37 research outputs found
Classical and Quantum Solitons in the Symmetric Space Sine-Gordon Theories
We construct the soliton solutions in the symmetric space sine-Gordon
theories. The latter are a series of integrable field theories in
1+1-dimensions which are associated to a symmetric space F/G, and are related
via the Pohlmeyer reduction to theories of strings moving on symmetric spaces.
We show that the solitons are kinks that carry an internal moduli space that
can be identified with a particular co-adjoint orbit of the unbroken subgroup H
of G. Classically the solitons come in a continuous spectrum which encompasses
the perturbative fluctuations of the theory as the kink charge becomes small.
We show that the solitons can be quantized by allowing the collective
coordinates to be time-dependent to yield a form of quantum mechanics on the
co-adjoint orbit. The quantum states correspond to symmetric tensor
representations of the symmetry group H and have the interpretation of a fuzzy
geometric version of the co-adjoint orbit. The quantized finite tower of
soliton states includes the perturbative modes at the base.Comment: 53 pages, additional comments and small errors corrected, final
journal versio
On the perturbative S-matrix of generalized sine-Gordon models
Motivated by its relation to the Pohlmeyer reduction of AdS_5 x S^5
superstring theory we continue the investigation of the generalized sine-Gordon
model defined by SO(N+1)/SO(N) gauged WZW theory with an integrable potential.
Extending our previous work (arXiv:0912.2958) we compute the one-loop
two-particle S-matrix for the elementary massive excitations. In the N = 2 case
corresponding to the complex sine-Gordon theory it agrees with the charge-one
sector of the quantum soliton S-matrix proposed in hep-th/9410140. In the case
of N > 2 when the gauge group SO(N) is non-abelian we find a curious anomaly in
the Yang-Baxter equation which we interpret as a gauge artifact related to the
fact that the scattered particles are not singlets under the residual global
subgroup of the gauge group
The AdS(5)xS(5) Semi-Symmetric Space Sine-Gordon Theory
The generalized symmetric space sine-Gordon theories are a series of
1+1-integrable field theories that are classically equivalent to superstrings
on symmetric space spacetimes F/G. They are formulated in terms of a
semi-symmetric space as a gauged WZW model with fermions and a potential term
to deform it away from the conformal fixed point. We consider in particular the
case of PSU(2,2|4)/Sp(2,2)xSp(4) which corresponds to AdS(5)xS(5). We argue
that the infinite tower of conserved charges of these theories includes an
exotic N=(8,8) supersymmetry that is realized in a mildy non-local way at the
Lagrangian level. The supersymmetry is associated to a double central extension
of the superalgebra psu(2|2)+psu(2|2) and includes a non-trivial R symmetry
algebra corresponding to global gauge transformations, as well as 2-dimensional
spacetime translations. We then explicitly construct soliton solutions and show
that they carry an internal moduli superspace CP(2|1)xCP(2|1) with both bosonic
and Grassmann collective coordinates. We show how to semi-classical quantize
the solitons by writing an effective quantum mechanical system on the moduli
space which takes the form of a co-adjoint orbit of SU(2|2)xSU(2|2). The
spectrum consists of a tower of massive states in the short, or atypical,
symmetric representations, just as the giant magnon states of the string world
sheet theory, although here the tower is truncated.Comment: 39 pages, references adde
The Relativistic Avatars of Giant Magnons and their S-Matrix
The motion of strings on symmetric space target spaces underlies the
integrability of the AdS/CFT correspondence. Although these theories, whose
excitations are giant magnons, are non-relativistic they are classically
equivalent, via the Polhmeyer reduction, to a relativistic integrable field
theory known as a symmetric space sine-Gordon theory. These theories can be
formulated as integrable deformations of gauged WZW models. In this work we
consider the class of symmetric spaces CP^{n+1} and solve the corresponding
generalized sine-Gordon theories at the quantum level by finding the exact
spectrum of topological solitons, or kinks, and their S-matrix. The latter
involves a trignometric solution of the Yang-Baxer equation which exhibits a
quantum group symmetry with a tower of states that is bounded, unlike for
magnons, as a result of the quantum group deformation parameter q being a root
of unity. We test the S-matrix by taking the semi-classical limit and comparing
with the time delays for the scattering of classical solitons. We argue that
the internal CP^{n-1} moduli space of collective coordinates of the solitons in
the classical theory can be interpreted as a q-deformed fuzzy space in the
quantum theory. We analyse the n=1 case separately and provide a further test
of the S-matrix conjecture in this case by calculating the central charge of
the UV CFT using the thermodynamic Bethe Ansatz.Comment: 33 pages, important correction to S-matrix to ensure crossing
symmetr
Supersymmetry Flows, Semi-Symmetric Space Sine-Gordon Models And The Pohlmeyer Reduction
We study the extended supersymmetric integrable hierarchy underlying the
Pohlmeyer reduction of superstring sigma models on semi-symmetric superspaces
F/G. This integrable hierarchy is constructed by coupling two copies of the
homogeneous integrable hierarchy associated to the loop Lie superalgebra
extension f of the Lie superalgebra f of F and this is done by means of the
algebraic dressing technique and a Riemann-Hilbert factorization problem. By
using the Drinfeld-Sokolov procedure we construct explicitly, a set of 2D spin
\pm1/2 conserved supercharges generating supersymmetry flows in the phase space
of the reduced model. We introduce the bi-Hamiltonian structure of the extended
homogeneous hierarchy and show that the two brackets are of the
Kostant-Kirillov type on the co-adjoint orbits defined by the light-cone Lax
operators L_\pm. By using the second symplectic structure, we show that these
supersymmetries are Hamiltonian flows, we compute part of the supercharge
algebra and find the supersymmetric field variations they induce. We also show
that this second Poisson structure coincides with the canonical
Lorentz-Invariant symplectic structure of the WZNW model involved in the
Lagrangian formulation of the extended integrable hierarchy, namely, the
semi-symmetric space sine-Gordon model (SSSSG), which is the Pohlmeyer reduced
action functional for the transverse degrees of freedom of superstring sigma
models on the cosets F/G. We work out in some detail the Pohlmeyer reduction of
the AdS_2xS^2 and the AdS_3xS^3 superstrings and show that the new conserved
supercharges can be related to the supercharges extracted from 2D superspace.
