drinfel'd algebra gives the systematic construction of generalized parallelizable spaces and this allows us to study an extended T-duality, known as the Poisson-Lie T-duality. Recently, in order to find a generalized U-duality, an extended Drinfel'd algebra (ExDA), called the Exceptional Drinfel'd algebra (EDA) was proposed and a natural extension of the usual U-duality was studied both in the context of supergravity and membrane theory. In this paper, we clarify the general structure of ExDAs and show that an ExDA always gives a generalized parallelizable space, which may be regarded as a group manifold with generalized Nambu-Lie structures. We also discuss generalized Yang-Baxter deformations that are based on coboundary ExDAs. As important examples, we consider the $E_{n(n)}$ EDA for $n\leq 8$ and study various aspects, both in terms of M-theory and type IIB theory.

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arXiv2020

E$_{6(6)}$ Exceptional Drinfel'd Algebras

The exceptional Drinfel'd algebra (EDA) is a Leibniz algebra introduced to provide an algebraic underpinning with which to explore generalised notions of U-duality in M-theory. In essence it provides an M-theoretic analogue of the way a Drinfel'd double encodes generalised T-dualities of strings. In this note we detail the construction of the EDA in the case where the regular U-duality group is $E_{6(6)}$. We show how the EDA can be realised geometrically as a generalised Leibniz parallelisation of the exceptional generalised tangent bundle for a six-dimensional group manifold $G$, endowed with a Nambu-Lie structure. When the EDA is of coboundary type, we show how a natural generalisation of the classical Yang-Baxter equation arises. The construction is illustrated with a selection of examples including some which embed Drinfel'd doubles and others that are not of this type.

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arXiv2020

Born sigma model for branes in exceptional geometry

In double field theory, the physical space has been understood as a subspace of the doubled space. Recently, the doubled space is defined as the para-Hermitian manifold and the physical space is realized as a leaf of a foliation of the doubled space. This construction naturally introduces the fundamental 2-form, which plays an important role in a reformulation of string theory known as the Born sigma model. In this paper, we present the Born sigma model for $p$-branes in M-theory and type IIB theory by extending the fundamental 2-form into U-duality-covariant $(p+1)$-forms.

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arXiv2020

U-duality extension of Drinfel'd double

A family of algebras $\mathcal{E}_n$ that extends the Lie algebra of the Drinfel'd double is proposed. This allows us to systematically construct the generalized frame fields $E_A{}^I$ which realize the proposed algebra by means of the generalized Lie derivative, i.e., $\hat{\mathcal{L}}_{E_A}E_B{}^I = - \mathcal{F}_{AB}{}^C\,E_C{}^I$. By construction, the generalized frame fields include a twist by a Nambu-Poisson tensor. A possible application to the non-Abelian extension of U-duality and a generalization of the Yang-Baxter deformation are also discussed.

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arXiv2020

Exotic branes and mixed-symmetry potentials I: predictions from $E_{11}$ symmetry

Type II string theory or M-theory contains a broad spectrum of gauge potentials. In addition to the standard $p$-form potentials, various mixed-symmetry potentials have been predicted, which may couple to exotic branes with non-standard tensions. Together with $p$-forms, mixed-symmetry potentials turn out to be essential to build the multiplets of the U-duality symmetry in each dimension. In this paper, we systematically determine the set of mixed-symmetry potentials and exotic branes on the basis of the $E_{11}$ conjecture. We also study the decompositions of U-duality multiplets into T-duality multiplets and determine which mixed-symmetry tensors are contained in each of the U-/T-duality multiplets.

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