Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHomogeneous Yang-Baxter deformations as non-abelian duals of the AdS_5 sigma-model
149
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We propose that the Yang-Baxter deformation of the symmetric space sigma-model parameterized by an r-matrix solving the homogeneous (classical) Yang-Baxter equation is equivalent to the non-abelian dual of the undeformed model with respect to a subgroup determined by the structure of the r-matrix. We explicitly demonstrate this on numerous examples in the case of the AdS_5 sigma-model. The same should also be true for the full AdS_5 x S^5 supercoset model, providing an explanation for and generalizing several recent observations relating homogeneous Yang-Baxter deformations based on non-abelian r-matrices to the undeformed AdS_5 x S^5 model by a combination of T-dualities and non-linear coordinate redefinitions. This also includes the special case of deformations based on abelian r-matrices, which correspond to TsT transformations: they are equivalent to non-abelian duals of the original model with respect to a central extension of abelian subalgebras.
rate research
Read More
We present homogeneous Yang-Baxter deformations of the AdS$_5times$S$^5$ supercoset sigma model as boundary conditions of a 4D Chern-Simons theory. We first generalize the procedure for the 2D principal chiral model developed by Delduc et al [arXiv:1909.13824] so as to reproduce the 2D symmetric coset sigma model, and specify boundary conditions governing homogeneous Yang-Baxter deformations. Then the conditions are applicable for the AdS$_5times$S$^5$ supercoset sigma model case as well. In addition, homogeneous bi-Yang-Baxter deformation is also discussed.
A large class of integrable deformations of the Principal Chiral Model, known as the Yang-Baxter deformations, are governed by skew-symmetric R-matrices solving the (modified) classical Yang-Baxter equation. We carry out a systematic investigation of these deformations in the presence of the Wess-Zumino term for simple Lie groups, working in a framework that treats both inhomogeneous and homogeneous deformations on the same footing. After analysing the cohomological conditions under which such a deformation is admissible, we consider an action for the general Yang-Baxter deformation of the Principal Chiral Model plus Wess-Zumino term and prove its classical integrability. We also show how the model is found from a number of alternative formulations: affine Gaudin models, E-models, 4-dimensional Chern-Simons theory and, for homogeneous deformations, non-abelian T-duality.
The eta-deformation of the AdS_5 x S^5 superstring depends on a non-split r matrix for the superalgebra psu(2,2|4). Much of the investigation into this model has considered one particular choice, however there are a number of inequivalent alternatives. This is also true for the bosonic sector of the theory with su(2,2), the isometry algebra of AdS_5, admitting one split and three non-split r matrices. In this article we explore these r matrices and the corresponding geometries. We investigate their contraction limits, comment on supergravity backgrounds and demonstrate their relation to gauged-WZW deformations. We then extend the three non-split cases to AdS_5 x S^5 and compute four separate bosonic two-particle tree-level S-matrices based on inequivalent BMN-type light-cone gauges. The resulting S-matrices, while different, are related by momentum-dependent one-particle changes of basis.
We study Yang-Baxter deformations of the Nappi-Witten model with a prescription invented by Delduc, Magro and Vicedo. The deformations are specified by skew-symmetric classical $r$-matrices satisfying (modified) classical Yang-Baxter equations. We show that the sigma-model metric is invariant under arbitrary deformations (while the coefficient of $B$-field is changed) by utilizing the most general classical $r$-matrix. Furthermore, the coefficient of $B$-field is determined to be the original value from the requirement that the one-loop $beta$-function should vanish. After all, the Nappi-Witten model is the unique conformal theory within the class of the Yang-Baxter deformations preserving the conformal invariance.
Poisson-Lie dualising the eta deformation of the G/H symmetric space sigma model with respect to the simple Lie group G is conjectured to give an analytic continuation of the associated lambda deformed model. In this paper we investigate when the eta deformed model can be dualised with respect to a subgroup G_0 of G. Starting from the first-order action on the complexified group and integrating out the degrees of freedom associated to different subalgebras, we find it is possible to dualise when G_0 is associated to a sub-Dynkin diagram. Additional U_1 factors built from the remaining Cartan generators can also be included. The resulting construction unifies both the Poisson-Lie dual with respect to G and the complete abelian dual of the eta deformation in a single framework, with the integrated algebras unimodular in both cases. We speculate that extending these results to the path integral formalism may provide an explanation for why the eta deformed AdS_5 x S^5 superstring is not one-loop Weyl invariant, that is the couplings do not solve the equations of type IIB supergravity, yet its complete abelian dual and the lambda deformed model are.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
