January 1993 arXiv papers — page 4

Alon E. Faraggi

I discuss the construction of realistic superstring standard--like models in the four dimensional free fermionic formulation. I discuss proton lifetime constraints on superstring models. I discuss the massless spectrum of the superstring standard--like models, the texture of fermion mass matrices in these models and argue that the realistic features of these

Christian Holm, Wolfhard Janke

We have simulated the three-dimensional Heisenberg model on simple cubic lattices, using the single-cluster Monte Carlo update algorithm. The expected pronounced reduction of critical slowing down at the phase transition is verified. This allows simulations on significantly larger lattices than in previous studies and consequently a better control over syste

S. Carlip

A real tunneling solution is an instanton for the Hartle-Hawking path integral with vanishing extrinsic curvature (vanishing ``momentum'') at the boundary. Since the final momentum is fixed, its conjugate cannot be specified freely; consequently, such an instanton will contribute to the wave function at only one or a few isolated spatial geometries.

Raymond Laflamme

We investigate the time neutral formulation of quantum cosmology of Gell-Mann and Hartle. In particular we study the proposal discussed by them that our Universe corresponds to the time symmetric decoherence functional with initial and final density matrix of low entropy. We show that our Universe does not correspond to this proposal by investigating the beh

A. H. Castro Neto, Eduardo Fradkin

In this paper we examine the behavior in temperature of the free energy on quantum systems in an arbitrary number of dimensions. We define from the free energy a function $C$ of the coupling constants and the temperature, which in the regimes where quantum fluctuations dominate, is a monotonically increasing function of the temperature. We show that at very

M. R. Gallis

We construct model master equations for local quantum dissipation. The master equations are in the form of Lindblad generators, with imposed constraints that the dissipations be strictly linear (i.e. ohmic), isotropic and translationally invariant. A particular form for is chosen to satisfy the constraints. The resulting master equations are given in both th

M. A. Abramowicz, G. Bao, V. Karas, A. Lanza

The Seyfert galaxy NGC 6814 is known to show periodic variation of its X-ray luminosity. We found that the sequences of peaks (variability patterns) in the folded X-ray light curves constructed from the {\it Exosat} and {\it Ginga} data are remarkably similar when one ignores amplitudes of the peaks and considers only their phases. The stable pattern consist

Adel Bilal

Extending the work of Park and Strominger, we prove a positive energy theorem for the exactly solvable quantum-corrected 2D dilaton gravity theories. The positive energy functional we construct is shown to be unique (within a reasonably broad class of such functionals). For field configurations asymptotic to the LDV we show that this energy functional (if de

A. Kuniba, T. Nakanishi, J. Suzuki

We propose a new $q$-series formula for a character of parafermion conformal field theories associated to arbitrary non-twisted affine Lie algebra $\widehat{g}$. We show its natural origin from a thermodynamic Bethe ansatz analysis including chemical potentials.

M. Baldo, A. Causa, A. Rapisarda

The distortion on the intermittency signal, due to detection efficiency and to the presence of pre--equilibrium emitted particles, is studied in a schematic model of nuclear multi- fragmentation. The source of the intermittency signal is modeled with a percolating system. The efficiency is schematized by a simple function of the fragment size, and the presen

Tsukasa TADA, Shozo UEHARA

For the two dimensional dilaton-coupled quantum gravity model, we give the local black hole mass, which is an analogue of what was first introduced by Fischler, Morgan and Polchinski in the four dimensional gravitational systems. We analyze the original CGHS model with this local mass and find that the local mass is decreasing in the future direction on the

A. Aurilia, A. Smailagic, E. Spallucci

A relativistic string is usually represented by the Nambu-Goto action in terms of the extremal area of a 2-dimensional timelike submanifold of Minkowski space. Alternatively, a family of classical solutions of the string equation of motion can be globally described in terms of the associated geodesic field. In this paper we propose a new gauge theory for the

E. Shuryak, L. Xiong

Perturbative analysis of parton kinetics for high energy nuclear collisions shows, that thermal equilibration of gluons happens very fast, while quark production is much slower. A simple 'minimal model' is proposed which includes only in-coming quarks and anti-quarks. We have found that a smaller quark number is more than compensated by the fact, tha

