Pole structure of the Hamiltonian ζ\zeta-function for a singular potential

We study the pole structure of the $\zeta$-function associated to the Hamiltonian $H$ of a quantum mechanical particle living in the half-line $\mathbf{R}^+$, subject to the singular potential $g x^{-2}+x^2$. We show that $H$ admits nontrivial self-adjoint extensions (SAE) in a given range of values of the parameter $g$. The $\zeta$-functions of these operators present poles which depend on $g$ and, in general, do not coincide with half an integer (they can even be irrational). The corresponding residues depend on the SAE considered.Comment: 12 pages, 1 figure, RevTeX. References added. Version to appear in Jour. Phys. A: Math. Ge

Body composition using bio-impedance analysis in pediatric patients with inflammatory bowel disease. Corcordance with dual energy X-ray absorptiometry and comparison with healthy controls

Introduction: Growth is a central process in paediatrics. Weight and height evaluation are therefore routine exams for every child but in some situation, particularly inflammatory bowel disease (IBD), a wider evaluation of nutritional status needs to be performed. Objectives: To assess the accuracy of bio-impedance analysis (BIA) compared to the gold standard dual energy X-ray absorptiometry (DEXA) in estimating percentage body fat (fat mass; FM) and lean body mass (fat free mass; FFM) in children with inflammatory bowel disease (IBD). To compare FM and FFM levels between patients with IBD and healthy controls. Methods: Twenty-nine healthy controls (12 females; mean age: 12.7 ± 1.9 years) and 21 patients (11 females; 14.3 ± 1.3 years) were recruited from August 2011 to October 2012 at our institution. BIA was performed in all children and DEXA in patients only. Concordance between BIA and DEXA was assessed using Lin's concordance correlation and the Bland-Altman method. Between-group comparisons were made using analysis of variance adjusting for age. Results: BIA-derived FM% showed a good concordance with DEXA-derived values, while BIA-derived FFM% tended to be slightly higher than DEXA-derived values (table). No differences were found between patients and controls regarding body mass index (mean ± SD: 19.3 ± 3.3 vs. 20.1 ± 2.8 kg/m2, respectively; age-adjusted P = 0.08) and FM% (boys: 25.3 ± 10.2 vs. 22.6 ± 7.1%, for patients and controls, respectively; P = 0.20; girls: 28.2 ± 5.7 vs. 26.4 ± 7.7%; P = 0.91). Also, no differences were found regarding FFM% in boys (74.9 ± 10.2 vs. 77.4 ± 7.1%; P = 0.22) and girls (71.8 ± 5.6 vs. 73.5 ± 7.7%; P = 0.85). Conclusion: BIA adequately assesses body composition (FM%) in children with IBD and could advantageously replace DEXA, which is more expensive and less available. No differences in body composition were found between children with IBD and healthy controls

Dynamics of N=2 Supersymmetric Gauge Theories in Three Dimensions

We study the structure of the moduli spaces of vacua and superpotentials of N=2 supersymmetric gauge theories in three dimensions. By analyzing the instanton corrections, we compute the exact superpotentials and determine the quantum Coulomb and Higgs branches of the theories in the weak coupling regions. We find candidates for non-trivial N=2 superconformal field theories at the singularities of the moduli spaces. The analysis is carried out explicitly for gauge groups U(N_c) and SU(N_c) with N_f flavors. We show that the field theory results are in complete agreement with the intersecting branes picture. We also compute the exact superpotentials for arbitrary gauge groups and arbitrary matter content.Comment: 33 pages, Latex, 6 figure

Discontinuous BPS spectra in N=2N = 2 gauge theory

We consider the spectrum of BPS saturated states in $N = 2$ gauge theories in four dimensions. This spectrum may be discontinuous across real codimension one submanifolds of marginal stability in the moduli space of vacua. An example, which can be treated with semiclassical methods in the weak coupling limit, is the decay of quark-soliton bound states. For a quark and a soliton of electric-magnetic charge vectors $Q$ and $Q^\prime$ respectively, we find that as the manifold of marginal stability is crossed, the number of soliton states changes by a factor of $2^{Q \cdot Q^\prime}$, where the dot denotes the symplectic product.Comment: 10 pages, uses harvma

Three Dimensional Gauge Theories and Monopoles

The coulomb branch of $N=4$ supersymmetric Yang-Mills gauge theories in $d=2+1$ is studied. A direct connection between gauge theories and monopole moduli spaces is presented. It is proposed that the hyper-K\"ahler metric of supersymmetric $N=4$ $SU(N)$ Yang-Mills theory is given by the charge $N$ centered moduli space of BPS monopoles in $SU(2)$. The theory is compared to $N=2$ supersymmetric Yang-Mills theory in four dimensions through compactification on a circle of the latter. It is found that rational maps are appropriate to this comparison. A BPS mass formula is also written for particles in three dimensions and strings in four dimensions.Comment: 25 page

Self-Adjointness of the Dirac Hamiltonian and Fermion Number Fractionization in the Background of a Singular Magnetic Vortex

The method of self-adjoint extensions is employed to determine the vacuum quantum numbers induced by a singular static magnetic vortex in $2+1$-dimensional spinor electrodynamics. The results obtained are gauge-invariant and, for certain values of the extension parameter, both periodic in the value of the vortex flux and possessing definite parity with respect to the charge conjugation.Comment: LaTe

Index Theorems and Loop Space Geometry

We investigate the evaluation of the Dirac index using symplectic geometry in the loop space of the corresponding supersymmetric quantum mechanical model. In particular, we find that if we impose a simple first class constraint, we can evaluate the Callias index of an odd dimensional Dirac operator directly from the quantum mechanical model which yields the Atiyah-Singer index of an even dimensional Dirac operator in one more dimension. The effective action obtained by BRST quantization of this constrained system can be interpreted in terms of loop space symplectic geometry, and the corresponding path integral for the index can be evaluated exactly using the recently developed localization techniques.Comment: 15 pages, report CERN-TH-6471 and HU-TFT-92-1

Low Energy Dynamics of N=2 Supersymmetric Monopoles

It is argued that the low-energy dynamics of $k$ monopoles in N=2 supersymmetric Yang-Mills theory are determined by an N=4 supersymmetric quantum mechanics based on the moduli space of $k$ static monople solutions. This generalises Manton's ``geodesic approximation" for studying the low-energy dynamics of (bosonic) BPS monopoles. We discuss some aspects of the quantisation and in particular argue that dolbeault cohomology classes of the moduli space are related to bound states of the full quantum field theory.Comment: 20 pages, EFI-93-0

Monopole and Dyon Bound States in N=2 Supersymmetric Yang-Mills Theories

We study the existence of monopole bound states saturating the BPS bound in N=2 supersymmetric Yang-Mills theories. We describe how the existence of such bound states relates to the topology of index bundles over the moduli space of BPS solutions. Using an $L^2$ index theorem, we prove the existence of certain BPS states predicted by Seiberg and Witten based on their study of the vacuum structure of N=2 Yang-Mills theories.Comment: 34 pages, harvma

Derivation of Index Theorems by Localization of Path Integrals

We review the derivation of the Atiyah-Singer and Callias index theorems using the recently developed localization method to calculate exactly the relevant supersymmetric path integrals. (Talk given at the III International Conference on Mathematical Physics, String Theory and Quantum Gravity, Alushta, Ukraine, June 13-24, 1993)Comment: 11 pages in LaTeX, HU-TFT-93-3