In particular, for the AdS_2xS^2 example, they are formally the same.Comment: V2: Two references added, V3: Modifications in section 2.6, V4:
Published versio
Spiky Strings and Giant Holes
We analyse semiclassical strings in AdS in the limit of one large spin. In
this limit, classical string dynamics is described by a finite number of
collective coordinates corresponding to spikes or cusps of the string. The
semiclassical spectrum consists of two branches of excitations corresponding to
"large" and "small" spikes respectively. We propose that these states are dual
to the excitations known as large and small holes in the spin chain description
of N=4 SUSY Yang-Mills. The dynamics of large spikes in classical string theory
can be mapped to that of a classical spin chain of fixed length. In turn, small
spikes correspond to classical solitons propagating on the background formed by
the large spikes. We derive the dispersion relation for these excitations
directly in the finite gap formalism.Comment: 36 pages, 9 figure
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
Scattering and duality in the 2 dimensional OSP(2|2) Gross Neveu and sigma models
We write the thermodynamic Bethe ansatz for the massive OSp(2|2) Gross Neveu
and sigma models. We find evidence that the GN S matrix proposed by Bassi and
Leclair [12] is the correct one. We determine features of the sigma model S
matrix, which seem highly unconventional; we conjecture in particular a
relation between this sigma model and the complex sine-Gordon model at a
particular value of the coupling. We uncover an intriguing duality between the
OSp(2|2) GN (resp. sigma) model on the one hand, and the SO(4) sigma (resp. GN
model) on the other, somewhat generalizing to the massive case recent results
on OSp(4|2). Finally, we write the TBA for the (SUSY version of the) flow into
the random bond Ising model proposed by Cabra et al. [39], and conclude that
their S matrix cannot be correct.Comment: 41 pages, 27 figures. v2: minor revisio
Series Solution and Minimal Surfaces in AdS
According to the Alday-Maldacena program the strong coupling limit of Super
Yang-Mills scattering amplitudes is given by minimal area surfaces in AdS
spacetime with a boundary consisting of a momentum space polygon. The string
equations in AdS systematically reduce to coupled Toda type equations whose
Euclidean classical solutions are then of direct relevance. While in the
simplest case of AdS_3 exact solutions were known from earlier studies of the
sinh-Gordon equation, there exist at present no similar exact forms for the
generalized Toda equations related to AdS_d with d>=4. In this paper we develop
a series method for the solution to those equations and evaluate their
contribution to the finite piece of the worldsheet area. For the known
sinh-Gordon case the method is seen to give results in excellent agreement with
the exact answer.Comment: 19 pages, no figures; references added, one note adde
g-Functions and gluon scattering amplitudes at strong coupling
We study gluon scattering amplitudes/Wilson loops in N=4 super Yang-Mills
theory at strong coupling by calculating the area of the minimal surfaces in
AdS_3 based on the associated thermodynamic Bethe ansatz system. The remainder
function of the amplitudes is computed by evaluating the free energy, the T-
and Y-functions of the homogeneous sine-Gordon model. Using conformal field
theory (CFT) perturbation, we examine the mass corrections to the free energy
around the CFT point corresponding to the regular polygonal Wilson loop. Based
on the equivalence between the T-functions and the g-functions, which measure
the boundary entropy, we calculate corrections to the T- and Y-functions as
well as express them at the CFT point by the modular S-matrix. We evaluate the
remainder function around the CFT point for 8 and 10-point amplitudes
explicitly and compare these analytic expressions with the 2-loop formulas. The
two rescaled remainder functions show very similar power series structures.Comment: 51 pages, 4 figures, v2: some comments and references added, based on
the published version, v3: minor change