3,055 research outputs found
On the relation between p-adic and ordinary strings
The amplitudes for the tree-level scattering of the open string tachyons,
generalised to the field of p-adic numbers, define the p-adic string theory.
There is empirical evidence of its relation to the ordinary string theory in
the p_to_1 limit. We revisit this limit from a worldsheet perspective and argue
that it is naturally thought of as a continuum limit in the sense of the
renormalisation group.Comment: 13 pages harvmac (b), 2 eps figures; v2: revtex, shortened, published
versio
Growing distributed networks with arbitrary degree distributions
We consider distributed networks, such as peer-to-peer networks, whose
structure can be manipulated by adjusting the rules by which vertices enter and
leave the network. We focus in particular on degree distributions and show
that, with some mild constraints, it is possible by a suitable choice of rules
to arrange for the network to have any degree distribution we desire. We also
describe a mechanism based on biased random walks by which appropriate rules
could be implemented in practice. As an example application, we describe and
simulate the construction of a peer-to-peer network optimized to minimize
search times and bandwidth requirements.Comment: 10 pages, 2 figure
Bicomponents and the robustness of networks to failure
A common definition of a robust connection between two nodes in a network
such as a communication network is that there should be at least two
independent paths connecting them, so that the failure of no single node in the
network causes them to become disconnected. This definition leads us naturally
to consider bicomponents, subnetworks in which every node has a robust
connection of this kind to every other. Here we study bicomponents in both real
and model networks using a combination of exact analytic techniques and
numerical methods. We show that standard network models predict there to be
essentially no small bicomponents in most networks, but there may be a giant
bicomponent, whose presence coincides with the presence of the ordinary giant
component, and we find that real networks seem by and large to follow this
pattern, although there are some interesting exceptions. We study the size of
the giant bicomponent as nodes in the network fail, using a specially developed
computer algorithm based on data trees, and find in some cases that our
networks are quite robust to failure, with large bicomponents persisting until
almost all vertices have been removed.Comment: 5 pages, 1 figure, 1 tabl
The SO(N) principal chiral field on a half-line
We investigate the integrability of the SO(N) principal chiral model on a
half-line, and find that mixed Dirichlet/Neumann boundary conditions (as well
as pure Dirichlet or Neumann) lead to infinitely many conserved charges
classically in involution. We use an anomaly-counting method to show that at
least one non-trivial example survives quantization, compare our results with
the proposed reflection matrices, and, based on these, make some preliminary
remarks about expected boundary bound-states.Comment: 7 pages, Late
On a_2^(1) Reflection Matrices and Affine Toda Theories
We construct new non-diagonal solutions to the boundary Yang-Baxter-Equation
corresponding to a two-dimensional field theory with U_q(a_2^(1)) quantum
affine symmetry on a half-line. The requirements of boundary unitarity and
boundary crossing symmetry are then used to find overall scalar factors which
lead to consistent reflection matrices. Using the boundary bootstrap equations
we also compute the reflection factors for scalar bound states (breathers).
These breathers are expected to be identified with the fundamental quantum
particles in a_2^(1) affine Toda field theory and we therefore obtain a
conjecture for the affine Toda reflection factors. We compare these factors
with known classical results and discuss their duality properties and their
connections with particular boundary conditions.Comment: 34 pages, 4 figures, Latex2e, mistake in App. A corrected, some
references adde
Integrable Boundary Conditions and Reflection Matrices for the O(N) Nonlinear Sigma Model
We find new integrable boundary conditions, depending on a free parameter
, for the O(N) nonlinear model, which are of nondiagonal type, that
is, particles can change their ``flavor'' through scattering off the boundary.
These boundary conditions are derived from a microscopic boundary lagrangian,
which is used to establish their integrability, and exhibit integrable flows
between diagonal boundary conditions investigated earlier. We solve the
boundary Yang-Baxter equation, connect these solutions to the boundary
conditions, and examine the corresponding integrable flows.Comment: 21 pages, 2 figures. v2: References added, typos corrected, few
comments adde
Kink-boundary collisions in a two dimensional scalar field theory
In a two-dimensional toy model, motivated from five-dimensional heterotic
M-theory, we study the collision of scalar field kinks with boundaries. By
numerical simulation of the full two-dimensional theory, we find that the kink
is always inelastically reflected with a model-independent fraction of its
kinetic energy converted into radiation. We show that the reflection can be
analytically understood as a fluctuation around the scalar field vacuum. This
picture suggests the possibility of spontaneous emission of kinks from the
boundary due to small perturbations in the bulk. We verify this picture
numerically by showing that the radiation emitted from the collision of an
initial single kink eventually leads to a bulk populated by many kinks.
Consequently, processes changing the boundary charges are practically
unavoidable in this system. We speculate that the system has a universal final
state consisting of a stack of kinks, their number being determined by the
initial energy
Supersymmetric WZW Model on Full and Half Plane
We study classical integrability of the supersymmetric U(N) model
with the Wess-Zumino-Witten term on full and half plane. We demonstrate the
existence of nonlocal conserved currents of the model and derive general
recursion relations for the infinite number of the corresponding charges in a
superfield framework. The explicit form of the first few supersymmetric charges
are constructed. We show that the considered model is integrable on full plane
as a concequence of the conservation of the supersymmetric charges. Also, we
study the model on half plane with free boundary, and examine the conservation
of the supersymmetric charges on half plane and find that they are conserved as
a result of the equations of motion and the free boundary condition. As a
result, the model on half plane with free boundary is integrable. Finally, we
conclude the paper and some features and comments are presented.Comment: 12 pages. submitted to IJMP
Exact solutions for models of evolving networks with addition and deletion of nodes
There has been considerable recent interest in the properties of networks,
such as citation networks and the worldwide web, that grow by the addition of
vertices, and a number of simple solvable models of network growth have been
studied. In the real world, however, many networks, including the web, not only
add vertices but also lose them. Here we formulate models of the time evolution
of such networks and give exact solutions for a number of cases of particular
interest. For the case of net growth and so-called preferential attachment --
in which newly appearing vertices attach to previously existing ones in
proportion to vertex degree -- we show that the resulting networks have
power-law degree distributions, but with an exponent that diverges as the
growth rate vanishes. We conjecture that the low exponent values observed in
real-world networks are thus the result of vigorous growth in which the rate of
addition of vertices far exceeds the rate of removal. Were growth to slow in
the future, for instance in a more mature future version of the web, we would
expect to see exponents increase, potentially without bound.Comment: 9 pages, 3 figure
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