On the Moduli Space of SU(3) Seiberg-Witten Theory with Matter

We present a qualitative model of the Coulomb branch of the moduli space of low-energy effective N=2 SQCD with gauge group SU(3) and up to five flavours of massive matter. Overall, away from double cores, we find a situation broadly similar to the case with no matter, but with additional complexity due to the proliferation of extra BPS states. We also include a revised version of the pure SU(3) model which can accommodate just the orthodox weak coupling spectrum.Comment: 32 pages, 25 figures, uses JHEP.cls, added references, deleted joke

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

Konishi anomaly and N=1 effective superpotentials from matrix models

We discuss the restrictions imposed by the Konishi anomaly on the matrix model approach to the calculation of the effective superpotentials in N=1 SUSY gauge theories with different matter content. It is shown that they correspond to the anomaly deformed Virasoro $L_0$ constraints .Comment: Latex, 8 pages, misprint and the normalization of the condensate in the elliptic model are correcte

Superconformal Vortex Strings

We study the low-energy dynamics of semi-classical vortex strings living above Argyres-Douglas superconformal field theories. The worldsheet theory of the string is shown to be a deformation of the CP^N model which flows in the infra-red to a superconformal minimal model. The scaling dimensions of chiral primary operators are determined and the dimensions of the associated relevant perturbations on the worldsheet and in the four dimensional bulk are found to agree. The vortex string thereby provides a map between the A-series of N=2 superconformal theories in two and four dimensions.Comment: 22 pages. v2: change to introductio

New Advances in Forming Functional Ceramics for Micro Devices

Micro electromechanical systems (MEMS) are finding uses in an increasing number of diverse applications. Currently the fabrication techniques used to produce such MEMS devices are primarily based on 2-D processing of thin films. The challenges faced by producing more complex structures (e.g. high aspect ratio, spans, and multi-material structures) require the development of new processing techniques. Potential solutions to these challenges based on low temperature processing of functional ceramics, selective chemical patterning, and micro-moulding are presented to show that it is possible to create complex functional ceramic structures which incorporate non-ceramic conducting and support structures. The capabilities of both techniques are compared and the relative advantages of each explored

PT-Symmetric Versus Hermitian Formulations of Quantum Mechanics

A non-Hermitian Hamiltonian that has an unbroken PT symmetry can be converted by means of a similarity transformation to a physically equivalent Hermitian Hamiltonian. This raises the following question: In which form of the quantum theory, the non-Hermitian or the Hermitian one, is it easier to perform calculations? This paper compares both forms of a non-Hermitian $ix^3$ quantum-mechanical Hamiltonian and demonstrates that it is much harder to perform calculations in the Hermitian theory because the perturbation series for the Hermitian Hamiltonian is constructed from divergent Feynman graphs. For the Hermitian version of the theory, dimensional continuation is used to regulate the divergent graphs that contribute to the ground-state energy and the one-point Green's function. The results that are obtained are identical to those found much more simply and without divergences in the non-Hermitian PT-symmetric Hamiltonian. The $\mathcal{O}(g^4)$ contribution to the ground-state energy of the Hermitian version of the theory involves graphs with overlapping divergences, and these graphs are extremely difficult to regulate. In contrast, the graphs for the non-Hermitian version of the theory are finite to all orders and they are very easy to evaluate.Comment: 13 pages, REVTeX, 10 eps figure

On the BPS Spectrum at the Root of the Higgs Branch

We study the BPS spectrum and walls of marginal stability of the $\mathcal{N}=2$ supersymmetric theory in four dimensions with gauge group SU(n) and $n\le N_{f}<2n$ 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 $\mathbb{CP}^{2n-N_{f}-1}$ 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 $W$ 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 $\mathbb{Z}_{n}$-symmetric masses, there are bound states with one quark for odd $n$ and no bound states for even $n$.Comment: 11 pages, 4 figure

Duality Symmetries for N=2 Supersymmetric QCD with Vanishing beta-Functions

We construct the duality groups for N=2 Supersymmetric QCD with gauge group SU(2n+1) and N_f=4n+2 hypermultiplets in the fundamental representation. The groups are generated by two elements $S$ and $T$ that satisfy a relation $(STS^{-1}T)^{2n+1}=1$. Thus, the groups are not subgroups of $SL(2,Z)$. We also construct automorphic functions that map the fundamental region of the group generated by $T$ and $STS$ to the Riemann sphere. These automorphic functions faithfully represent the duality symmetry in the Seiberg-Witten curve.Comment: 20 pages, 3 figures, harvmac (b); v2, typos corrected, statement about curves of marginal stability is correcte

On Pseudo-Hermitian Hamiltonians and Their Hermitian Counterparts

In the context of two particularly interesting non-Hermitian models in quantum mechanics we explore the relationship between the original Hamiltonian H and its Hermitian counterpart h, obtained from H by a similarity transformation, as pointed out by Mostafazadeh. In the first model, due to Swanson, h turns out to be just a scaled harmonic oscillator, which explains the form of its spectrum. However, the transformation is not unique, which also means that the observables of the original theory are not uniquely determined by H alone. The second model we consider is the original PT-invariant Hamiltonian, with potential V=igx^3. In this case the corresponding h, which we are only able to construct in perturbation theory, corresponds to a complicated velocity-dependent potential. We again explore the relationship between the canonical variables x and p and the observables X and P.Comment: 9 pages, no figure

All Hermitian Hamiltonians Have Parity

It is shown that if a Hamiltonian $H$ is Hermitian, then there always exists an operator P having the following properties: (i) P is linear and Hermitian; (ii) P commutes with H; (iii) P^2=1; (iv) the nth eigenstate of H is also an eigenstate of P with eigenvalue (-1)^n. Given these properties, it is appropriate to refer to P as the parity operator and to say that H has parity symmetry, even though P may not refer to spatial reflection. Thus, if the Hamiltonian has the form H=p^2+V(x), where V(x) is real (so that H possesses time-reversal symmetry), then it immediately follows that H has PT symmetry. This shows that PT symmetry is a generalization of Hermiticity: All Hermitian Hamiltonians of the form H=p^2+V(x) have PT symmetry, but not all PT-symmetric Hamiltonians of this form are Hermitian