J. Ignatius

Free energy as a function of temperature and the bubble radius is determined for spherical bubbles created in cosmological first order phase transitions. The phase transition is assumed to be driven by an order parameter (e.g. a Higgs field) with quartic potential. The definition of the bubble radius and the corresponding generalized, curvature-dependent sur

Jon Pumplin

I describe possible ways to discover hard double pomeron exchange (HDPE) with the existing detectors at the Fermilab Tevatron, by using the small-angle ``luminosity'' counters as a veto. Estimates of the cross sections and backgrounds are made. In addition to the intrinsic importance of HDPE, its observation would be useful for calibrating the detectors, and

Jon Pumplin

A new method to identify the gluon jet in 3-jet ``{\bf Y}'' decays of $Z^0$ is presented. The method is based on differences in particle multiplicity between quark jets and gluon jets, and is more effective than tagging by leptonic decay. An experimental test of the method and its application to a study of the ``string effect'' are proposed.

George Triantaphyllou

In view of the recent interest in the decays of mesons into a pair of light leptons, a computation of the QED radiative corrections to the decay of $π^{0}$ into an electron-positron pair is presented here. The results indicate that the peak value of the differential decay rate is reduced by about $50 \%$, because of soft-photon radiation. The number of $e^{+

J. Finkelstein

We examine the relationship between the decoherence of quantum-mechanical histories of a closed system (as discussed by Gell-Mann and Hartle) and environmentally-induced diagonalization of the density operator for an open system. We study a definition of decoherence which incorporates both of these ideas, and show that it leads to a consistent probabilistic

Steven C. Erwin, Mark R. Pederson

We report the results of first-principles electronic-structure calculations for superconducting Ba6C60. Unlike the A3C60 superconductors, this new compound shows strong Ba-C hybridization in the valence and conduction regions, mixed covalent/ionic bonding character, partial charge transfer, and insulating zero-gap band structure.

Didier Poilblanc, Timothy Ziman, Jean Bellissard, Frederic Mila

We calculate the level statistics by finding the eigenvalue spectrum for a variety of one-dimensional many-body models, namely the Heisenberg chain, the t-J model and the Hubbard model. In each case the generic behaviour is GOE, however at points corresponding to models known to be exactly integrable Poisson statistics are found, in agreement with an argumen

Scott Dodelson, Jay M. Jubas

The recent COBE measurement of anisotropies in the cosmic microwave background and the recent South Pole experiment of Gaier {\it et al.} offer an excellent opportunity to probe cosmological theories. We test a class of theories in which the Universe today is flat and matter dominated, and primordial perturbations are adiabatic parameterized by an index $n$.

P. Marziani, J. W. Sulentic, M. Calvani, E. Perez

We present spectrophotometric observations of the Broad Line Radio Galaxy OQ 208 (Mrk 668, 1404+286) obtained between 1985 and 1991. We show that the Balmer line fluxes and profile shapes undergo remarkable changes. The ratio of intensities between the broad and narrow components of Hbeta increased monotonically from 15 in 1985 to 40 in 1991. The peak of the

A. A. Tseytlin

We suggest how to derive the exact (all order in $\a'$) expressions for the background fields for string solutions corresponding to gauged WZW models directly at the $2d$ field theory level. One is first to replace the classical gauged WZW action by the quantum effective one and then to integrate out the gauge field. We find the explicit expression for t

N. E. Bonesteel

To leading order in displacement size, the scattering of electrons in a Cu-O plane from O displacements perpendicular to that plane is due to spin-orbit coupling. This scattering is investigated with the following results: (1) As a consequence of time-reversal symmetry, spin fluctuations, which can strongly enhance scattering from a spin impurity, do not enh

Olivier Debarre

We show that on the Jacobian $(JC,θ)$ of a smooth curve $C$ of genus $g$, any effective cycle in $JC$ with cohomology class $θ^d/d!$ is a translate of $W_{g-d}(C)$ or $-W_{g-d}(C)$. We then use this result to prove that for $1<d<g$, the Jacobian locus (\resp the locus of intermediate Jacobians of cubic threefolds) is an irreducible component of the set of pr

S. S. Kamalov, L. Tiator, C. Bennhold

Pion elastic, charge exchange scattering and induced eta production on the trinucleon systems are investigated in a coupled-channels approach in momentum space with Fadeev wave functions. The channel $πN \rightarrow ηN$ is included using an isobar model with S-, P-, and D-wave resonances. While the coherent reactions like $^3$He($π,π)^3$He can be reasonably

