1,048 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
Yang-Baxter sigma models based on the CYBE
It is known that Yang-Baxter sigma models provide a systematic way to study
integrable deformations of both principal chiral models and symmetric coset
sigma models. In the original proposal and its subsequent development, the
deformations have been characterized by classical -matrices satisfying the
modified classical Yang-Baxter equation (mCYBE). In this article, we propose
the Yang-Baxter sigma models based on the classical Yang-Baxter equations
(CYBE) rather than the mCYBE. This generalization enables us to utilize various
kinds of solutions of the CYBE to classify integrable deformations. In
particular, it is straightforward to realize partial deformations of the target
space without loss of the integrability of the parent theory.Comment: 23 pages; v2: a reference added, small modifications; v3: minor
correction
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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