June 1992 arXiv papers — page 3

George Andrews, Shalsoh B. Ekhad, Doron Zeilberger

A short and elementary proof, and a finite-form generalization, are given of Jacobi's formula for the number of ways of writing an integer as a sum of four squares (that implies Lagrange's famous 1777 theorem.)

Ashoke Sen

Classical solutions of equations of motion in low energy effective field theory, describing fundamental charged heterotic string, are found. These solutions automatically carry an electric current equal to the charge per unit length, and hence are accompanied by both, electric and magnetic fields. Force between two parallel strings vanish due to cancellation

V. A. Kazakov, A. A. Migdal

We propose and study at large N a new lattice gauge model , in which the Yang-Mills interaction is induced by the heavy scalar field in adjoint representation. At any dimension of space and any $ N $ the gauge fields can be integrated out yielding an effective field theory for the gauge invariant scalar field, corresponding to eigenvalues of the initial matr

Neil Marcus, Yaron Oz

We find the discrete states of the c=1 string in the light-cone gauge of Polyakov. When the state space of the gravitational sector of the theory is taken to be the irreducible representations of the SL(2,R) current algebra, the cohomology of the theory is NOT the same as that in the conformal gauge. In particular, states with ghost numbers up to 4 appear. H

Shahn Majid, M. J Rodriguez-Plaza

We describe the quasitriangular structure (universal $R$-matrix) on the non-standard quantum group $U_q(H_1,H_2,X^\pm)$ associated to the Alexander-Conway matrix solution of the Yang-Baxter equation. We show that this Hopf algebra is connected with the super-Hopf algebra $U_qgl(1|1)$ by a general process of superization.

Geoffrey B. West

Reply to Comments on ``Asymptotic Estimate of the {\it n}-Loop QCD Contribution to the Total $e^{+}e^{-}$ Annihilation Cross Section''

Mary K. Gaillard, Rulin Xiu

We use recently obtained 2-loop string coupling constants to analyze a class of string models based on orbifold compactification. Assuming weak coupling at the string scale and single-scale unification leads to restrictions on the spectrum of massive (between the string scale and the weak scale) matter supermultiplets and/or on the Kac-Moody algebra level.

Aram Antaramian, Lawrence J. Hall, Andrija Rašin

The quark and lepton mass matrices possess approximate flavor symmetries. Several results follow if the interactions of new scalars possess these approximate symmetries. Present experimental bounds allow these exotic scalars to have a weak scale mass. The Glashow-Weinberg criterion is rendered unnecessary. Finally, rare leptonic B meson decays provide powerf

Wolfgang Bock, Jan Smit, Jeroen C. Vink

We introduce a lattice fermion-Higgs model with one component `reduced staggered' fermions. In order to use the fermion field as efficiently as possible we couple the two {\em staggered} flavors to the O(4) Higgs field leading to a model with only one SU(2) doublet in the scaling region. The number of fermions is doubled in a numerical investigation of t

Jeroen C. Vink, Uwe-Jens Wiese

A new gauge fixing condition is discussed, which is (lattice) rotation invariant, has the `smoothness' properties of the Landau gauge but can be efficiently computed and is unambiguous for almost all lattice gauge field configurations.

J. L. Alonso, Ph. Boucaud, J. L. Cortes, F. Lesmes

We present a new method for regularizing chiral theories on the lattice. The arbitrariness in the regularization is used in order to decouple massless replica fermions. A continuum limit with only one fermion is obtained in perturbation theory and a Golterman-Petcher like symmetry related to the decoupling of the replicas in the non-perturbative regime is id

C. R. Gattringer, C. B. Lang

We study a simple 2-d model representing two fields with different mass and a 3-point coupling term. The phase shift in the resonating 2-particle channel is determined from the energy spectrum obtained in Monte Carlo simulations on finite lattices. Masses and wave function renormalization constants of the fields as well as mass and width of the resonance are

A. C. Irving, C. Michael

We present model predictions for the spectrum of $CP^{N-1}$ in a periodic box and use them to interpret the strong finite size effects observed in lattice simulations at medium values of $N$. The asymptotic scaling behaviour of alternative lattice actions is discussed along with some aspects of multigrid algorithm efficiency.