K. Becker, M. Becker

We present the solution of the discrete super-Virasoro constraints to all orders of the genus expansion. Integrating over the fermionic variables we get a representation of the partition function in terms of the one-matrix model. We also obtain the nonperturbative solution of the super-Virasoro constraints in the double scaling limit but do not find agreemen

H. Arfaei, A. Shirzad

Using shift vector method we obtain a large class of self-dual lattices of dimension $(l,l)$, which has a one to one correspondence with modular invariants of free bosonic theory compactified on co-root lattice of a rank $l$ Lie group. Then a large number of modular invariants of affine Lie algebras are derived explicitly. As two applications of this method,

K. S. Babu, I. Z. Rothstein, D. Seckel

Majoron models provide neutrino masses via the spontaneous breaking of a global $U(1)$ symmetry. However, it may be argued that all global symmetries will be explicitly violated by gravitational effects. We show that it is possible to preserve most of the usual features of majoron models by invoking $U(1)_{B-L}$ to be a gauge symmetry and adding a second sin

Thorsten Ohl, Giulia Ricciardi, Elizabeth H. Simmons

We perform a quantitative analysis of $D\bar{D}$ mixing in Heavy Quark Effective Field Theory (HqEFT) including leading order QCD corrections. We find an enhancement of the short-distance contribution by a factor of two or three.

E. Kh. Akhmedov, S. T. Petcov, A. Yu. Smirnov

Transitions in a system of neutrinos with vacuum mixing and magnetic moments, propagating in matter and transverse magnetic field, are considered. It is shown that in the realistic case of magnetic field direction varying along the neutrino path qualitatively new phenomena become possible: permutation of neutrino conversion resonances, appearance of resonanc

A. Duncan, E. Eichten, H. Thacker

Using a multistate smearing method, Coulomb gauge wave functions of heavy-light mesons are studied in lattice QCD. Wave functions for the ground state, the first radially excited S-wave state, and the lowest P-wave states of a heavy-light meson are calculated in quenched approximation. The results are found to be in remarkably good agreement with the predict

Lee Samuel Finn, David F. Chernoff

We investigate the sensitivity of individual LIGO/VIRGO-like interferometers and the precision with which they can determine the characteristics of an inspiralling binary system. Since the two interferometers of the LIGO detector share nearly the same orientation, their joint sensitivity is similar to that of a single, more sensitive interferometer. We expre

Edward Malec

Spherical configurations that are very massive must be surrounded by apparent horizons. These in turn, when placed outside a collapsing body, must propagate outward with a velocity equal to the velocity of radially outgoing photons. That proves, within the framework of (1+3) formalism and without resorting to the Birkhoff theorem, that apparent horizons coin

Jysoo Lee

Using molecular dynamics (MD) simulations, we find the formation of heaps in a system of granular particles contained in a box with oscillating bottom and fixed sidewalls. The simulation includes the effect of static friction, which is found to be crucial in maintaining a stable heap. We also find another mechanism for heap formation in systems under constan

Marc Coppens, Takao Kato

Let $C$ be a smooth plane curve of degree $d$ defined over an algebraically closed field $k$. A base point free complete very special linear system $g^r_n$ on $C$ is trivial if there exists an integer $m\ge 0$ and an effective divisor $E$ on $C$ of degree $md-n$ such that $g^r_n=|mg^2_d-E|$ and $r=(m^2+3m)/2-(md-n)$. In this paper, we prove the following: Th

Zvonimir Hlousek, Donald Spector

We give model-independent arguments, valid in nearly any number of spacetime dimensions, that topological solitons and instantons satisfy Bogomol'nyi-type bounds and, when these bounds are saturated, satisfy self-duality equations. In the supersymmetric case, we also show that, in spacetime dimensions greater than two, theories with topological charges neces

K. S. Gupta, S. Guruswamy, S. G. Rajeev

We propose a model for Quantum Chromodynamics, obtained by ignoring the angular dependence of the gluon fields, which could qualitatively describe systems containing one heavy quark. This leads to a two dimensional gauge theory which has chiral symmetry and heavy quark symmetry. We show that in a light cone formalism, the Hamiltonian of this spherical QCD ca

