Two-dimensional SU(N) Higgs theory: An instanton approach

The two-dimensional non-abelian Higgs model is studied by employing a dilute gas of Z_N vortices. The results obtained are similar to the corresponding results of the abelian model, studied by Callan, Dashen and Gross, and Raby and Ukawa. The most interesting conclusion is that in the presence of some number, N_F, of massless fermion flavors, the theory behaves differently for N > N_crit or N < N_crit where N_crit = N_F/(N_F?2).     

On Eigenvalues of the Sum of Two Random Projections

We study the behavior of eigenvalues of matrix P _N +Q _N where P _N and Q _N are two N-by-N random orthogonal projections. We relate the joint eigenvalue distribution of this matrix to the Jacobi matrix ensemble and establish the universal behavior of eigenvalues for large N. The limiting local behavior of eigenvalues is governed by the sine kernel in the bulk and by either the Bessel or the Airy kernel at the edge depending on parameters. We also study an exceptional case when the local behavior of eigenvalues of P _N +Q _N is not universal in the usual sense.     

1/N topological expansion for lattice QCD

A U(N_c) gauge theory with a global U(N_f) flavor symmetry is investigated in the limit both N_c and N_f large with the ratio ξ ≡ N_f/N_c fixed.     

AdS superalgebras with brane charges

We consider the inclusion of brane charges in AdS₅ superalgebras that contain the maximal central extension of the super-Poincaré algebra on ∂AdS₅. For theories with N supersymmetries on the boundary, the maximal extension is OSp(1/8N,R), which contains the group Sp(8N,R)⊃U(2N,2N)⊃SU(2,2)×U(N) as extension of the conformal group. An “intermediate” extension to U(2N,2N/1) is also discussed, as well as the inclusion of brane charges in AdS₇ and AdS₄ superalgebras. BPS conditions in the presence of brane charges are studied in some details.     

Instanton zero modes and β-functions in conformal supergravity

We show that one-loop infinities in N-extended conformal supergravities are produced only by zero modes when calculated on gravitational self-dual (N?1), de Sitter (N?3) and SU_N gauge instanton (N?3) backgrounds. Guided by analogy with the super Yang-Mills case we then discuss how to extract information about exact β-functions. We also establish a part of the N?4 lagrangian sufficient for one loop calculations in the U_N sector and carry out independent calculations of one-loop N?4 gauge β-functions separately in U₁ and SU_N background sectors.     

Current-voltage dependencies of heterogeneous semiconductor systems

Computed current-voltage (J–V) dependencies of heterogeneous (powder) semiconductor systems reveal an anomalous dependence between the constant-voltage current J and the uncompensated donor (acceptor) concentration N. Over a range of N(N₁ < n < N₂) of approximately one decade, J decreases by as much as four decades with increasing N. For N > N₂, the grain Schottky barrier thickness d is less than the grain half-width l/2, the grain surface potential V_s is almost independent of N and the J–V dependence is superlinear. For N₁ < N < N₂, d > l/2, V_s decreases linearly with N, J increases strongly with decreasing N and the J–V dependence is superlinear. For N < N₁, d > l/2. V_s ? V_th ( = kT/q) and J ∝ NV. The phenomenon is used to account for some observed J–V dependencies with column II-chalcogenide and ZnO powder semiconductor systems (electro-optic displays, electrophotographic receptors and heterogeneous catalysts).     

Pathologies of the large-N limit for RPN−1, CPN−1, QPN−1 and mixed isovector/isotensor σ-models

We compute the phase diagram in the N→∞ limit for lattice RP^N−1, CP^N−1 and QP^N−1 σ-models with the quartic action, and more generally for mixed isovector/isotensor models. We show that the N=∞ limit exhibits phase transitions that are forbidden for any finite N. We clarify the origin of these pathologies by examining the exact solution of the one-dimensional model: we find that there are complex zeros of the partition function that tend to the real axis as N→∞. We conjecture the correct phase diagram for finite N as a function of the spatial dimension d. Along the way, we prove some new correlation inequalities for a class of N-component σ-models, and we obtain some new results concerning the complex zeros of confluent hypergeometric functions.     