Naichang Yu, Michael Fowler

The one-dimensional attractive lattice fermion gas equivalent to the Heisenberg-Ising spin 1/2 chain is studied for a ring geometry threaded by magnetic flux. We find that for charged fermions having interaction strength $Δ=\cos(π/ p)$ with $p$ {\it noninteger}, the adiabatic ground state is periodic in the magnetic flux threading the chain, with period 2 fl

A. A. Migdal

We find the exact solution of a recently proposed model of the lattice gauge theory induced by heavy scalar field in adjoint representation at $ N= \infty $ for arbitrary dimension $D$. The nonlinear integral equation for the gauge invariant density of eigenvalues of the vacuum average of the scalar field is derived. In the continuum limit, the density grows

S. Pratik Khastgir, Jnanadeva Maharana

Two dimensional charged black hole solution is obtained by implementing an $O(2,2)$ transformation on the three dimensional black string solution. Two different monopole backgrounds in five dimensions are related through an $O(2,2)$ transformation. It has been shown in these examples that the particular $O(2,2)$ transformation corresponds to duality transfor

Daniel C. Cabra

We construct the Zamolodchikov's c-function for the Chiral Gross-Neveu Model up to two loops. We show that the c-function interpolates between the two known critical points of the theory, it is stationary at them and it decreases with the running coupling constant. In particular one can infer the non-existence of additional critical points in the region

A. Hietamaki, A. J. Niemi

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

Jin-Min Shen, Zheng-Mao Sheng, Zhong-Hau Wang

We have studied the quantum Liouville theory on the Riemann sphere with n>3 punctures. While considering the theory on the Riemann surfaces with n=4 punctures, the quantum theory near an arbitrary but fixed puncture can be obtained via canonical quantization and an extra symmetry is explored. While considering more than four distinguished punctures, we have

Katri Huitu

We study the modular invariance of $N=2$ superconformal $SU(1,1)$ models. By decomposing the characters of Kazama-Suzuki model $SU(3)/(SU(2)\times U(1))$ into an infinite sum of the characters of $(SU(1,1)/U(1))\times U(1)$ we construct modular invariant partition functions of $(SU(1,1)/U(1))\times U(1)$.

G. Giavarini, C. P. Martin, F. Ruiz Ruiz

We study quantum Chern-Simons theory as the large mass limit of the limit $D\to 3$ of dimensionally regularized topologically massive Yang-Mills theory. This approach can also be interpreted as a BRS-invariant hybrid regularization of Chern-Simons theory, consisting of a higher-covariant derivative Yang-Mills term plus dimensional regularization. Working in

I. Bars, K. Sfetsos

Using a Hamiltonian approach to gauged WZW models, we present a general method for computing the conformally exact metric and dilaton, to all orders in the $1/k$ expansion, for any bosonic, heterotic, or type-II superstring model based on a coset $G/H$. We prove the following relations: (i) For type-II superstrings the conformally exact metric and dilaton ar

Frank R. Brown, Hong Chen, Norman H. Christ, Zhihua Dong

QCD with eight flavors is studied on $16^3\times N_t$ lattices with $N_t=4$, 6, 8, 16 and 32, a dynamical quark mass $ma=0.015$ and lattice coupling $β=6/g^2$ between 4.5 and 5.0. For $N_t=16$ and 32, hadron masses and screening lengths are computed for a variety of valence quark masses. The previously observed, strong, first-order transition for $N_t=4$, 6

Ofer Biham, A. Alan Middleton, Dov Levine

A simple model that describes traffic flow in two dimensions is studied. A sharp {\it jamming transition } is found that separates between the low density dynamical phase in which all cars move at maximal speed and the high density jammed phase in which they are all stuck. Self organization effects in both phases are studied and discussed.

Paolo Aluffi, Carel Faber

The group PGL(3) of linear transformations of the projective plane acts naturally on the projective space parametrizing curves of a given degree. In this note we begin the study of the orbits of smooth curves under this action: we construct a resolution of the closure of the orbit of a given curve, and we use it to compute its degree. This turns out to depen

Stephen J. Dilworth, Stephen J. Montgomery-Smith

Let $X=\sum ε_n x_n$ be a Rademacher series with vector-valued coefficients. We obtain an approximate formula for the distribution of the random variable $||X||$ in terms of its mean and a certain quantity derived from the K-functional of interpolation theory. Several applications of the formula are given.

