909 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
On the BPS Spectrum at the Root of the Higgs Branch
We study the BPS spectrum and walls of marginal stability of the
supersymmetric theory in four dimensions with gauge group SU(n)
and fundamental flavours at the root of the Higgs branch. The
strong-coupling spectrum of this theory was conjectured in hep-th/9902134 to
coincide with that of the two-dimensional supersymmetric
sigma model. Using the Kontsevich--Soibelman
wall-crossing formula, we start with the conjectured strong-coupling spectrum
and extrapolate it to all other regions of the moduli space. In the
weak-coupling regime, our results precisely agree with the semiclassical
analysis of hep-th/9902134: in addition to the usual dyons, quarks, and
bosons, if the complex masses obey a particular inequality, the resulting
weak-coupling spectrum includes a tower of bound states consisting of a dyon
and one or more quarks. In the special case of -symmetric
masses, there are bound states with one quark for odd and no bound states
for even .Comment: 11 pages, 4 figure
Non-Abelian Meissner Effect in Yang--Mills Theories at Weak Coupling
We present a weak-coupling Yang--Mills model supporting non-Abelian magnetic
flux tubes and non-Abelian confined magnetic monopoles. In the dual description
the magnetic flux tubes are prototypes of the QCD strings. Dualizing the
confined magnetic monopoles we get gluelumps which convert a "QCD string" in
the excited state to that in the ground state. Introducing a mass parameter m
we discover a phase transition between the Abelian and non-Abelian confinement
at a critical value m=m_* of order of Lambda. Underlying dynamics are governed
by a Z_N symmetry inherent to the model under consideration. At m>m_* the Z_N
symmetry is spontaneously broken, resulting in N degenerate Z_N (Abelian)
strings. At m<m_* the Z_N symmetry is restored, the degeneracy is lifted, and
the strings become non-Abelian. We calculate tensions of the non-Abelian
strings, as well as the decay rates of the metastable strings, at N >> 1.Comment: Reference [45] corrected. Final version, to appear in Phys. Rev.
New Results from Glueball Superpotentials and Matrix Models: the Leigh-Strassler Deformation
Using the result of a matrix model computation of the exact glueball
superpotential, we investigate the relevant mass perturbations of the
Leigh-Strassler marginal ``q'' deformation of N=4 supersymmetric gauge theory.
We recall a conjecture for the elliptic superpotential that describes the
theory compactified on a circle and identify this superpotential as one of the
Hamiltonians of the elliptic Ruijsenaars-Schneider integrable system. In the
limit that the Leigh-Strassler deformation is turned off, the integrable system
reduces to the elliptic Calogero-Moser system which describes the N=1^* theory.
Based on these results, we identify the Coulomb branch of the partially
mass-deformed Leigh-Strassler theory as the spectral curve of the
Ruijsenaars-Schneider system. We also show how the Leigh-Strassler deformation
may be obtained by suitably modifying Witten's M theory brane construction of
N=2 theories.Comment: 13 pages, JHEP, amstex, changed JHEP to JHEP
D3 instantons in Calabi-Yau orientifolds with(out) fluxes
We investigate the instanton effect due to D3 branes wrapping a four-cycle in
a Calabi-Yau orientifold with D7 branes. We study the condition for the nonzero
superpotentials from the D3 instantons. For that matter we work out the zero
mode structures of D3 branes wrapping a four-cycle both in the presence of the
fluxes and in the absence of the fluxes. In the presence of the fluxes, the
condition for the nonzero superpotential could be different from that without
the fluxes. We explicitly work out a simple example of the orientifold of with a suitable flux to show such behavior. The effects of
D3-D7 sectors are interesting and give further constraints for the nonzero
superpotential. In a special configuration where D3 branes and D7 branes wrap
the same four-cycle, multi-instanton calculus of D3 branes could be reduced to
that of a suitable field theory. The structure of D5 instantons in Type I
theory is briefly discussed.Comment: 17 pages; Typos corrected, arguments improved and references adde
Spectral zeta functions of a 1D Schr\"odinger problem
We study the spectral zeta functions associated to the radial Schr\"odinger
