179 research outputs found
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
Constant mean curvature surfaces in AdS_3
We construct constant mean curvature surfaces of the general finite-gap type
in AdS_3. The special case with zero mean curvature gives minimal surfaces
relevant for the study of Wilson loops and gluon scattering amplitudes in N=4
super Yang-Mills. We also analyze properties of the finite-gap solutions
including asymptotic behavior and the degenerate (soliton) limit, and discuss
possible solutions with null boundaries.Comment: 19 pages, v2: minor corrections, to appear in JHE
Classical integrability in the BTZ black hole
Using the fact the BTZ black hole is a quotient of AdS_3 we show that
classical string propagation in the BTZ background is integrable. We construct
the flat connection and its monodromy matrix which generates the non-local
charges. From examining the general behaviour of the eigen values of the
monodromy matrix we determine the set of integral equations which constrain
them. These equations imply that each classical solution is characterized by a
density function in the complex plane. For classical solutions which correspond
to geodesics and winding strings we solve for the eigen values of the monodromy
matrix explicitly and show that geodesics correspond to zero density in the
complex plane. We solve the integral equations for BMN and magnon like
solutions and obtain their dispersion relation. Finally we show that the set of
integral equations which constrain the eigen values of the monodromy matrix can
be identified with the continuum limit of the Bethe equations of a twisted
SL(2, R) spin chain at one loop.Comment: 45 pages, Reference added, typos corrected, discussion on geodesics
improved to include all geodesic
The Combinatorics of Alternating Tangles: from theory to computerized enumeration
We study the enumeration of alternating links and tangles, considered up to
topological (flype) equivalences. A weight is given to each connected
component, and in particular the limit yields information about
(alternating) knots. Using a finite renormalization scheme for an associated
matrix model, we first reduce the task to that of enumerating planar
tetravalent diagrams with two types of vertices (self-intersections and
tangencies), where now the subtle issue of topological equivalences has been
eliminated. The number of such diagrams with vertices scales as for
. We next show how to efficiently enumerate these diagrams (in time
) by using a transfer matrix method. We give results for various
generating functions up to 22 crossings. We then comment on their large-order
asymptotic behavior.Comment: proceedings European Summer School St-Petersburg 200
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
Large Representation Recurrences in Large N Random Unitary Matrix Models
In a random unitary matrix model at large N, we study the properties of the
expectation value of the character of the unitary matrix in the rank k
symmetric tensor representation. We address the problem of whether the standard
semiclassical technique for solving the model in the large N limit can be
applied when the representation is very large, with k of order N. We find that
the eigenvalues do indeed localize on an extremum of the effective potential;
however, for finite but sufficiently large k/N, it is not possible to replace
the discrete eigenvalue density with a continuous one. Nonetheless, the
expectation value of the character has a well-defined large N limit, and when
the discreteness of the eigenvalues is properly accounted for, it shows an
intriguing approximate periodicity as a function of k/N.Comment: 24 pages, 11 figure
Large-N spacetime reduction and the sign and silver-blaze problems of dense QCD
We study the spacetime-reduced (Eguchi-Kawai) version of large-N QCD with
nonzero chemical potential. We explore a method to suppress the sign
fluctuations of the Dirac determinant in the hadronic phase; the method employs
a re-summation of gauge configurations that are related to each other by center
transformations. We numerically test this method in two dimensions, and find
that it successfully solves the silver-blaze problem. We analyze the system
further, and measure its free energy F, the average phase theta of its Dirac
determinant, and its chiral condensate . We show that F and
are independent of mu in the hadronic phase but that, as chiral
perturbation theory predicts, the quenched chiral condensate drops from its
mu=0 value when mu~(pion mass)/2. Finally, we find that the distribution of
theta qualitatively agrees with further, more recent, predictions from chiral
perturbation theory.Comment: 43 pages, 17 figure
Lorentzian and Euclidean Quantum Gravity - Analytical and Numerical Results
We review some recent attempts to extract information about the nature of
quantum gravity, with and without matter, by quantum field theoretical methods.
More specifically, we work within a covariant lattice approach where the
individual space-time geometries are constructed from fundamental simplicial
building blocks, and the path integral over geometries is approximated by
summing over a class of piece-wise linear geometries. This method of
``dynamical triangulations'' is very powerful in 2d, where the regularized
theory can be solved explicitly, and gives us more insights into the quantum
nature of 2d space-time than continuum methods are presently able to provide.
It also allows us to establish an explicit relation between the Lorentzian- and
Euclidean-signature quantum theories. Analogous regularized gravitational
models can be set up in higher dimensions. Some analytic tools exist to study
their state sums, but, unlike in 2d, no complete analytic solutions have yet
been constructed. However, a great advantage of our approach is the fact that
it is well-suited for numerical simulations. In the second part of this review
we describe the relevant Monte Carlo techniques, as well as some of the
physical results that have been obtained from the simulations of Euclidean
gravity. We also explain why the Lorentzian version of dynamical triangulations
is a promising candidate for a non-perturbative theory of quantum gravity.Comment: 69 pages, 16 figures, references adde
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