Traces on the Sklyanin algebra and correlation functions of the eight-vertex model

We propose a conjectural formula for correlation functions of the Z-invariant (inhomogeneous) eight-vertex model. We refer to this conjecture as Ansatz. It states that correlation functions are linear combinations of products of three transcendental functions, with theta functions and derivatives as coefficients. The transcendental functions are essentially logarithmic derivatives of the partition function per site. The coefficients are given in terms of a linear functional on the Sklyanin algebra, which interpolates the usual trace on finite dimensional representations. We establish the existence of the functional and discuss the connection to the geometry of the classical limit. We also conjecture that the Ansatz satisfies the reduced qKZ equation. As a non-trivial example of the Ansatz, we present a new formula for the next-nearest neighbor correlation functions.Comment: 35 pages, 2 figures, final versio

Effective Lagrangians for physical degrees of freedom in the Randall-Sundrum model

We derive the second variation Lagrangian of the Randall-Sundrum model with two branes, study its gauge invariance and diagonalize it in the unitary gauge. We also show that the effective four-dimensional theory looks different on different branes and calculate the observable mass spectra and the couplings of the physical degrees of freedom of 5-dimensional gravity to matter.Comment: 22 pages, LaTeX, typos correcte

Holonomy of the Ising model form factors

We study the Ising model two-point diagonal correlation function $C(N,N)$ by presenting an exponential and form factor expansion in an integral representation which differs from the known expansion of Wu, McCoy, Tracy and Barouch. We extend this expansion, weighting, by powers of a variable $\lambda$, the $j$-particle contributions, $f^{(j)}_{N,N}$. The corresponding $\lambda$ extension of the two-point diagonal correlation function, $C(N,N; \lambda)$, is shown, for arbitrary $\lambda$, to be a solution of the sigma form of the Painlev{\'e} VI equation introduced by Jimbo and Miwa. Linear differential equations for the form factors $f^{(j)}_{N,N}$ are obtained and shown to have both a ``Russian doll'' nesting, and a decomposition of the differential operators as a direct sum of operators equivalent to symmetric powers of the differential operator of the elliptic integral $E$. Each $f^{(j)}_{N,N}$ is expressed polynomially in terms of the elliptic integrals $E$ and $K$. The scaling limit of these differential operators breaks the direct sum structure but not the ``Russian doll'' structure. The previous $\lambda$-extensions, $C(N,N; \lambda)$ are, for singled-out values $\lambda= \cos(\pi m/n)$ ($m, n$ integers), also solutions of linear differential equations. These solutions of Painlev\'e VI are actually algebraic functions, being associated with modular curves.Comment: 39 page

A geometrical angle on Feynman integrals

A direct link between a one-loop N-point Feynman diagram and a geometrical representation based on the N-dimensional simplex is established by relating the Feynman parametric representations to the integrals over contents of (N-1)-dimensional simplices in non-Euclidean geometry of constant curvature. In particular, the four-point function in four dimensions is proportional to the volume of a three-dimensional spherical (or hyperbolic) tetrahedron which can be calculated by splitting into birectangular ones. It is also shown that the known formula of reduction of the N-point function in (N-1) dimensions corresponds to splitting the related N-dimensional simplex into N rectangular ones.Comment: 47 pages, including 42 pages of the text (in plain Latex) and 5 pages with the figures (in a separate Latex file, requires axodraw.sty) a note and three references added, minor problem with notation fixe

Three Numerical Puzzles and the Top Quark's Chiral Weak-Moment

Versus the standard model's t --> W b decay helicity amplitudes, three numerical puzzles occur at the 0.1 % level when one considers the amplitudes in the case of an additional (f_M + f_E) coupling of relative strength 53 GeV. The puzzles are theoretical ones which involve the t --> W b decay helicity amplitudes in the two cases, the relative strength of this additional coupling, and the observed masses of these three particles. A deeper analytic realization is obtained for two of them. Equivalent realizations are given for the remaining one. An empirical consequence of these analytic realizations is that it is important to search for effects of a large chiral weak-moment of the top-quark, the effective mass-scale is about 53 GeV. A full theoretical resolution would include relating the origin of such a chiral weak-moment and the mass generation of the top-quark, the W-boson, and probably the b-quark.Comment: 18 pages, 1 postscript table (revised to better explain notation, model #1, add a little material...