A. Berkovich, G. Sierra, C. Gomez

We study the thermodynamic properties of a family of integrable 1D spin chain hamiltonians associated with quantum groups at roots of unity. These hamiltonians depend for each primitive root of unit on a parameter $s$ which plays the role of a continuous spin. The model exhibits ferrimagnetism even though the interaction involved is between nearest neighbors

Andreas Kriegl, Peter W. Michor

A topological space $X$ is called $\Cal A$-real compact, if every algebra homomorphism from $\Cal A$ to the reals is an evaluation at some point of $X$, where $\Cal A$ is an algebra of continuous functions. Our main interest lies on algebras of smooth functions. In \cite{AdR} it was shown that any separable Banach space is smoothly real compact. Here we gene

Jouko Mickelsson

An algebraic rule is presented for computing expectation values of products of local nonabelian charge operators for fermions coupled to an external vector potential in $3+1$ space-time dimensions. The vacuum expectation value of a product of four operators is closely related to a cyclic cocycle in noncommutative geometry of Alain Connes. The relevant repres

Mirjam Cvetic, Stephen Griffies, Soo-Jong Rey

We investigate the possibility of false vacuum decay in $N=1$ supergravity theories. By establishing a Bogomol'nyi bound for the energy density stored in the domain wall of the $O(4)$ invariant bubble, we show that supersymmetric vacua remain absolutely stable against false vacuum decay into another supersymmetric vacuum. This conforms with and completes

Olivier Babelon, Denis Bernard

Using exact expressions for the Ising form factors, we give a new very simple proof that the spin-spin and disorder-disorder correlation functions are governed by the Painlevé III non linear differential equation. We also show that the generating function of the correlation functions of the descendents of the spin and disorder operators is a $N$-soliton, $N\

Olivier Babelon, Denis Bernard

We reconsider the construction of solitons by dressing transformations in the sine-Gordon model. We show that the $N$-soliton solutions are in the orbit of the vacuum, and we identify the elements in the dressing group which allow us to built the $N$-soliton solutions from the vacuum solution. The dressed $τ$-functions can be computed in two different ways~:

John Ellis, S. Kelley, D. V. Nanopoulos

We reanalyze precision LEP data and coupling constant unification in the minimal supersymmetric $SU(5)$ model including the evolution of the gaugino masses. We derive general bounds on the primordial gaugino supersymmetry-breaking mass-scale $m_{1/2}$ in terms of the various input parameters. The model cannot accommodate $m_{1/2}<1\TeV$ for values of $\as <

T. Elliott, S. F. King

We study the consequences of the existence and breaking of a Peccei--Quinn symmetry within the context of a dynamical model of electroweak symmetry breaking based on broken gauged flavour symmetries. We perform an estimate of the axion mass by including flavour instanton effects and show that, for low cut--offs, the axion is sufficiently massive to prevent i

Shahar Ben-Menahem, Adrian R. Cooper

There exists a class of cosmic strings that turn matter into antimatter (Alice strings). In a GUT where the unbroken gauge group contains charge conjugation ($C$), such strings form when a phase transition renders $C$ a discrete symmetry. They become boundaries of domain walls at a later, $C$-breaking transition. These `Alice walls&#39; are cosmologically ha

V. Azcoiti, G. Di Carlo, A. F. Grillo

In the framework of noncompact lattice QED with light fermions, we derive the functional dependence of the average energy per plaquette on the bare parameters using block-spin Renormalization Group arguments and assuming that the renormalized coupling vanishes. Our numerical results for this quantity in $8^4$ and $10^4$ lattices show evidence for triviality

R. L. Renken, S. M. Catterall, J. B. Kogut

We establish the phase diagram of three--dimensional quantum gravity coupled to Ising matter. We find that in the negative curvature phase of the quantum gravity there is no disordered phase for ferromagnetic Ising matter because the coordination number of the sites diverges. In the positive curvature phase of the quantum gravity there is evidence for two sp