F. D. T. Smith

A 130 GeV mass is calculated for the t-quark, also called the truth quark or the top quark. The 130 GeV T-quark mass is consistent with the analysis of Dalitz and Goldstein (131 GeV (-11, +22 )) of a CDF T-quark candidate event [1]. It is not consistent with the theoretical calculations of Dimopoulos, Hall, and Raby that the T-quark mass range should be 176

Yi-Zhi Huang, James Lepowsky

Vertex operator algebras are mathematically rigorous objects corresponding to chiral algebras in conformal field theory. Operads are mathematical devices to describe operations, that is, $n$-ary operations for all $n$ greater than or equal to $0$, not just binary products. In this paper, a reformulation of the notion of vertex operator algebra in terms of op

Donald Spector

I provide an extremely simple argument that the kink-type solitons in certain theories are fermionic. The argument is based on the Witten index, but can in fact be used to determine soliton statistics in non-supersymmetric theories as well.

H. Mishra, S. P. Misra, P. K. Panda, B. K. Parida

We consider the neutron matter quark matter phase transition along with possible existence of hybrid quark stars. The equation of state for neutron matter is obtained using a nonperturbative method with pion dressing of the neutron matter and an analysis similar to that of symmetric nuclear matter. The quark matter sector is treated perturbatively in the sma

M. P. Fry

A representation for the fermionic determinant of the massive Schwinger model, or $QED_2$, is obtained that makes a clean separation between the Schwinger model and its massive counterpart. From this it is shown that the index theorem for $QED_2$ follows from gauge invariance, that the Schwinger model&#39;s contribution to the determinant is canceled in the

Bernard Nienhuis, Ronald Rietman

We show that some models with non-local (and non-localizable) interactions have a property, called quasi-locality, which allows for the definition of a transfer matrix. We give the Yang-Baxter equation as a sufficient condition for the existence of a family of commuting transfer matrices and solve them for a loop model with intersections. This solvable model

E. Ragoucy

We present a classification of characteristic Dynkin diagrams for the $A_N$, $B_N$, $C_N$ and $D_N$ algebras. This classification is related to the classification of \cw(\cg,\ck) algebras arising from non-Abelian Toda models, and we argue that it can give new insight on the structure of $W$ algebras.

K. Demeterfi, I. R. Klebanov

We review the recently proposed \lc\ quantization of the matrix model which is expected to have a critical point describing 2-d quantum gravity coupled to $c=2$ matter. In the $N\to\infty$ limit, we derive a linear Schroedinger equation for the free string spectrum. Numerical study of this equation suggests that the spectrum is tachyonic, and that the string

Alan R. White, Ian G. Knowles, Kyungsik Kang

The $η_6$, a ``heavy axion&#39;&#39; associated with sextet quark electroweak symmetry breaking, may have been seen at LEP via its two-photon decay mode and also at TRISTAN via its hadronic decay modes. - presented at DPF 92.

O. W. Greenberg

I review the discovery of the color degree of freedom in hadronic physics, and the developments which led from that discovery to the local gauge theory of color, quantum chromodynamics.

Harry J. Lipkin

Recent reports of the observation of the decay $τ\rarrow ν_τ + K + π+ π$ raise interesting questions. The $u-s$ quark mass difference can induce an effective second-class current in the strange sector and enhance decays to helicity-suppressed scalar states. This suggests searches for scalar strange mesons in the $τ\rarrow ν_τ + K + η&#39; $ and $τ\rarrow ν_τ

John F. Gunion, Howard E. Haber

Errata are given for J.F. Gunion and H.E. Haber, Nucl. Phys. B272 (1986) 1, Nucl. Phys. B278 (1986) 449, and Nucl. Phys. B307 (1988) 445.

Olivier Coussaert, Marc Henneaux

We analyze carefully the problem of gauge symmetries for Bianchi models, from both the geometrical and dynamical points of view. Some of the geometrical definitions of gauge symmetries (=``homogeneity preserving diffeomorphisms&#39;&#39;) given in the literature do not incorporate the crucial feature that local gauge transformations should be independent at

O. W. Greenberg

After a brief mention of Bose and Fermi oscillators and of particles which obey other types of statistics, including intermediate statistics, parastatistics, paronic statistics, anyon statistics and infinite statistics, I discuss the statistics of ``quons&#39;&#39; (pronounced to rhyme with muons), particles whose annihilation and creation operators obey the

