10,038 research outputs found
Algorithms for anti-powers in strings
A string S[1,n] is a power (or tandem repeat) of order k and period n/k if it can be decomposed into k consecutive equal-length blocks of letters. Powers and periods are fundamental to string processing, and algorithms for their efficient computation have wide application and are heavily studied. Recently, Fici et al. (Proc. ICALP 2016) defined an anti-power of order k to be a string composed of k pairwise-distinct blocks of the same length (n/k, called anti-period). Anti-powers are a natural converse to powers, and are objects of combinatorial interest in their own right. In this paper we initiate the algorithmic study of anti-powers. Given a string S, we describe an optimal algorithm for locating all substrings of S that are anti-powers of a specified order. The optimality of the algorithm follows form a combinatorial lemma that provides a lower bound on the number of distinct anti-powers of a given order: we prove that a string of length n can contain Î(n2/k) distinct anti-powers of order k.Peer reviewe
The spectrum of tachyons in AdS/CFT
We analyze the spectrum of open strings stretched between a D-brane and an
anti-D-brane in planar AdS/CFT using various tools. We focus on open strings
ending on two giant gravitons with different orientation in
and study the spectrum of string excitations using the following approaches:
open spin-chain, boundary asymptotic Bethe ansatz and boundary thermodynamic
Bethe ansatz (BTBA). We find agreement between a perturbative high order
diagrammatic calculation in SYM and the leading finite-size
boundary Luscher correction. We study the ground state energy of the system at
finite coupling by deriving and numerically solving a set of BTBA equations.
While the numerics give reasonable results at small coupling, they break down
at finite coupling when the total energy of the string gets close to zero,
possibly indicating that the state turns tachyonic. The location of the
breakdown is also predicted analytically.Comment: 40 pages, lots of figures, v2: typos corrected, accepted for
publication in JHE
Cadabra: reference guide and tutorial
Cadabra is a computer algebra system for the manipulation of tensorial mathematical expressions such as they occur in âfield theory problemsâ. It is aimed at, but not necessarily restricted to, high-energy physicists. It is constructed as a simple tree-manipulating core, a large collection of standalone algorithmic modules which act on the expression tree, and a set of modules responsible for output of nodes in the tree. All of these parts are written in C++. The input and output formats closely follow TEX, which in many cases means that cadabra is much simpler to use than other similar programs. It intentionally does not contain its own programming language; instead, new functionality is added by writing new modules in C++
QCD and String Theory
This talk begins with some history and basic facts about string theory and
its connections with strong interactions. Comparisons of stacks of Dirichlet
branes with curved backgrounds produced by them are used to motivate the
AdS/CFT correspondence between superconformal gauge theory and string theory on
a product of Anti-de Sitter space and a compact manifold. The ensuing duality
between semi-classical spinning strings and long gauge theory operators is
briefly reviewed. Strongly coupled thermal SYM theory is explored via a black
hole in 5-dimensional AdS space, which leads to explicit results for its
entropy and shear viscosity. A conjectured universal lower bound on the
viscosity to entropy density ratio, and its possible relation to recent results
from RHIC, are discussed. Finally, some available results on string duals of
confining gauge theories are briefly reviewed.Comment: 12 pages, prepared for the Proceedings of the 2005 Lepton-Photon
Symposium; v2: minor revisions, references added, the version to appear in
the proceeding
Generic Construction of Efficient Matrix Product Operators
Matrix Product Operators (MPOs) are at the heart of the second-generation
Density Matrix Renormalisation Group (DMRG) algorithm formulated in Matrix
Product State language. We first summarise the widely known facts on MPO
arithmetic and representations of single-site operators. Second, we introduce
three compression methods (Rescaled SVD, Deparallelisation and Delinearisation)
for MPOs and show that it is possible to construct efficient representations of
arbitrary operators using MPO arithmetic and compression. As examples, we
construct powers of a short-ranged spin-chain Hamiltonian, a complicated
Hamiltonian of a two-dimensional system and, as proof of principle, the
long-range four-body Hamiltonian from quantum chemistry.Comment: 13 pages, 10 figure
On the Parikh-de-Bruijn grid
We introduce the Parikh-de-Bruijn grid, a graph whose vertices are
fixed-order Parikh vectors, and whose edges are given by a simple shift
operation. This graph gives structural insight into the nature of sets of
Parikh vectors as well as that of the Parikh set of a given string. We show its
utility by proving some results on Parikh-de-Bruijn strings, the abelian analog
of de-Bruijn sequences.Comment: 18 pages, 3 figures, 1 tabl
Hypermatrix factors for string and membrane junctions
The adjoint representations of the Lie algebras of the classical groups
SU(n), SO(n), and Sp(n) are, respectively, tensor, antisymmetric, and symmetric
products of two vector spaces, and hence are matrix representations. We
consider the analogous products of three vector spaces and study when they
appear as summands in Lie algebra decompositions. The Z3-grading of the
exceptional Lie algebras provide such summands and provides representations of
classical groups on hypermatrices. The main natural application is a formal
study of three-junctions of strings and membranes. Generalizations are also
considered.Comment: 25 pages, 4 figures, presentation improved, minor correction
Digitizing the Neveu-Schwarz Model on the Lightcone Worldsheet
The purpose of this article is to extend the lightcone worldsheet lattice
description of string theory to include the Neveu-Schwarz model. We model each
component of the fermionic worldsheet field by a critical Ising model. We show
that a simple choice of boundary conditions for the Ising variables leads to
the half integer modes required by the model. We identify the G-parity
operation within the Ising model and formulate the procedure for projecting
onto the even G-parity sector. We construct the lattice version of the three
open string vertex, with the necessary operator insertion at the interaction
point. We sketch a formalism for summing planar open string multi-loop
amplitudes, and we discuss prospects for numerically summing them. If
successful, the methods described here could provide an alternative to lattice
gauge theory for computations in large N QCD.Comment: 23 pages, 7 figure
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