A Comparative Analysis of In-Medium Spectral Functions for N(940) and N ∗(1535) in Real-Time Thermal Field Theory

In the real-time thermal field theory, the nucleon self-energy at finite temperature and density is evaluated where an extensive set of pion-baryon (π B) loops are consider. On the other side, the in-medium self-energy of N ^?(1535) for π N and η N loops is also determined in the same framework. The detail branch cut structures for these different π B loops for nucleon N(940) and π N, η N loops for N ^?(1535) are addressed. Using the total self-energy of N(940) and N ^?(1535), which contain the contributions of their corresponding loop diagrams, the complete structures of their in-medium spectral functions have been obtained. The Landau and unitary cut contributions provide two separate peak structures in the nucleon spectral function while N ^?(1535) has a single peak structure in its unitary cuts. At high temperature, the peak structures of both at their individual poles are attenuated while at high density Landau peak structure of nucleon is completely suppressed and its unitary peak structure is tending to be shifted towards the melted peak of N ^?(1535). The non-trivial modifications of these chiral partners may indicate some association of chiral symmetry restoration.     

Some nuclear and atomic properties of201Hg determined by conversion electron spectroscopy

Conversion electron measurements with an electrostatic spectrometer proved the existence of the 1,565±6 eV transition in²⁰¹Hg. The conversion intensity ratios,N ₁/N ₂ =1.2±0.2,N ₁/N ₃=1.1±0.2,N ₂/N ₃=0.92±0.15,N ₄/N ₃=0.03± 0.02 andN ₅/N ₃=0.04 ±0.02 were determined. These values agree with our calculations for the M1±E2 multipolarity with theE2/M1 mixing ratioδ ²=(l.l±0.3)xl0^?4 and exclude all pure multipolarities withL≦4. The total conversion coefficient for the aboveM1 +E2 mixture was evaluated to be (4.7±0.7)× 10⁴. The reducedB(M1, 1/2→3/2) probability was derived to be (3.9 ±1.2) × 10^?3 (e?/2Mc)². The natural widths of theN-subshell conversion lines in mercury were found to beΓ(N ₁)=8.3± 1.5,Γ(N ₂) =5.8±1.5 and Γ(N ₃) =6.5±1.0 eV. Monte Carlo calculations of electron scattering in matter yielded the conversion line shapes in qualitative agreement with the experiment.     

A new mass formula and new neutron and proton magic numbers in light nuclei

This mass formula explains gross features of the binding energy curves for all the elements from Li to Bi. It has no shell effects incorporated. Comparisons of separation energies computed from this formula and measured masses show extra-stability at N=6 (Z=3?8), Z=6 (N=6?9), N=14 (Z=7?10), Z=14 (N=14?19), N=16 (Z=7?8), Z=16 (N=24?26), loss of magicity at N=8 (Z=4), N=20 (Z=12?15) and quenching of N=50, 82, 126, Z=50 near driplines. Z=82 magicity rises at N=104 after strong quenching near N=107.     

Seiberg-Witten geometry with various matter contents

We obtain the Seiberg-Witten geometry for four-dimensional N = 2 gauge theory with gauge group SO(2N_c) (N_c ⩽ 5) with massive spinor and vector hypermultiplets by considering the gauge symmetry breaking in the N = 2 E₆ theory with massive fundamental hypermultiplets. In a similar way the Seiberg-Witten geometry is determined for N = 2 SU(N_c) (N_c ⩽ 6) gauge theory with massive antisymmetric and fundamental hypermultiplets. Whenever possible we compare our results expressed in the form of ALE fibrations with those obtained by geometric engineering and brane dynamics, and find a remarkable agreement. We also show that these results are reproduced by using N = 1 confining phase superpotentials.     

Monotonicity of Quantum Ground State Energies: Bosonic Atoms and Stars

The N-dependence of the non-relativistic bosonic ground state energy ? ^B (N) is studied for quantum N-body systems with either Coulomb or Newton interactions. The Coulomb systems are “bosonic atoms,” with their nucleus fixed, and it is shown that $\mathcal {E}_{{C}}^{{B}}(N)/\mathcal {P}_{{C}}(N)$ grows monotonically in N>1, where ? _C (N)=N ²(N?1). The Newton systems are “bosonic stars,” and it is shown that when the Bosons are centrally attracted to a fixed gravitational “grain” of mass M>0, and N>2, then $\mathcal {E}_{{N}}^{{B}}(N;M)/\mathcal {P}_{\!{N}}(N)$ grows monotonically in N, where ? _N (N)=N(N?1)(N?2); in the translation-invariant problem (M=0), it is shown that when N>1 then $\mathcal {E}_{{N}}^{{B}}(N;0)/\mathcal {P}_{{C}}(N)$ grows monotonically in N, with ? _C (N) from the Coulomb problem. Some applications of the new monotonicity results are discussed.     

