874 research outputs found
Schr\"odinger geometries arising from Yang-Baxter deformations
We present further examples of the correspondence between solutions of type
IIB supergravity and classical -matrices satisfying the classical
Yang-Baxter equation (CYBE). In the previous works, classical -matrices have
been composed of generators of only one of either or
. In this paper, we consider some examples of -matrices
with both of them. The -matrices of this kind contain (generalized)
Schr\"odinger spacetimes and gravity duals of dipole theories. It is known that
the generalized Schr\"odinger spacetimes can also be obtained via a certain
class of TsT transformations called null Melvin twists. The metric and NS-NS
two-form are reproduced by following the Yang-Baxter sigma-model description.Comment: 25 pages, LaTeX, no figure, v2: references and minor clarifications
adde
Yang-Baxter deformations and string dualities
We further study integrable deformations of the AdSS
superstring by following the Yang-Baxter sigma model approach with classical
-matrices satisfying the classical Yang-Baxter equation (CYBE). Deformed
string backgrounds specified by -matrices are considered as solutions of
type IIB supergravity, and therefore the relation between gravitational
solutions and -matrices may be called the gravity/CYBE correspondence. In
this paper, we present a family of string backgrounds associated with a
classical -matrices carrying two parameters and its three-parameter
generalization. The two-parameter case leads to the metric and NS-NS two-form
of a solution found by Hubeny-Rangamani-Ross [hep-th/0504034] and another
solution in [arXiv:1402.6147]. For all of the backgrounds associated with the
three-parameter case, the metric and NS-NS two-form are reproduced by
performing TsT transformations and S-dualities for the undeformed
AdSS background. As a result, one can anticipate the R-R sector
that should be reproduced via a supercoset construction.Comment: 23 pages, 1 tabl
Integrability of classical strings dual for noncommutative gauge theories
We derive the gravity duals of noncommutative gauge theories from the
Yang-Baxter sigma model description of the AdS_5xS^5 superstring with classical
r-matrices. The corresponding classical r-matrices are 1) solutions of the
classical Yang-Baxter equation (CYBE), 2) skew-symmetric, 3) nilpotent and 4)
abelian. Hence these should be called abelian Jordanian deformations. As a
result, the gravity duals are shown to be integrable deformations of AdS_5xS^5.
Then, abelian twists of AdS_5 are also investigated. These results provide a
support for the gravity/CYBE correspondence proposed in arXiv:1404.1838.Comment: 16 pages, no figure, LaTe
A Jordanian deformation of AdS space in type IIB supergravity
We consider a Jordanian deformation of the AdS_5xS^5 superstring action by
taking a simple R-operator which satisfies the classical Yang-Baxter equation.
The metric and NS-NS two-form are explicitly derived with a coordinate system.
Only the AdS part is deformed and the resulting geometry contains the 3D
Schrodinger spacetime as a subspace. Then we present the full solution in type
IIB supergravity by determining the other field components. In particular, the
dilaton is constant and a R-R three-form field strength is turned on. The
symmetry of the solution is [SL(2,R)xU(1)^2] x [SU(3)xU(1)] and contains an
anisotropic scale symmetry.Comment: 29 pages, no figure, LaTeX, typos corrected, references added,
further clarification adde
Jordanian deformations of the AdS_5xS^5 superstring
We consider Jordanian deformations of the AdS_5xS^5 superstring action. The
deformations correspond to non-standard q-deformation. In particular, it is
possible to perform partial deformations, for example, only for the S^5 part.
Then the classical action and the Lax pair are constructed with a linear,
twisted and extended R operator. It is shown that the action preserves the
kappa-symmetry.Comment: 22 pages, no figure, LaTeX, typos corrected and further clarification
adde
Deformations of as Yang-Baxter sigma models
We consider a family of deformations of T^{1,1} in the Yang-Baxter sigma
model approach. We first discuss a supercoset description of T^{1,1}, which
makes manifest the full symmetry of the space and leads to the standard
Sasaki-Einstein metric. Next, we consider three-parameter deformations of
T^{1,1} by using classical r-matrices satisfying the classical Yang-Baxter
equation (CYBE). The resulting metric and NS-NS two-form agree exactly with the
ones obtained via TsT transformations, and contain the Lunin-Maldacena
background as a special case. It is worth noting that for AdS_5 x T^{1,1},
classical integrability for the full sector has been argued to be lost. Hence
our result indicates that the Yang-Baxter sigma model approach is applicable
even for non-integrable cosets. This observation suggests that the gravity/CYBE
correspondence can be extended beyond integrable cases.Comment: 21 pages, no figure, LaTeX, v2:clarifications and references added,
v3:minor corrections, further clarifications adde
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