815 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
A Quantum Affine Algebra for the Deformed Hubbard Chain
The integrable structure of the one-dimensional Hubbard model is based on
Shastry's R-matrix and the Yangian of a centrally extended sl(2|2)
superalgebra. Alcaraz and Bariev have shown that the model admits an integrable
deformation whose R-matrix has recently been found. This R-matrix is of
trigonometric type and here we derive its underlying exceptional quantum affine
algebra. We also show how the algebra reduces to the above mentioned Yangian
and to the conventional quantum affine sl(2|2) algebra in two special limits.Comment: 24 pages, v2: minor amendment of (7.2), v3: accepted for publication
in JPA, minor correction
Kinetic theory for a simple modeling of phase transition: Dynamics out of local equilibrium
This is a continuation of the previous work (Takata & Noguchi, J. Stat.
Phys., 2018) that introduces the presumably simplest model of kinetic theory
for phase transition. Here, main concern is to clarify the stability of uniform
equilibrium states in the kinetic regime, rather than that in the continuum
limit. It is found by the linear stability analysis that the linear neutral
curve is invariant with respect to the Knudsen number, though the transition
process is dependent on the Knudsen number. In addition, numerical computations
of the (nonlinear) kinetic model are performed to investigate the transition
processes in detail. Numerical results show that (unexpected) incomplete
transitions may happen as well as clear phase transitions.Comment: 21 pages, 7 figure
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