250 research outputs found
Towards a two-parameter q-deformation of AdS_3 x S^3 x M^4 superstrings
We construct a two-parameter deformation of the Metsaev-Tseytlin action for
supercosets with isometry group of the form G x G. The resulting action is
classically integrable and is Poisson-Lie symmetric suggesting that the
symmetry of the model is q-deformed, U_q_L(G) x U_q_R(G). Focusing on the cases
relevant for strings moving in AdS_3 x S^3 x T^4 and AdS_3 x S^3 x S^3 x S^1,
we analyze the corresponding deformations of the AdS_3 and S^3 metrics. We also
construct a two-parameter -deformation of the u(1) + psu(1|1)^2 x u(1) x
R^3-invariant R-matrix and closure condition, which underlie the light-cone
gauge S-matrix and dispersion relation of the aforementioned string theories.
With the appropriate identification of parameters, the near-BMN limit of the
dispersion relation is shown to agree with that found from the deformed
supercoset sigma model.Comment: 35 page
Poisson-Lie duals of the eta deformed symmetric space sigma model
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.Comment: 37 pages, v2: minor change
Maximally extended sl(2|2), q-deformed d(2,1;epsilon) and 3D kappa-Poincar\'e
We show that the maximal extension sl(2) times psl(2|2) times C3 of the
sl(2|2) superalgebra can be obtained as a contraction limit of the semi-simple
superalgebra d(2,1;epsilon) times sl(2). We reproduce earlier results on the
corresponding q-deformed Hopf algebra and its universal R-matrix by means of
contraction. We make the curious observation that the above algebra is related
to kappa-Poincar\'e symmetry. When dropping the graded part psl(2|2) we find a
novel one-parameter deformation of the 3D kappa-Poincar\'e algebra. Our
construction also provides a concise exact expression for its universal
R-matrix.Comment: 25 page
q-Deformation of the AdS5 x S5 Superstring S-matrix and its Relativistic Limit
A set of four factorizable non-relativistic S-matrices for a multiplet of
fundamental particles are defined based on the R-matrix of the quantum group
deformation of the centrally extended superalgebra su(2|2). The S-matrices are
a function of two independent couplings g and q=exp(i\pi/k). The main result is
to find the scalar factor, or dressing phase, which ensures that the unitarity
and crossing equations are satisfied. For generic (g,k), the S-matrices are
branched functions on a product of rapidity tori. In the limit k->infinity, one
of them is identified with the S-matrix describing the magnon excitations on
the string world sheet in AdS5 x S5, while another is the mirror S-matrix that
is needed for the TBA. In the g->infinity limit, the rapidity torus
degenerates, the branch points disappear and the S-matrices become meromorphic
functions, as required by relativistic S-matrix theory. However, it is only the
mirror S-matrix which satisfies the correct relativistic crossing equation. The
mirror S-matrix in the relativistic limit is then closely related to that of
the semi-symmetric space sine-Gordon theory obtained from the string theory by
the Pohlmeyer reduction, but has anti-symmetric rather than symmetric bound
states. The interpolating S-matrix realizes at the quantum level the fact that
at the classical level the two theories correspond to different limits of a
one-parameter family of symplectic structures of the same integrable system.Comment: 41 pages, late
string S-matrices from unitarity cuts
Continuing the program initiated in arXiv:1304.1798 we investigate unitarity
methods applied to two-dimensional integrable field theories. The one-loop
computation is generalized to encompass theories with different masses in the
asymptotic spectrum and external leg corrections. Additionally, the
prescription for working with potentially singular cuts is modified to cope
with an ambiguity that was not encountered before. The resulting methods are
then applied to three light-cone gauge string theories; i) supported by RR flux, ii)
supported by RR flux and iii) supported by a mix
of RR and NSNS fluxes. In the first case we find agreement with the exact
result following from symmetry considerations and in the second case with
one-loop semiclassical computations. This agreement crucially includes the
rational terms and hence supports the conjecture that S-matrices of integrable
field theories are cut-constructible, up to a possible shift in the coupling.
In the final case, under the assumption that our methods continue to give all
rational terms, we give a conjecture for the one-loop phases
Marginal and non-commutative deformations via non-abelian T-duality
In this short article we develop recent proposals to relate Yang-Baxter sigma-models and non-abelian T-duality. We demonstrate explicitly that the holographic space-times associated to both (multi-parameter)-β-deformations and non-commutative deformations of N=4 super Yang-Mills gauge theory including the RR fluxes can be obtained via the machinery of non-abelian T-duality in Type II supergravity
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