N = 1 superspace formulation of N = 2 and N = 4 super-Yang-Mills models with central charge

The component models of N = 2 and N = 4 supersymmetric Yang-Mills theories of Sohnius, Stelle and West are reformulated in terms of N = 1 superfields. The non-supersymmetric constraints are supersymmetrized generalizing the linear multiplet in the presence of the non-abelian gauge superfield and (in the N = 4 case) a doublet of chiral superfields. The extended supersymmetry transformations preserving constraints are explicitly given in terms of N = 1 superfields. We are able to introduce the constraints back into the lagrangian using superfield Lagrange multipliers. The on-shell equivalence of this formulation with the formulation of Fayet with one (for N = 2) and three (for N = 4) chiral superfields is shown. The abelian N = 2 model is worked out to show the connection between full superspace treatment and the N = 1 superfield formulation.     

Calculation of gauge couplings and compact circumferences from self-consistent dimensional reduction

We consider a system of gravity plus free massless matter fields in 4 + N dimensions, and look for solutions in which N dimensions form a compact curved manifold, with the energy-momentum tensor responsible for the curvature produced by quantum fluctuations in the matter fields. For manifolds of sufficient symmetry (including spheres, CP^N, and manifolds of simple Lie groups) the metric depends on only a single multiplicative parameter ?², and the field equations reduce to an algebraic equation for ?, involving the potential of the matter fields in the metric of the manifold. With a large number of species of matter fields, the manifold will be larger than the Planck length, and the potential can be calculated using just one-loop graphs. In odd dimensions these are finite, and give a potential of form C_N/?⁴. Also there are induced Yang-Mills and Einstein-Hilbert terms in the effective 4-dimensional action, proportional to additional numerical coefficients, D_N and E_N. General formulas are given for the gauge coupling g² in terms of C_N and D_N, and the ratio ?²/8πG in terms of C_N and E_N. Numerical values for C_N, D_N, and E_N are obtained for scalar and spinor fields on spheres of odd dimensionality N. It is found that the potential, g² and ?²/8πG can all be positive but only when the compact manifold has N = 3 + 4 k dimensions. (The positivity of the potential is needed for stability of the sphere against uniform dilations or contractions). In this case, solutions exist either for spinor fields alone or for suitable mixes of spinor and scalar fields provided the ratio of the number of scalar fields to the number of fermion fields is not too large. Numerical values of the O(N + 1) gauge couplings and 8φG/?² are calculated for illustrative values of the numbers of spinor fields. It turns out that large numbers of matter fields are needed to make these parameters reasonably small.     

Absence of discrete spectrum in highly negative ions

We extend the results of [1] to fermions, i.e., we show that ifH _N is the Hamiltonian forN electrons in the field of a fixed point chargeZ, then there is a constantc such thatH _N has no discrete spectrum forN≧N ₀=cZ ^6/5.     

Phase transitions in one dimension and less

Phase transitions can occur in one-dimensional classical statistical mechanics at non-zero temperature when the number of components N of the spin is infinite. We show how to solve such magnets in one dimension for any N, and how the phase transition develops at N=∞. We discuss SU(N) and Sp(N) magnets, where the transition is second-order. In the new high-temperature phase, the correlation length is zero. We also show that for the SU(N) magnet on exactly three sites with periodic boundary conditions the transition becomes first order.     

Comparison of the quark model with SU3 inelastic amplitudes

A complete disagreement is found between the signs of resonance formation amplitudes for π + N → ? + N and π + N → πΔ as predicted by the quark and as given by the recent isobar partial wave analysis. This dis-agreement is in strong contrast to the corresponding agreement for resonant formation amplitudes in γ + N → π + N.