problem with potential V(x)=x^{2M}+alpha x^{M-1}+(lambda^2-1/4)/x^2. Using the
quantum Wronskian equation, we provide results such as closed-form evaluations
for some of the second zeta functions i.e. the sum over the inverse eigenvalues
squared. Also we discuss how our results can be used to derive relationships
and identities involving special functions, using a particular 5F_4
hypergeometric series as an example. Our work is then extended to a class of
related PT-symmetric eigenvalue problems. Using the fused quantum Wronskian we
give a simple method for calculating the related spectral zeta functions. This
method has a number of applications including the use of the ODE/IM
correspondence to compute the (vacuum) nonlocal integrals of motion G_n which
appear in an associated integrable quantum field theory.Comment: 15 pages, version
Effect of retardation on dynamical mass generation in two-dimensional QED at finite temperature
The effect of retardation on dynamical mass generation in is studied, in the
imaginary time formalism. The photon porarization tensor is evaluated to
leading order in 1/N (N is the number of flavours), and simple closed form
expressions are found for the fully retarded longitudinal and transverse
propagators, which have the correct limit when T goes to zero. The resulting
S-D equation for the fermion mass (at order 1/N) has an infrared divergence
associated with the contribution of the transverse photon propagator; only the
longitudinal contribution is retained, as in earlier treatments. For solutions
of constant mass, it is found that the retardation reduces the value of the
parameter r (the ratio of twice the mass to the critical temperature) from
about 10 to about 6. The gap equation is then solved allowing for the mass to
depend on frequency. It was found that the r value remained close to 6.
Possibilities for including the transverse propagator are discussed.Comment: 26 pages 8 figure
Identification of observables in quantum toboggans
Quantum systems with real energies generated by an apparently non-Hermitian
Hamiltonian may re-acquire the consistent probabilistic interpretation via an
ad hoc metric which specifies the set of observables in the updated Hilbert
space of states. The recipe is extended here to quantum toboggans. In the first
step the tobogganic integration path is rectified and the Schroedinger equation
is given the generalized eigenvalue-problem form. In the second step the
general double-series representation of the eligible metric operators is
derived.Comment: 25 p
From Marginal Deformations to Confinement
We consider type IIB supergravity backgrounds which describe marginal
deformations of the Coulomb branch of N=4 super Yang-Mills theory with SO(4) x
SO(2) global symmetry. Wilson loop calculations indicate that certain
deformations enhance the Coulombic attraction between quarks and anti-quarks at
the UV conformal fixed-point. In the IR region, these deformations can induce a
transition to linear confinement.Comment: 14 pages, 4 figures, minor corrections, comments and references adde
Exact low-energy effective actions for hypermultiplets in four dimensions
We consider the general hypermultiplet Low-Energy Effective Action (LEEA)
that may appear in quantized, four-dimensional, N=2 supersymmetric, gauge
theories, e.g. in the Coulomb and Higgs branches. Our main purpose is a
description of the exact LEEA of n magnetically charged hypermultiplets. The
hypermultiplet LEEA is given by the N=2 supersymmetric Non-Linear Sigma-Model
(NLSM) with a 4n-dimensional hyper-K"ahler metric, subject to non-anomalous
symmetries. Harmonic Superspace (HSS) and the NLSM isometries are very useful
to constrain the hyper-K"ahler geometry of the LEEA. We use N=2 supersymmetric
projections of HSS superfields to N=2 linear (tensor) O(2) and O(4) multiplets
in N=2 Projective Superspace (PSS) to deduce the explicit form of the LEEA in
some particular cases. As the by-product, a simple new classification of all
multi-monopole moduli space metrics having su(2)_R symmetry is proposed in
terms of real quartic polynomials of 2n variables, modulo Sp(n)
transformations. The 4d hypermultiplet LEEA for n=2 can be encoded in terms of
an elliptic curve.Comment: 60 pages, LaTeX, macros included, references adde
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