6,163 research outputs found
Perturbation Theory for Singular Potentials in Quantum Mechanics
We study perturbation theory in certain quantum mechanics problems in which
the perturbing potential diverges at some points, even though the energy
eigenvalues are smooth functions of the coefficient of the potential. We
discuss some of the unusual techniques which are required to obtain
perturbative expansions of the energies in such cases. These include a
point-splitting prescription for expansions around the Dirichlet (fermionic)
limit of the -function potential, and performing a similarity
transformation to a non-Hermitian potential in the Calogero-Sutherland model.
As an application of the first technique, we study the ground state of the
-function Bose gas near the fermionic limit.Comment: LaTeX, 19 pages, no figure
Quark mass and condensate in HQCD
We extend the Sakai-Sugimoto holographic model of QCD (HQCD) by including the
scalar bi-fundamental "tachyon" field in the 8-brane-anti-8-brane probe theory.
We show that this field is responsible both for the spontaneous breaking of the
chiral symmetry, and for the generation of (current algebra) quark masses, from
the point of view of the bulk theory. As a by-product we show how this leads to
the Gell-Mann- Oakes-Renner relation for the pion mass.Comment: 23 pages, 7 figures; v2: corrected typos in eqs. (4.3), (4.4), (4.5),
(4.9) and (4.11), and corrected figures 3, 4, 5 and 6; v3: section 5.3 on the
pion mass rewritten in a clearer way, version published in JHE
DDF Construction and D-Brane Boundary States in Pure Spinor Formalism
Open string boundary conditions for non-BPS D-branes in type II string
theories discussed in hep-th/0505157 give rise to two sectors with integer (R
sector) and half-integer (NS sector) modes for the combined fermionic matter
and bosonic ghost variables in pure spinor formalism. Exploiting the manifest
supersymmetry of the formalism we explicitly construct the DDF (Del Giudice, Di
Vecchia, Fubini) states in both the sectors which are in one-to-one
correspondence with the states in light-cone Green-Schwarz formalism. We also
give a proof of validity of this construction. A similar construction in the
closed string sector enables us to define a physical Hilbert space in pure
spinor formalism which is used to project the covariant boundary states of both
the BPS and non-BPS instantonic D-branes. These projected boundary states take
exactly the same form as those found in light-cone Green-Schwarz formalism and
are suitable for computing the cylinder diagram with manifest open-closed
duality.Comment: 37 pages, typos corrected, some organisational changes mad
Momentum modes of M5-branes in a 2d space
We study M5 branes by considering the selfdual strings parallel to a plane.
With the internal oscillation frozen, each selfdual string gives a 5d SYM
field. All selfdual strings together give a 6d field with 5 scalars, 3 gauge
degrees of freedom and 8 fermionic degrees of freedom in adjoint representation
of U(N). Selfdual strings with the same orientation have the SYM-type
interaction. For selfdual strings with the different orientations, which could
also be taken as the unparallel momentum modes of the 6d field on that plane or
the (p,q) (r,s) strings on D3 with (p,q)\neq (r,s), the [i,j]+[j,k]\rightarrow
[i,k] relation is not valid, so the coupling cannot be written in terms of the
standard N \times N matrix multiplication. 3-string junction, which is the
bound state of the unparallel [i,j] [j,k] selfdual strings, may play a role
here.Comment: 37 pages, 5 figures, to appear in JHEP; v2: reference adde
D-brane interactions in type IIB plane-wave background
The cylinder diagrams that determine the static interactions between pairs of
Dp-branes in the type IIB plane wave background are evaluated. The resulting
expressions are elegant generalizations of the flat-space formulae that depend
on the value of the Ramond-Ramond flux of the background in a non-trivial
manner. The closed-string and open-string descriptions consistently transform
into each other under a modular transformation only when each of the
interacting D-branes separately preserves half the supersymmetries. These
results are derived for configurations of euclidean signature
D(p+1)-instantons but also generalize to lorentzian signature Dp-branes.Comment: 24 pages, Normalisation of boundary states correcte
Lectures on Non-BPS Dirichlet branes
A comprehensive introduction to the boundary state approach to Dirichlet
branes is given. Various examples of BPS and non-BPS Dirichlet branes are
discussed. In particular, the non-BPS states in the duality of Type IIA on K3
and the heterotic string on T4 are analysed in detail.Comment: 46 pages, 5 figures, LaTeX; lectures given at the TMR network school
on `Quantum aspects of gauge theories, supersymmetry and quantum gravity',
Torino, 26 January - 2 February 2000, and at the `Spring workshop on
Superstrings and related matters', Trieste, 27 March - 4 April 2000;
references adde
Absorption of dilaton s-wave in type 0B string theory
We find the absorption probability of dilaton field in type 0B string theory.
Since the background solutions are of the form on both
regions, we use the semiclassical formalism adopted in type IIB theory to find
the absorption cross section. The background tachyon field solution was used as
a reference to relate the solutions of the two regions. We also consider the
possible corrections to absorption probability and the form of the
correction is expected as in the calculation of the confinement solution.Comment: minor corrections, reference added, version to appear PR
Aspects of Type 0 String Theory
A construction of compact tachyon-free orientifolds of the non-supersymmetric
Type 0B string theory is presented. Moreover, we study effective
non-supersymmetric gauge theories arising on self-dual D3-branes in Type 0B
orbifolds and orientifolds.Comment: 9 pages, LATEX; submitted to Proceedings of Strings '9
KO-Homology and Type I String Theory
We study the classification of D-branes and Ramond-Ramond fields in Type I
string theory by developing a geometric description of KO-homology. We define
an analytic version of KO-homology using KK-theory of real C*-algebras, and
construct explicitly the isomorphism between geometric and analytic
KO-homology. The construction involves recasting the Cl(n)-index theorem and a
certain geometric invariant into a homological framework which is used, along
with a definition of the real Chern character in KO-homology, to derive
cohomological index formulas. We show that this invariant also naturally
assigns torsion charges to non-BPS states in Type I string theory, in the
construction of classes of D-branes in terms of topological KO-cycles. The
formalism naturally captures the coupling of Ramond-Ramond fields to background
D-branes which cancel global anomalies in the string theory path integral. We
show that this is related to a physical interpretation of bivariant KK-theory
in terms of decay processes on spacetime-filling branes. We also provide a
construction of the holonomies of Ramond-Ramond fields in Type II string theory
in terms of topological K-chains.Comment: 40 pages; v4: Clarifying comments added, more detailed proof of main
isomorphism theorem given; Final version to be published in Reviews in
Mathematical Physic
Feasibility study for a numerical aerodynamic simulation facility. Volume 1
A Numerical Aerodynamic Simulation Facility (NASF) was designed for the simulation of fluid flow around three-dimensional bodies, both in wind tunnel environments and in free space. The application of numerical simulation to this field of endeavor promised to yield economies in aerodynamic and aircraft body designs. A model for a NASF/FMP (Flow Model Processor) ensemble using a possible approach to meeting NASF goals is presented. The computer hardware and software are presented, along with the entire design and performance analysis and evaluation
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