228 research outputs found
An integrable deformation of the AdS5 x S5 superstring action
An integrable deformation of the type IIB AdS5xS5 superstring action is presented. The deformed field equations, Lax connection, and k-symmetry transformations are given. The original psu (2,2\4) symmetry is expected to become q deformed.Peer reviewedSubmitted Versio
A lattice Poisson algebra for the Pohlmeyer reduction of the AdS_5 x S^5 superstring
The Poisson algebra of the Lax matrix associated with the Pohlmeyer reduction
of the AdS_5 x S^5 superstring is computed from first principles. The resulting
non-ultralocality is mild, which enables to write down a corresponding lattice
Poisson algebra.Comment: 5 page
Vertex Lie algebras and cyclotomic coinvariants
Electronic version of an article published as Benoît Vicedo and Charles Young, Commun. Contemp. Math. 0, 1650015 (2016) [62 pages] DOI: http://dx.doi.org/10.1142/S0219199716500152 Vertex Lie algebras and cyclotomic coinvariants.Given a vertex Lie algebra equipped with an action by automorphisms of a cyclic group , we define spaces of cyclotomic coinvariants over the Riemann sphere. These are quotients of tensor products of smooth modules over `local' Lie algebras assigned to marked points , by the action of a `global' Lie algebra of -equivariant functions. On the other hand, the universal enveloping vertex algebra of is itself a vertex Lie algebra with an induced action of . This gives `big' analogs of the Lie algebras above. From these we construct the space of `big' cyclotomic coinvariants, i.e. coinvariants with respect to . We prove that these two definitions of cyclotomic coinvariants in fact coincide, provided the origin is included as a marked point. As a corollary we prove a result on the functoriality of cyclotomic coinvariants which we require for the solution of cyclotomic Gaudin models in arXiv:1409.6937. At the origin, which is fixed by , one must assign a module over the stable subalgebra of . This module becomes a -quasi-module in the sense of Li. As a bi-product we obtain an iterate formula for such quasi-modules.Peer reviewe
Giant Magnons and Singular Curves
We obtain the giant magnon of Hofman-Maldacena and its dyonic generalisation
on R x S^3 < AdS_5 x S^5 from the general elliptic finite-gap solution by
degenerating its elliptic spectral curve into a singular curve. This alternate
description of giant magnons as finite-gap solutions associated to singular
curves is related through a symplectic transformation to their already
established description in terms of condensate cuts developed in
hep-th/0606145.Comment: 34 pages, 17 figures, minor change in abstrac
Quantum Wrapped Giant Magnon
Understanding the finite-size corrections to the fundamental excitations of a
theory is the first step towards completely solving for the spectrum in finite
volume. We compute the leading exponential correction to the quantum energy of
the fundamental excitation of the light-cone gauged string in AdS(5) x S(5),
which is the giant magnon solution. We present two independent ways to obtain
this correction: the first approach makes use of the algebraic curve
description of the giant magnon. The second relies on the purely
field-theoretical Luscher formulas, which depend on the world-sheet S-matrix.