J. Piekarewicz, A. G. Williams

We calculate the momentum dependence of the $ρ-ω$ mixing amplitude in a purely hadronic model. The basic assumption of the model is that the mixing amplitude is generated by $N{\bar{N}}$ loops and thus driven entirely by the neutron-proton mass difference. The value of the amplitude at the $ω$-meson point is expressed in terms of only the $NNω$ and the $NNρ$

Abbas Ali, Alok Kumar

It is shown that the previously known $N=3$ and $N=4$ superconformal algebras can be contracted consistently by singular scaling of some of the generators. For the later case, by a contraction which depends on the central term, we obtain a new $N=4$ superconformal algebra which contains an $SU(2)\times {U(1)}^4$ Kac-Moody subalgebra and has nonzero central e

F. W. Nijhoff, H. W. Capel

We apply the fusion procedure to a quantum Yang-Baxter algebra associated with time-discrete integrable systems, notably integrable quantum mappings. We present a general construction of higher-order quantum invariants for these systems. As an important class of examples, we present the Yang-Baxter structure of the Gel&#39;fand-Dikii mapping hierarchy, that

Måns Henningson, Chiara R. Nappi

We study duality transformations for two-dimensional sigma models with abelian chiral isometries and prove that generic such transformations are equivalent to integrated marginal perturbations by bilinears in the chiral currents, thus confirming a recent conjecture by Hassan and Sen formulated in the context of Wess-Zumino-Witten models. Specific duality tra

B. Eynard, J. Zinn-Justin

We discuss the large order behaviour and Borel summability of the topological expansion of models of 2D gravity coupled to general $(p,q)$ conformal matter. In a previous work it was proven that at large order $k$ the string susceptibility had a generic $a^kΓ(2k-\ud)$ behaviour. Moreover the constant $a$, relevant for the problem of Borel summability, was de

J. H. K&#34;uhn, E. Mirkes

Toponium production at future hadron colliders is investigated. Perturbative QCD corrections to the production cross section for gluon fusion are calculated as well as the contributions from gluon-quark and quark-antiquark collisions to the total cross section. The dependence on the renormalization and factorization scales and on the choice of the parton dis

R. Decker, E. Mirkes

We propose to measure the Wess-Zumino anomaly contribution by considering angular distributions in the decays $τ\toν_τηπ^{-}π^{0}$, $τ\toν_τK^- π^{-} K^+ $ and $τ\toν_τK^- π^- π^+$. Radial excitations of the $K^*$, which cannot be seen in $e^++e^-$, should be observed in the $ K^- π^+ π^-$ decay channel.

J. R. Forshaw

The validity of using QCD perturbation theory to generate dynamically the parton distribution functions of hadrons, starting from a valencelike input at low $Q^2$, is discussed. In particular, we consider the prescription of Barone {\em et al} who evolve from $Q^2 = 0$, and that of Glück {\em et al} who start evolution from $Q^2 \simeq (2Λ_{QCD})^2$.

A. Libgober, J. Teitelbaum

A relation between the number of rational curves of fixed degree on Calabi Yau threefolds and the Picard Fuchs equations, which was suggested as part of the study of mirror symmetry, is verified in the case of complete intersection of two cubics and lines.

Doron Zeilberger

The future of mathematics is described, by using the WZ algorithmic proof theory as a parable.

T. Vachaspati

I describe the string solutions in the standard electroweak model and argue that they may be stabilized by quark, lepton or other bound states. I then reinterpret the sphaleron in terms of electroweak strings and show that it can be viewed as a loop of W-string or a segment of Z-string. (Talk presented at Texas/Pascos 1992 at Berkeley.)

Bo-Qiang Ma

The off-shell behaviors of bound nucleons in deep inelastic lepton nucleus scattering are discussed in two scenarios with the basic constituents chosen to be baryon-mesons and quark-gluons respectively in light-cone formalism. It is found that when taking into account the effect due to internal quark structure of nucleons, the derived scaling variable for bo

Joseph A. Minahan

Following some recent work by Gross, we consider the partition function for QCD on a two dimensional torus and study its stringiness. We present strong evidence that the free energy corresponds to a sum over branched surfaces with small handles mapped into the target space. The sum is modded out by all diffeomorphisms on the world-sheet. This leaves a sum ov

I. Antoniadis, P. O. Mazur, E. Mottola

We propose that large quantum fluctuations of the conformal factor drastically modify classical general relativity at cosmological distance scales, resulting in a scale invariant phase of quantum gravity in the far infrared. We derive scaling relations for the partition function and physical observables in this conformal phase, and suggest quantitative tests

