220 research outputs found
Weyl invariance for generalized supergravity backgrounds from the doubled formalism
It has recently been shown that a set of the generalized type IIB
supergravity equations follows from the requirement of kappa symmetry of the
type IIB Green-Schwarz superstring theory defined on an arbitrary background.
In this paper, we show that the whole bosonic part of the generalized type II
supergravity equations can be reproduced from the T-duality covariant equations
of motion of the double field theory by choosing a non-standard solution of the
strong constraint. Then, by using the doubled formalism, we show the Weyl
invariance of the bosonic string sigma model on a generalized gravity
background. According to the dual-coordinate dependence of the dilaton, the
Fradkin-Tseytlin term nicely removes the Weyl anomaly. This result seems likely
to support that string theories can be consistently defined on arbitrary
generalized supergravity backgrounds.Comment: 28 pages; v2: typos corrected, clarifications added; v3: typos
corrected, references added, to appear in PTE
Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
Yang-Baxter (YB) deformations of string sigma model provide deformed target
spaces. We propose that homogeneous YB deformations always lead to a certain
class of -twisted backgrounds and represent the bosonic part of the
supergravity fields in terms of the classical r-matrix associated with the YB
deformation. We then show that various -twisted backgrounds can be
realized by considering generalized diffeomorphisms in the undeformed
background. Our result extends the notable relation between the YB deformations
and (non-commuting) TsT transformations. We also discuss more general
deformations beyond the YB deformations.Comment: 8 pages; v2: typos corrected, clarifications added, references adde
Lax pairs on Yang-Baxter deformed backgrounds
We explicitly derive Lax pairs for string theories on Yang-Baxter deformed
backgrounds, 1) gravity duals for noncommutative gauge theories, 2)
-deformations of S, 3) Schr\"odinger spacetimes and 4) abelian
twists of the global AdS\,. Then we can find out a concise derivation of
Lax pairs based on simple replacement rules. Furthermore, each of the above
deformations can be reinterpreted as a twisted periodic boundary conditions
with the undeformed background by using the rules. As another derivation, the
Lax pair for gravity duals for noncommutative gauge theories is reproduced from
the one for a -deformed AdSS by taking a scaling limit.Comment: 1+39 pages, v3: typos corrected and the reference [42] adde
Generalized type IIB supergravity equations and non-Abelian classical r-matrices
We study Yang-Baxter deformations of the superstring with
non-Abelian classical -matrices which satisfy the homogeneous classical
Yang-Baxter equation (CYBE). By performing a supercoset construction, we can
get deformed backgrounds. While this is a new area of
research, the current understanding is that Abelian classical -matrices give
rise to solutions of type IIB supergravity, while non-Abelian classical
-matrices lead to solutions of the generalized supergravity equations. We
examine here some examples of non-Abelian classical r-matrices and derive the
associated backgrounds explicitly. All of the resulting backgrounds satisfy the
generalized equations. For some of them, we derive "T-dualized" backgrounds by
adding a linear coordinate dependence to the dilaton and show that these
satisfy the usual type IIB supergravity equations. Remarkably, some of the
"T-dualized" backgrounds are locally identical to undeformed
after an appropriate coordinate transformation, but this seems not to be
generally the case.Comment: typos correcte
Local -deformations and Yang-Baxter sigma model
Homogeneous Yang-Baxter (YB) deformation of AdSS 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
-deformations of the AdSS background when the classical
-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 -flux, it
is not straightforward to perform homogeneous YB deformations. In order to get
any hint for such YB deformations, we study -deformations of -fluxed
AdS backgrounds and obtain various solutions of (generalized) type II
supergravity.Comment: 95 pages; v2: clarifications and references added; v3: published
versio
Yang-Baxter deformations of Minkowski spacetime
We study Yang-Baxter deformations of 4D Minkowski spacetime. The Yang-Baxter
sigma model description was originally developed for principal chiral models
based on a modified classical Yang-Baxter equation. It has been extended to
coset curved spaces and models based on the usual classical Yang-Baxter
equation. On the other hand, for flat space, there is the obvious problem that
the standard bilinear form degenerates if we employ the familiar coset
Poincar\'e group/Lorentz group. Instead we consider a slice of AdS by
embedding the 4D Poincar\'e group into the 4D conformal group . With
this procedure we obtain metrics and -fields as Yang-Baxter deformations
which correspond to well-known configurations such as T-duals of Melvin
backgrounds, Hashimoto-Sethi and Spradlin-Takayanagi-Volovich backgrounds, the
T-dual of Grant space, pp-waves, and T-duals of dS and AdS. Finally we
consider a deformation with a classical -matrix of Drinfeld-Jimbo type and
explicitly derive the associated metric and -field which we conjecture to
correspond to a new integrable system.Comment: 27 pages, no figure, LaTe
Yang-Baxter sigma models and Lax pairs arising from -Poincar\'e -matrices
We study Yang-Baxter sigma models with deformed 4D Minkowski spacetimes
arising from classical -matrices associated with -deformations of
the Poincar\'e algebra. These classical -Poincar\'e -matrices
describe three kinds of deformations: 1) the standard deformation, 2) the
tachyonic deformation, and 3) the light-cone deformation. For each deformation,
the metric and two-form -field are computed from the associated -matrix.
The first two deformations, related to the modified classical Yang-Baxter
equation, lead to T-duals of dS and AdS\,, respectively. The third
deformation, associated with the homogeneous classical Yang-Baxter equation,
leads to a time-dependent pp-wave background. Finally, we construct a Lax pair
for the generalized -Poincar\'e -matrix that unifies the three kinds
of deformations mentioned above as special cases.Comment: 31 pages, v2: some clarifications and references added, published
versio
- …