Abstract
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., . 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.
Abstract
The Drinfel’d algebra provides a method to construct 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 Abelian $U$-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 then discuss the non-Abelian duality that is based on a general ExDA. For a coboundary ExDA, this non-Abelian duality reduces to a generalized Yang–Baxter deformation and we find a general formula for the twist matrix. In order to study the non-Abelian $U$-duality, we particularly focus on the $E_{n(n)}$ EDA for $n\leq 8$ and study various aspects, both in terms of M-theory and type IIB theory.
Abstract
The 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. We construct the ExDA for half-maximal supergravities in d ≥ 4. We also find an extension of the homogeneous classical Yang–Baxter equation in these theories.
E6(6) exceptional Drinfel’d algebras Malek, Emanuel; Sakatani, Yuho; Thompson, Daniel C.
The journal of high energy physics,
01/2021, Letnik:
2021, Številka:
1
Journal Article
Recenzirano
Odprti dostop
A
bstract
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.
Generalized gravity from modified DFT Sakatani, Yuho; Uehara, Shozo; Yoshida, Kentaroh
The journal of high energy physics,
04/2017, Letnik:
2017, Številka:
4
Journal Article
Recenzirano
Odprti dostop
A
bstract
Recently, generalized equations of type IIB supergravity have been derived from the requirement of classical kappa-symmetry of type IIB superstring theory in the Green-Schwarz formulation. ...These equations are covariant under generalized
T
-duality transformations and hence one may expect a formulation similar to double field theory (DFT). In this paper, we consider a modification of the DFT equations of motion by relaxing a condition for the generalized covariant derivative with an extra generalized vector. In this modified double field theory (mDFT), we show that the flatness condition of the modified generalized Ricci tensor leads to the NS-NS part of the generalized equations of type IIB supergravity. In particular, the extra vector fields appearing in the generalized equations correspond to the extra generalized vector in mDFT. We also discuss duality symmetries and a modification of the string charge in mDFT.
A
bstract
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
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
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.
We propose a novel approach to the brane worldvolume theory based on the geometry of extended field theories: double field theory and exceptional field theory. We demonstrate the effectiveness of ...this approach by showing that one can reproduce the conventional bosonic string and membrane actions, and the M5-brane action in the weak-field approximation. At a glance, the proposed 5-brane action without approximation looks different from the known M5-brane actions, but it is consistent with the known nonlinear self-duality relation, and it may provide a new formulation of a single M5-brane action. Actions for exotic branes are also discussed.
A
bstract
Homogeneous Yang-Baxter (YB) deformation of AdS
5
× S
5
superstring is revisited. We calculate the YB sigma model action up to quadratic order in fermions and show that homogeneous YB ...deformations are equivalent to
β
-deformations of the AdS
5
×S
5
background when the classical
r
-matrices consist of bosonic generators. In order to make our discussion clearer, we discuss YB deformations in terms of the double-vielbein formalism of double field theory. We further provide an O(10
,
10)-invariant string action that reproduces the Green-Schwarz type II superstring action up to quadratic order in fermions. When an AdS background contains a non-vanishing
H
-flux, it is not straightforward to perform homogeneous YB deformations. In order to get any hint for such YB deformations, we study
β
-deformations of
H
-fluxed AdS backgrounds and obtain various solutions of (generalized) type II supergravity.
Non-Abelian U -duality for membranes Sakatani, Yuho; Uehara, Shozo
Progress of theoretical and experimental physics,
07/2020, Letnik:
2020, Številka:
7
Journal Article
Recenzirano
Odprti dostop
Abstract
The $T$-duality of string theory can be extended to the Poisson–Lie $T$-duality when the target space has a generalized isometry group given by a Drinfel’d double. In M-theory, $T$-duality ...is understood as a subgroup of $U$-duality, but the non-Abelian extension of $U$-duality is still a mystery. In this paper we study membrane theory on a curved background with a generalized isometry group given by the $\mathcal E_n$ algebra. This provides a natural setup to study non-Abelian $U$-duality because the $\mathcal E_n$ algebra has been proposed as a $U$-duality extension of the Drinfel’d double. We show that the standard treatment of Abelian $U$-duality can be extended to the non-Abelian setup. However, a famous issue in Abelian $U$-duality still exists in the non-Abelian extension.
T -folds from Yang-Baxter deformations Fernández-Melgarejo, José J.; Sakamoto, Jun-ichi; Sakatani, Yuho ...
The journal of high energy physics,
12/2017, Letnik:
2017, Številka:
12
Journal Article
Recenzirano
Odprti dostop
A
bstract
Yang-Baxter (YB) deformations of type IIB string theory have been well studied from the viewpoint of classical integrability. Most of the works, however, are focused upon the local ...structure of the deformed geometries and the global structure still remains unclear. In this work, we reveal a non-geometric aspect of YB-deformed backgrounds as
T
-fold by explicitly showing the associated O(
D
,
D
;
ℤ
)
T
-duality monodromy. In particular, the appearance of an extra vector field in the generalized supergravity equations (GSE) leads to the non-geometric
Q
-flux. In addition, we study a particular solution of GSE that is obtained by a non-Abelian
T
-duality but cannot be expressed as a homogeneous YB deformation, and show that it can also be regarded as a
T
-fold. This result indicates that solutions of GSE should be non-geometric quite in general beyond the YB deformation.
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