1,294 research outputs found
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
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
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
Field theories with anisotropic scaling in 2D, solitons and the microscopic entropy of asymptotically Lifshitz black holes
Field theories with anisotropic scaling in 1+1 dimensions are considered. It
is shown that the isomorphism between Lifshitz algebras with dynamical
exponents z and 1/z naturally leads to a duality between low and high
temperature regimes. Assuming the existence of gap in the spectrum, this
duality allows to obtain a precise formula for the asymptotic growth of the
number of states with a fixed energy which depends on z and the energy of the
ground state, and reduces to the Cardy formula for z=1. The holographic
realization of the duality can be naturally inferred from the fact that
Euclidean Lifshitz spaces in three dimensions with dynamical exponents and
characteristic lengths given by z, l, and 1/z, l/z, respectively, are
diffeomorphic. The semiclassical entropy of black holes with Lifshitz
asymptotics can then be recovered from the generalization of Cardy formula,
where the ground state corresponds to a soliton. An explicit example is
provided by the existence of a purely gravitational soliton solution for BHT
massive gravity, which precisely has the required energy that reproduces the
entropy of the analytic asymptotically Lifshitz black hole with z=3.
Remarkably, neither the asymptotic symmetries nor central charges were
explicitly used in order to obtain these results.Comment: 17 pages, no figures, references corrected and update
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
The Regge Limit for Green Functions in Conformal Field Theory
We define a Regge limit for off-shell Green functions in quantum field
theory, and study it in the particular case of conformal field theories (CFT).
Our limit differs from that defined in arXiv:0801.3002, the latter being only a
particular corner of the Regge regime. By studying the limit for free CFTs, we
are able to reproduce the Low-Nussinov, BFKL approach to the pomeron at weak
coupling. The dominance of Feynman graphs where only two high momentum lines
are exchanged in the t-channel, follows simply from the free field analysis. We
can then define the BFKL kernel in terms of the two point function of a simple
light-like bilocal operator. We also include a brief discussion of the gravity
dual predictions for the Regge limit at strong coupling.Comment: 23 pages 2 figures, v2: Clarification of relation of the Regge limit
defined here and previous work in CFT. Clarification of causal orderings in
the limit. References adde
Long term time variability of cosmic rays and possible relevance to the development of life on Earth
An analysis is made of the manner in which the cosmic ray intensity at Earth
has varied over its existence and its possible relevance to both the origin and
the evolution of life. Much of the analysis relates to the 'high energy' cosmic
rays () and their variability due to the changing
proximity of the solar system to supernova remnants which are generally
believed to be responsible for most cosmic rays up to PeV energies. It is
pointed out that, on a statistical basis, there will have been considerable
variations in the likely 100 My between the Earth's biosphere reaching
reasonable stability and the onset of very elementary life. Interestingly,
there is the increasingly strong possibility that PeV cosmic rays are
responsible for the initiation of terrestrial lightning strokes and the
possibility arises of considerable increases in the frequency of lightnings and
thereby the formation of some of the complex molecules which are the 'building
blocks of life'. Attention is also given to the well known generation of the
oxides of nitrogen by lightning strokes which are poisonous to animal life but
helpful to plant growth; here, too, the violent swings of cosmic ray
intensities may have had relevance to evolutionary changes. A particular
variant of the cosmic ray acceleration model, put forward by us, predicts an
increase in lightning rate in the past and this has been sought in Korean
historical records. Finally, the time dependence of the overall cosmic ray
intensity, which manifests itself mainly at sub-10 GeV energies, has been
examined. The relevance of cosmic rays to the 'global electrical circuit'
points to the importance of this concept.Comment: 18 pages, 5 figures, accepted by 'Surveys in Geophysics
Holographic c-theorems in arbitrary dimensions
We re-examine holographic versions of the c-theorem and entanglement entropy
in the context of higher curvature gravity and the AdS/CFT correspondence. We
select the gravity theories by tuning the gravitational couplings to eliminate
non-unitary operators in the boundary theory and demonstrate that all of these
theories obey a holographic c-theorem. In cases where the dual CFT is
even-dimensional, we show that the quantity that flows is the central charge
associated with the A-type trace anomaly. Here, unlike in conventional
holographic constructions with Einstein gravity, we are able to distinguish
this quantity from other central charges or the leading coefficient in the
entropy density of a thermal bath. In general, we are also able to identify
this quantity with the coefficient of a universal contribution to the
entanglement entropy in a particular construction. Our results suggest that
these coefficients appearing in entanglement entropy play the role of central
charges in odd-dimensional CFT's. We conjecture a new c-theorem on the space of
odd-dimensional field theories, which extends Cardy's proposal for even
dimensions. Beyond holography, we were able to show that for any
even-dimensional CFT, the universal coefficient appearing the entanglement
entropy which we calculate is precisely the A-type central charge.Comment: 62 pages, 4 figures, few typo's correcte
Comments on Holographic Entanglement Entropy and RG Flows
Using holographic entanglement entropy for strip geometry, we construct a
candidate for a c-function in arbitrary dimensions. For holographic theories
dual to Einstein gravity, this c-function is shown to decrease monotonically
along RG flows. A sufficient condition required for this monotonic flow is that
the stress tensor of the matter fields driving the holographic RG flow must
satisfy the null energy condition over the holographic surface used to
calculate the entanglement entropy. In the case where the bulk theory is
described by Gauss-Bonnet gravity, the latter condition alone is not sufficient
to establish the monotonic flow of the c-function. We also observe that for
certain holographic RG flows, the entanglement entropy undergoes a 'phase
transition' as the size of the system grows and as a result, evolution of the
c-function may exhibit a discontinuous drop.Comment: References adde
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