Two-loop corrections to the correlator of tensor currents in gluodynamics

Results of evaluating the leading order $\alpha_s$ corrections to the correlator of tensor currents in pure gluodynamics are presented. These corrections to the parton result for the correlator are not large numerically that allows one to use perturbation theory for the analysis of the resonance spectrum within the sum rules method.Comment: 10 pages, latex, no figure

Asymptotics of Toeplitz Determinants and the Emptiness Formation Probability for the XY Spin Chain

We study an asymptotic behavior of a special correlator known as the Emptiness Formation Probability (EFP) for the one-dimensional anisotropic XY spin-1/2 chain in a transverse magnetic field. This correlator is essentially the probability of formation of a ferromagnetic string of length $n$ in the antiferromagnetic ground state of the chain and plays an important role in the theory of integrable models. For the XY Spin Chain, the correlator can be expressed as the determinant of a Toeplitz matrix and its asymptotical behaviors for $n \to \infty$ throughout the phase diagram are obtained using known theorems and conjectures on Toeplitz determinants. We find that the decay is exponential everywhere in the phase diagram of the XY model except on the critical lines, i.e. where the spectrum is gapless. In these cases, a power-law prefactor with a universal exponent arises in addition to an exponential or Gaussian decay. The latter Gaussian behavior holds on the critical line corresponding to the isotropic XY model, while at the critical value of the magnetic field the EFP decays exponentially. At small anisotropy one has a crossover from the Gaussian to the exponential behavior. We study this crossover using the bosonization approach.Comment: 40 pages, 9 figures, 1 table. The poor quality of some figures is due to arxiv space limitations. If You would like to see the pdf with good quality figures, please contact Fabio Franchini at "[email protected]

Detection of the heavy Higgs boson at γγ\gamma\gamma colliders

We consider the possibility of detecting a heavy Higgs boson ($m_H>2m_Z$) in proposed $\gamma\gamma$ colliders through the semi-leptonic mode $\gamma\gamma \rightarrow H \rightarrow ZZ \rightarrow q\bar q \ell^+\ell^-$. We show that due to the non-monochromatic nature of the photon beams produced by the laser-backscattering method, the resultant cross section for Higgs production is much smaller than the on-resonance cross section and generally {\it decreases} with increasing collider energy. Although continuum $ZZ$ production is expected to be negligible, we demonstrate the presence of and calculate sizeable backgrounds from $\gamma\gamma\rightarrow \ell^+\ell^-Z,\,q\bar qZ$, with $Z\rightarrow q\bar q,\,\ell^+\ell^-$, respectively, and $\gamma\gamma\rightarrow t\bar t\rightarrow b\bar b\ell^+\ell^-\nu\bar\nu$. This channel may be used to detect a Higgs of mass $m_H$ up to around 350~GeV at a 0.5~TeV $e^+e^-$ collider, assuming a nominal yearly luminosity of 10--20~fb$^{-1}$.Comment: 18 pages (in RevTeX) plus Postscript figures (available by email or FAX), NUHEP-TH-92-29 and DOE-309-CPP-47. (Revised version: NO CHANGES to the manuscript, simply removed corrupted figure files

Investigation of correlation of generated nuclearactive particles in the protonantiproton annihilation at momenta 22.4 and 32 GeV / c

Separation of the individual events corresponding to antiproton-proton annihilation gives the possibility to carry out the analysis of multiparticle correlations for generated particles and to compare them with corresponding data for inelastic pp and non-annihilation p̃p interactions..

Investigation of correlation of generated nuclearactive particles in the protonantiproton annihilation at momenta 22.4 and 32 GeV / c

Separation of the individual events corresponding to antiproton-proton annihilation gives the possibility to carry out the analysis of multiparticle correlations for generated particles and to compare them with corresponding data for inelastic pp and non-annihilation p̃p interactions..