695 research outputs found
-Poincar\'e supersymmetry in
We consider the exact S-matrix governing the planar spectral problem for
strings on and super Yang-Mills, and we show
that it is invariant under a novel "boost" symmetry, which acts as a
differentiation with respect to the particle momentum. This generator leads us
also to reinterpret the usual centrally extended
symmetry, and to conclude that the S-matrix is invariant under a -Poincar\'e
supersymmetry algebra, where the deformation parameter is related to the 't
Hooft coupling. We determine the two-particle action (coproduct) that turns out
to be non-local, and study the property of the new symmetry under crossing
transformations. We look at both the strong-coupling (large tension in the
string theory) and weak-coupling (spin-chain description of the gauge theory)
limits; in the former regime we calculate the cobracket utilising the universal
classical r-matrix of Beisert and Spill. In the eventuality that the boost has
higher partners, we also construct a quantum affine version of 2D Poincar\'e
symmetry, by contraction of the quantum affine algebra
in Drinfeld's second realisation.Comment: 35 pages. Added discussion on antipode in the presence of the phase.
Published versio
-Poincar\'e invariance of the -matrix
We consider the exact -matrix of , which is the building
block for describing the scattering of worldsheet excitations of the light-cone
gauge-fixed backgrounds and with pure Ramond-Ramond fluxes. We show that is
invariant under a "deformed boost" symmetry, for which we write an explicit
exact coproduct, i.e. its action on 2-particle states. When we include the
boost, the symmetries of the -matrix close into a -Poincar\'e
superalgebra. Our findings suggest that the recently discovered boost
invariance in may be a common feature of systems that
are treatable with the exact techniques of integrability. With the aim of going
towards a universal formulation of the underlying Hopf algebra, we also propose
a universal form of the classical -matrix.Comment: 26 pages. Minor improvements and references added. Published versio
Puzzles of eta-deformed AdS_5 x S^5
We derive the part of the Lagrangian for the sigma model on the eta-deformed
AdS_5 x S^5 space which is quadratic in fermions and has the full dependence on
bosons. We then show that there exists a field redefinition which brings the
corresponding Lagrangian to the standard form of type IIB Green-Schwarz
superstring. Reading off the corresponding RR couplings, we observe that they
fail to satisfy the supergravity equations of motion, despite the presence of
kappa-symmetry. However, in a special scaling limit our solution reproduces the
supergravity background found by Maldacena and Russo. Further, using the
fermionic Lagrangian, we compute a number of new matrix elements of the tree
level world-sheet scattering matrix. We then show that after a unitary
transformation on the basis of two-particle states which is not one-particle
factorisable, the corresponding T-matrix factorises into two equivalent parts.
Each part satisfies the classical Yang-Baxter equation and coincides with the
large tension limit of the q-deformed S-matrix.Comment: 59 pages, 1 figure, v2: minor correction
All-loop Bethe ansatz equations for AdS3/CFT2
Using the S-matrix for the d(2,1;alpha)^2 symmetric spin-chain of AdS3/CFT2,
we propose a new set of all-loop Bethe equations for the system. These
equations differ from the ones previously found in the literature by the choice
of relative grading between the two copies of the d(2,1;alpha) superalgebra,
and involve four undetermined scalar factors that play the role of dressing
phases. Imposing crossing symmetry and comparing with the near-BMN form of the
S-matrix found in the literature, we find several novel features. In
particular, the scalar factors must differ from the Beisert-Eden-Staudacher
phase, and should couple nodes of different masses to each other. In the
semiclassical limit the phases are given by a suitable generalization of
Arutyunov-Frolov-Staudacher phase.Comment: 26 pages, 2 figures. v2: references added. v3: changed notation for
the crossing equations, added references. Published versio
A dynamic su(1|1)^2 S-matrix for AdS3/CFT2
We derive the S-matrix for the d(2,1;alpha)^2 symmetric spin-chain of
AdS3/CFT2 by considering the centrally extended su(1|1)^2 algebra acting on the
spin-chain excitations. The S-matrix is determined uniquely up to four scalar
factors, which are further constrained by a set of crossing relations. The
resulting scattering includes non-trivial processes between magnons of
different masses that were previously overlooked.Comment: 41 pages, 4 figures. v2: corrected a misprint in appendix E, updated
references, corrected some typos. v3: added a new appendix F with comparison
to the literature, changed notation for the crossing equations, added
references. Published versio
Supergravity solution-generating techniques and canonical transformations of σ-models from O(D, D)
Within the framework of the flux formulation of Double Field Theory (DFT) we employ a generalised Scherk-Schwarz ansatz and discuss the classification of the twists that in the presence of the strong constraint give rise to constant generalised fluxes interpreted as gaugings. We analyse the various possibilities of turning on the fluxes Hijk, Fijk, Qijk and Rijk, and the solutions for the twists allowed in each case. While we do not impose the DFT (or equivalently supergravity) equations of motion, our results provide solution-generating techniques in supergravity when applied to a background that does solve the DFT equations. At the same time, our results give rise also to canonical transformations of 2-dimensional σ-models, a fact which is interesting especially because these are integrability-preserving transformations on the worldsheet. Both the solution-generating techniques of supergravity and the canonical transformations of 2-dimensional σ-models arise as maps that leave the generalised fluxes of DFT and their flat derivatives invariant. These maps include the known abelian/non-abelian/Poisson-Lie T-duality transformations, Yang-Baxter deformations, as well as novel generalisations of themS
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