1,159 research outputs found
Complex WKB Analysis of a PT Symmetric Eigenvalue Problem
The spectra of a particular class of PT symmetric eigenvalue problems has
previously been studied, and found to have an extremely rich structure. In this
paper we present an explanation for these spectral properties in terms of
quantisation conditions obtained from the complex WKB method. In particular, we
consider the relation of the quantisation conditions to the reality and
positivity properties of the eigenvalues. The methods are also used to examine
further the pattern of eigenvalue degeneracies observed by Dorey et al. in
[1,2].Comment: 22 pages, 13 figures. Added references, minor revision
Central Charge Anomalies in 2D Sigma Models with Twisted Mass
We discuss the central charge in supersymmetric sigma models in
two dimensions. The target space is a symmetric K\"ahler manifold, CP is
an example. The U(1) isometries allow one to introduce twisted masses in the
model. At the classical level the central charge contains Noether charges of
the U(1) isometries and a topological charge which is an integral of a total
derivative of the Killing potentials. At the quantum level the topological part
of the central charge acquires anomalous terms. A bifermion term was found
previously, using supersymmetry which relates it to the superconformal anomaly.
We present a direct calculation of this term using a number of regularizations.
We derive, for the first time, the bosonic part in the central charge anomaly.
We construct the supermultiplet of all anomalies and present its superfield
description. We also discuss a related issue of BPS solitons in the CP(1) model
and present an explicit form for the curve of marginal stability.Comment: 30 pages, 1 figure, references adde
Design-for-test structure to facilitate test vector application with low performance loss in non-test mode.
A switching based circuit is described which allows application of voltage test vectors to internal nodes of a chip without the problem of backdriving. The new circuit has low impact on the performance of an analogue circuit in terms of loss of bandwidth and allows simple application of analogue test voltages into internal nodes. The circuit described facilitates implementation of the forthcoming IEEE 1149.4 DfT philosophy [1]
Calculating the Prepotential by Localization on the Moduli Space of Instantons
We describe a new technique for calculating instanton effects in
supersymmetric gauge theories applicable on the Higgs or Coulomb branches. In
these situations the instantons are constrained and a potential is generated on
the instanton moduli space. Due to existence of a nilpotent fermionic symmetry
the resulting integral over the instanton moduli space localizes on the
critical points of the potential. Using this technology we calculate the one-
and two-instanton contributions to the prepotential of SU(N) gauge theory with
N=2 supersymmetry and show how the localization approach yields the prediction
extracted from the Seiberg-Witten curve. The technique appears to extend to
arbitrary instanton number in a tractable way.Comment: 24 pages, JHEP.cls, more references and extra discussion on N_F=2N
cas
Large N and double scaling limits in two dimensions
Recently, the author has constructed a series of four dimensional
non-critical string theories with eight supercharges, dual to theories of light
electric and magnetic charges, for which exact formulas for the central charge
of the space-time supersymmetry algebra as a function of the world-sheet
couplings were obtained. The basic idea was to generalize the old matrix model
approach, replacing the simple matrix integrals by the four dimensional matrix
path integrals of N=2 supersymmetric Yang-Mills theory, and the Kazakov
critical points by the Argyres-Douglas critical points. In the present paper,
we study qualitatively similar toy path integrals corresponding to the two
dimensional N=2 supersymmetric non-linear sigma model with target space CP^n
and twisted mass terms. This theory has some very strong similarities with N=2
super Yang-Mills, including the presence of critical points in the vicinity of
which the large n expansion is IR divergent. The model being exactly solvable
at large n, we can study non-BPS observables and give full proofs that double
scaling limits exist and correspond to universal continuum limits. A complete
characterization of the double scaled theories is given. We find evidence for
dimensional transmutation of the string coupling in some non-critical string
theories. We also identify en passant some non-BPS particles that become
massless at the singularities in addition to the usual BPS states.Comment: 38 pages, including an introductory section that makes the paper
self-contained, two figures and one appendix; v2: typos correcte
Tridiagonal PT-symmetric N by N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime
A generic PT-symmetric Hamiltonian is assumed tridiagonalized and truncated
to N dimensions, and its up-down symmetrized special cases with J=[N/2] real
couplings are considered. In the strongly non-Hermitian regime the secular
equation gets partially factorized at all N. This enables us to reveal a
fine-tuned alignment of the dominant couplings implying an asymptotically
sharply spiked shape of the boundary of the J-dimensional quasi-Hermiticity
domain in which all the spectrum of energies remains real and observable.Comment: 28 pp., 4 tables, 1 figur
Effect of Wavefunction Renormalisation in N-Flavour Qed3 at Finite Temperature
A recent study of dynamical chiral symmetry breaking in N-flavour QED at
finite temperature is extended to include the effect of fermion wavefunction
renormalisation in the Schwinger-Dyson equations. The simple ``zero-frequency''
truncation previously used is found to lead to unphysical results, especially
as . A modified set of equations is proposed, whose solutions behave
in a way which is qualitatively similar to the solutions of Pennington et
al. [5-8] who have made extensive studies of the effect of wavefunction
renormalisation in this context, and who concluded that there was no critical
(at T=0) above which chiral symmetry was restored. In contrast, we find
that our modified equations predict a critical at , and an
phase diagram very similar to the earlier study neglecting wavefunction
renormalisation. The reason for the difference is traced to the different
infrared behaviour of the vacuum polarisation at and at .Comment: 17 pages + 13 figures (available upon request), Oxford preprint
OUTP-93-30P, IFUNAM preprint FT94-39, LaTe
Does the complex deformation of the Riemann equation exhibit shocks?
The Riemann equation , which describes a one-dimensional
accelerationless perfect fluid, possesses solutions that typically develop
shocks in a finite time. This equation is \cP\cT symmetric. A one-parameter
\cP\cT-invariant complex deformation of this equation,
( real), is solved exactly using the
method of characteristic strips, and it is shown that for real initial
conditions, shocks cannot develop unless is an odd integer.Comment: latex, 8 page
Instanton Calculus and SUSY Gauge Theories on ALE Manifolds
We study instanton effects along the Coulomb branch of an N=2 supersymmetric
Yang-Mills theory with gauge group SU(2) on Asymptotically Locally Euclidean
(ALE) spaces. We focus our attention on an Eguchi-Hanson gravitational
background and on gauge field configurations of lowest Chern class.Comment: 15 pages, LaTeX file. Extended version to be published in Physical
Review
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