1,020 research outputs found
Superstrings with multiplicities
A superstring of a set of words P = s1, · · · , sp is a string that contains each word of P as substring. Given P, the well known Shortest Linear Superstring problem (SLS), asks for a shortest superstring of P. In a variant of SLS, called Multi-SLS, each word si comes with an integer m(i), its multiplicity, that sets a constraint on its number of occurrences, and the goal is to find a shortest superstring that contains at least m(i) occurrences of si. Multi-SLS generalizes SLS and is obviously as hard to solve, but it has been studied only in special cases (with words of length 2 or with a fixed number of words). The approximability of Multi-SLS in the general case remains open. Here, we study the approximability of Multi-SLS and that of the companion problem Multi-SCCS, which asks for a shortest cyclic cover instead of shortest superstring. First, we investigate the approximation of a greedy algorithm for maximizing the compression offered by a superstring or by a cyclic cover: the approximation ratio is 1/2 for Multi-SLS and 1 for Multi-SCCS. Then, we exhibit a linear time approximation algorithm, Concat-Greedy, and show it achieves a ratio of 4 regarding the superstring length. This demonstrates that for both measures Multi-SLS belongs to the class of APX problems. © 2018 Yoshifumi Sakai; licensed under Creative Commons License CC-BY.Peer reviewe
The open story of the magnetic fluxes
We discuss the effects of oblique internal magnetic fields on the spectrum of
type I superstrings compactified on tori. In particular we derive general
formulae for the magnetic shifts and multiplicities of open strings connecting
D9-branes with arbitrary magnetic fluxes. We discuss the flux induced potential
and offer an interpretation of the stabilization of R-R moduli associated to
deformations of the complex structure of T^6 in terms of non-derivative mixing
with NS-NS moduli. Finally we briefly comment on how to extract other low
energy couplings and generalize our results to toroidal orbifolds and other
configurations governed by rational conformal field theories on the worldsheet.Comment: 36 pages, LaTeX, References adde
Partition Functions of Pure Spinors
We compute partition functions describing multiplicities and charges of
massless and first massive string states of pure-spinor superstrings in
3,4,6,10 dimensions. At the massless level we find a spin-one gauge multiplet
of minimal supersymmetry in d dimensions. At the first massive string level we
find a massive spin-two multiplet. The result is confirmed by a direct analysis
of the BRST cohomology at ghost number one. The central charges of the pure
spinor systems are derived in a manifestly SO(d) covariant way confirming that
the resulting string theories are critical. A critical string model with
N=(2,0) supersymmetry in d=2 is also described.Comment: LaTex, 30 p
String Theory on Dp-plane waves
We study the spectrum of solvable string models on plane waves descending
from non-conformal Dp-brane geometries. We mainly focus on S-dual F1/D1-waves
in type IIB and type I/heterotic 10D superstrings. We derive the Kaluza-Klein
spectrum of N=1,2 10D supergravities on D1/F1-waves. We compute helicity
supertraces counting multiplicities and R-charges of string excitations in the
plane wave geometry. The results are compared against the expectations coming
from gauge/supergravity descriptions. In the type I case, the Klein, Annulus
and Moebius one-loop amplitudes are computed for ten-dimensional D1-waves. We
test the consistency of the open string descendant by showing that after
modular transformations to the closed string channel, the three amplitudes
combine themselves to reconstruct a complete square (|B>+|C>)^2. Tadpole
conditions are also discussed.Comment: 22 pages, Minor corrections, References adde
The Bosonic Ancestor of Closed and Open Fermionic Strings
We review the emergence of the ten-dimensional fermionic closed string
theories from subspaces of the Hilbert space of the 26-dimensional bosonic
closed string theory compactified on an lattice. They arise
from a consistent truncation procedure which generates space-time fermions out
of bosons. This procedure is extended to open string sectors. We prove, from
bosonic considerations alone, that truncation of the unique tadpole-free
bosonic string theory compactified on the above lattice determines
the anomaly free Chan-Paton group of the Type I theory. It also yields the
Chan-Paton groups making Type O theories tadpole-free. These results establish
a link between all M-theory strings and the bosonic string within the framework
of conformal field theory. Its significance is discussed.Comment: LaTeX files, 16 pages. Contribution to the Francqui meeting, Brussels
2001 and Corfu Summer Institute 2001. Based on hep-th/010623
A Note on Toroidal Compactifications of the Type I Superstring and Other Superstring Vacuum Configurations with 16 Supercharges
We show that various disconnected components of the moduli space of
superstring vacua with 16 supercharges admit a rationale in terms of BPS
un-orientifolds, i.e. type I toroidal compactifications with constant
non-vanishing but quantized vacuum expectation values of the NS-NS
antisymmetric tensor. These include various heterotic vacua with reduced rank,
known as CHL strings, and their dual type II (2,2) superstrings below D=6. Type
I vacua without open strings allow for an interpretation of several
disconnected components with N_V=10-D. An adiabatic argument relates these
unconventional type I superstrings to type II (4,0) superstrings without
D-branes. The latter are connected by U-duality below D=6 to type II (2,2)
superstrings. We also comment on the relation between some of these vacua and
compactifications of the putative M-theory on unorientable manifolds as well as
F-theory vacua.Comment: Expanded discussion of rational un-orientifolds. Comments on
disconnected components of type I moduli spaces. Several references added.
Final version to appear in Nuclear Physics B528 (1998). 22 pages, Late
Superstrings on AdS3 at k=1
We study superstring theory in three dimensional Anti-de Sitter spacetime
with NS-NS flux, focusing on the case where the radius of curvature is equal to
the string length. This corresponds to the critical level k=1 in the
Wess-Zumino-Witten description. Previously, it was argued that a transition
takes place at this special radius, from a phase dominated by black holes at
larger radius to one dominated by long strings at smaller radius. We argue that
the infinite tower of modes that become massless at k=1 is a signal of this
transition. We propose a simple two-dimensional conformal field theory as the
holographic dual to superstring theory at k=1. As evidence for our conjecture,
we demonstrate that at large N our putative dual exactly reproduces the full
spectrum of the long strings of the weakly coupled string theory, including
states unprotected by supersymmetry.Comment: 29 pages, one figure. An equivalent construction of the dual orbifold
CFT has been added, together with a discussion of the short string spectrum
and additional observations on interaction
Remarks on E11 approach
We consider a few topics in approach to superstring/M-theory: even
subgroups ( orbifolds) of , n=11,10,9 and their connection to
Kac-Moody algebras; subgroup of and coincidence of one of
its weights with the weight of , known to contain brane charges;
possible form of supersymmetry relation in ; decomposition of
w.r.t. the and its square root at first few levels; particle orbit
of . Possible relevance of coadjoint orbits method is
noticed, based on a self-duality form of equations of motion in .Comment: Two references adde
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