We demonstrate the agreement to all orders in g/Delta of these approaches,
which in particular presents a further test of the S-matrix. We comment on
generalizations of this method of computation to other string configurations.Comment: 17 pages, 2 figure
On classical q-deformations of integrable sigma-models
JHEP is an open-access journal funded by SCOAP3 and licensed under CC BY 4.0A procedure is developed for constructing deformations of integrable σ-models which are themselves classically integrable. When applied to the principal chiral model on any compact Lie group F, one recovers the Yang-Baxter σ-model introduced a few years ago by C. Klimčík. In the case of the symmetric space σ-model on F/G we obtain a new one-parameter family of integrable σ-models. The actions of these models correspond to a deformation of the target space geometry and include a torsion term. An interesting feature of the construction is the q-deformation of the symmetry corresponding to left multiplication in the original models, which becomes replaced by a classical q-deformed Poisson-Hopf algebra. Another noteworthy aspect of the deformation in the coset σ-model case is that it interpolates between a compact and a non-compact symmetric space. This is exemplified in the case of the SU(2)/U(1) coset σ-model which interpolates all the way to the SU(1, 1)/U(1) coset σ-modelPeer reviewedFinal Published versio
Integrable double deformation of the principal chiral model
© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3We define a two-parameter family of integrable deformations of the principal chiral model on an arbitrary compact group. The Yang–Baxter σ-model and the principal chiral model with a Wess–Zumino term both correspond to limits in which one of the two parameters vanishesPeer reviewe
On q-deformed symmetries as Poisson-Lie symmetries and application to Yang-Baxter type models
This is an author-created, un-copyedited version of an article accepted for publication in Journal of Physics A: Mathematical and Theoretical. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/1-.1088/1751-8113/49/41/415402. © 2016 IOP Publishing Ltd.Yang–Baxter type models are integrable deformations of integrable field theories, such as the principal chiral model on a Lie group G or σ-models on (semi-)symmetric spaces G/F. The deformation has the effect of breaking the global G-symmetry of the original model, replacing the associated set of conserved charges by ones whose Poisson brackets are those of the q-deformed Poisson–Hopf algebra Uq ( ) g . Working at the Hamiltonian level, we show how this q-deformed Poisson algebra originates from a Poisson–Lie G-symmetry. The theory of Poisson–Lie groups and their actions on Poisson manifolds, in particular the formalism of the non-abelian moment map, is reviewed. For a coboundary Poisson–Lie group G, this non-abelian moment map must obey the Semenov-TianShansky bracket on the dual group G*, up to terms involving central quantities. When the latter vanish, we develop a general procedure linking this Poisson bracket to the defining relations of the Poisson–Hopf algebra Uq ( ) g , including the q-Poisson–Serre relations. We consider reality conditions leading to q being either real or a phase. We determine the nonabelian moment map for Yang–Baxter type models. This enables to compute the corresponding action of G on the fields parametrising the phase space of these models.Peer reviewe
Exact computation of one-loop correction to energy of pulsating strings in AdS_5 x S^5
In the present paper, which is a sequel to arXiv:1001:4018, we compute the
one-loop correction to the energy of pulsating string solutions in AdS_5 x S^5.
We show that, as for rigid spinning string elliptic solutions, the fluctuation
operators for pulsating solutions can be also put into the single-gap Lame'
form. A novel aspect of pulsating solutions is that the one-loop correction to
their energy is expressed in terms of the stability angles of the quadratic
fluctuation operators. We explicitly study the "short string" limit of the
corresponding one-loop energies, demonstrating a certain universality of the
form of the energy of "small" semiclassical strings. Our results may help to
shed light on the structure of strong-coupling expansion of anomalous
dimensions of dual gauge theory operators.Comment: 49 pages; v2: appendix F and note about antiperiodic fermions added,
typos corrected, references adde
Alleviating the non-ultralocality of coset sigma models through a generalized Faddeev-Reshetikhin procedure
The Faddeev-Reshetikhin procedure corresponds to a removal of the
non-ultralocality of the classical SU(2) principal chiral model. It is realized
by defining another field theory, which has the same Lax pair and equations of
motion but a different Poisson structure and Hamiltonian. Following earlier
work of M. Semenov-Tian-Shansky and A. Sevostyanov, we show how it is possible
to alleviate in a similar way the non-ultralocality of symmetric space sigma
models. The equivalence of the equations of motion holds only at the level of
the Pohlmeyer reduction of these models, which corresponds to symmetric space
sine-Gordon models. This work therefore shows indirectly that symmetric space
sine-Gordon models, defined by a gauged Wess-Zumino-Witten action with an
integrable potential, have a mild non-ultralocality. The first step needed to
construct an integrable discretization of these models is performed by
determining the discrete analogue of the Poisson algebra of their Lax matrices.Comment: 31 pages; v2: minor change
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