Shuang Zhang

Let $\Scr A$ be a unital C*-algebra. We describe \it K-skeleton factorizations \rm of all invertible operators on a Hilbert C*-module $\Scr H_{\Scr A}$, in particular on $\Scr H=l^2$, with the Fredholm index as an invariant. We then outline the isomorphisms $K_0(\Scr A) \cong π_{2k}([p]_0)\cong π_{2k} ({GL}^p_r(\Scr A))$ and $K_1(\Scr A)\cong π_{2k+1}([p]_0)

Lang-Fang Wu

Given $\Bbb R^2, $ with a ``good&#39;&#39; complete metric, we show that the unique solution of the Ricci flow approaches a soliton at time infinity. Solitons are solutions of the Ricci flow, which move only by diffeomorphism. The Ricci flow on $\Bbb R^2$ is the limiting case of the porous medium equation when $m$ is zero. The results in the Ricci flow may t

Herbert Stahl

A strong error estimate for the uniform rational approximation of $x^α$ on $[0,1]$ is given, and its proof is sketched. Let $E_{nn}(x^α,[0,1])$ denote the minimal approximation error in the uniform norm. Then it is shown that $$\lim_{n\to\infty}e^{2π\sqrt{αn}}E_{nn}(x^α,[0,1]) = 4^{1+α}|\sinπα|$$ holds true for each $α>0$.

Neil Robertson, Paul Seymour, Robin Thomas

We announce results about flat (linkless) embeddings of graphs in 3-space. A piecewise-linear embedding of a graph in 3-space is called {\it flat} if every circuit of the graph bounds a disk disjoint from the rest of the graph. We have shown: (i) An embedding is flat if and only if the fundamental group of the complement in 3-space of the embedding of every

Alexander G. Ramm, Alexander I. Zaslavsky

Singularities of the Radon transform of a piecewise smooth function $f(x)$, $x\in R^n$, $n\geq 2$, are calculated. If the singularities of the Radon transform are known, then the equations of the surfaces of discontinuity of $f(x)$ are calculated by applying the Legendre transform to the functions, which appear in the equations of the discontinuity surfaces

Roger E. Howe

In this paper we study the reducibility, composition series and unitarity of the components of some degenerate principal series representations of $\RMO(p,q)$, $\RMU(p,q)$ and $\SP(p,q)$. This is done by realizing these representations in paces of homogeneous functions on light cones and writing down the explicit actions of the universal enveloping algebra o

Guihua Gong

In this paper, we discuss the following conjecture raised by Baum-Douglas: For any first-order elliptic differential operator $D$ on smooth manifold $M$ with boundary $\p M$, $D$ possesses an elliptic boundary condition if and only if $\partial [D]$ = 0 in $K_1(\partial M)$, where $[D]$ is the relative $K$-cycle in $K_0(M, \partial M)$ corresponding to $D$.

Steve Bryson, Michael H. Freedman, Zheng-Xu He, Zhenghan Wang

A physically natural potential energy for simple closed curves in $\bold R^3$ is shown to be invariant under Möbius transformations. This leads to the rapid resolution of several open problems: round circles are precisely the absolute minima for energy; there is a minimum energy threshold below which knotting cannot occur; minimizers within prime knot types

Alejandro Adem

Let $Γ$ be a discrete group of finite virtual cohomological dimension with certain finiteness conditions of the type satisfied by arithmetic groups. We define a representation ring for $Γ$, determined on its elements of finite order, which is of finite type. Then we determine the contribution of this ring to the topological $K$-theory $K^*(BΓ)$, obtaining an

G. K. Savvidy, K. G. Savvidy

Few natural basic principles allow to extend Feynman integral over the paths to an integral over the surfaces so, that they coincide at long time scale, that is when the surface degenerates into a single particle world line. In the first approximation the loop Green functions have perimeter behavior. That corresponds to the case when free quarks interact thr

Hisao Nakanishi

We study the effects of adding loops to a critical percolation cluster on the diffusional, and equivalently, (scalar) elastic properties of the fractal network. From the numerical calculations of the eigenspectrum of the transition probability matrix, we find that the spectral dimension $d_s$ and the walk dimension $d_w$ change suddenly as soon as the floppy