20 research outputs found
O(N) and RP^{N-1} Models in Two Dimensions
I provide evidence that the 2D model for is equivalent
to the -invariant non-linear -model in the continuum limit. To
this end, I mainly study particular versions of the models, to be called
constraint models. I prove that the constraint and models are
equivalent for sufficiently weak coupling. Numerical results for their
step-scaling function of the running coupling are
presented. The data confirm that the constraint model is in the samei
universality class as the model with standard action. I show that the
differences in the finite size scaling curves of i and models
observed by Caracciolo et al. can be explained as a boundary effect. It is
concluded, in contrast to Caracciolo et al., that and models
share a unique universality class.Comment: 14 pages (latex) + 1 figure (Postscript) ,uuencode
The Master Field for the Half-Planar Approximation for Large Matrix Models and Boltzmann Field Theory
In this talk results of study in various dimensions of the Boltzmann master
field for a subclass of planar diagrams, so called half-planar diagrams, found
in the recent work by Accardi, Volovich and one of us (I.A.) are presented.Comment: Contr. Proc. Buckow Symposium (1995); 6 pages, LATEX uses
twoside.sty, fleqn.sty, espcrc2.sty, emlines.sty, bezier.st
Absence of a fuzzy phase in the dimensionally reduced 5d Yang-Mills-Chern-Simons model
We perform nonperturbative studies of the dimensionally reduced 5d
Yang-Mills-Chern-Simons model, in which a four-dimensional fuzzy manifold,
``fuzzy S'', is known to exist as a classical solution. Although the
action is unbounded from below, Monte Carlo simulations provide an evidence for
a well-defined vacuum, which stabilizes at large , when the coefficient of
the Chern-Simons term is sufficiently small. The fuzzy S prepared as an
initial configuration decays rapidly into this vacuum in the process of
thermalization. Thus we find that the model does not possess a ``fuzzy S
phase'' in contrast to our previous results on the fuzzy S.Comment: 11 pages, 2 figures, (v2) typos correcte
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.Comment: 14 page
A toy model for the AdS/CFT correspondence
We study the large N gauged quantum mechanics for a single Hermitian matrix
in the Harmonic oscillator potential well as a toy model for the AdS/CFT
correspondence. We argue that the dual geometry should be a string in two
dimensions with a curvature of stringy size. Even though the dual geometry is
not weakly curved, one can still gain knowledge of the system from a detailed
study of the open-closed string duality. We give a mapping between the basis of
states made of traces (closed strings) and the eigenvalues of the matrix
(D-brane picture) in terms of Schur polynomials. We connect this model with the
study of giant gravitons in AdS_5 x S^5. We show that the two giant gravitons
that expand along AdS_5 and S^5 can be interpreted in the matrix model as
taking an eigenvalue from the Fermi sea and exciting it very much, or as making
a hole in the Fermi sea respectively. This is similar to recent studies of the
c=1 string. This connection gives new insight on how to perform calculations
for giant gravitons.Comment: 19 pages JHEP, 4 figures. v2: comments added, typos fixed, additional
refs. v3: The paper has been largely revised, to make the relation as a limit
of N=4 SYM clear, also some proofs have been written in full rather than
sketched. This updated version reflects the changes that were made in the
published versio
Hexatic-Herringbone Coupling at the Hexatic Transition in Smectic Liquid Crystals: 4- Renormalization Group Calculations Revisited
Simple symmetry considerations would suggest that the transition from the
smectic-A phase to the long-range bond orientationally ordered hexatic
smectic-B phase should belong to the XY universality class. However, a number
of experimental studies have constantly reported over the past twenty years
"novel" critical behavior with non-XY critical exponents for this transition.
Bruinsma and Aeppli argued in Physical Review Letters {\bf 48}, 1625 (1982),
using a renormalization-group calculation, that short-range
molecular herringbone correlations coupled to the hexatic ordering drive this
transition first order via thermal fluctuations, and that the critical behavior
observed in real systems is controlled by a `nearby' tricritical point. We have
revisited the model of Bruinsma and Aeppli and present here the results of our
study. We have found two nontrivial strongly-coupled herringbone-hexatic fixed
points apparently missed by those authors. Yet, those two new nontrivial
fixed-points are unstable, and we obtain the same final conclusion as the one
reached by Bruinsma and Aeppli, namely that of a fluctuation-driven first order
transition. We also discuss the effect of local two-fold distortion of the bond
order as a possible missing order parameter in the Hamiltonian.Comment: 1 B/W eps figure included. Submitted to Physical Review E. Contact:
[email protected]
Two-Dimensional Unoriented Strings And Matrix Models
We investigate unoriented strings and superstrings in two dimensions and
their dual matrix quantum mechanics. Most of the models we study have a tachyon
tadpole coming from the RP^2 worldsheet which needs to be cancelled by a
renormalization of the worldsheet theory. We find evidence that the dual matrix
models describe the renormalized theory. The singlet sector of the matrix
models is integrable and can be formulated in terms of fermions moving in an
external potential and interacting via the Calogero-Moser potential. We show
that in the double-scaling limit the latter system exhibits particle-hole
duality and interpret it in terms of the dual string theory. We also show that
oriented string theories in two dimensions can be continuously deformed into
unoriented ones by turning on non-local interactions on the worldsheet. We find
two unoriented superstring models for which only oriented worldsheets
contribute to the S-matrix. A simple explanation for this is found in the dual
matrix model.Comment: 36 pages, harvmac, 2 eps figure
Two-dimensional superstrings and the supersymmetric matrix model
We present evidence that the supersymmetric matrix model of Marinari and
Parisi represents the world-line theory of N unstable D-particles in type II
superstring theory in two dimensions. This identification suggests that the
matrix model gives a holographic description of superstrings in a
two-dimensional black hole geometry.Comment: 22 pages, 2 figures; v2: corrected eqn 4.6; v3: corrected appendices
and discussion of vacua, added ref
Theory of Two-Dimensional Quantum Heisenberg Antiferromagnets with a Nearly Critical Ground State
We present the general theory of clean, two-dimensional, quantum Heisenberg
antiferromagnets which are close to the zero-temperature quantum transition
between ground states with and without long-range N\'{e}el order. For
N\'{e}el-ordered states, `nearly-critical' means that the ground state
spin-stiffness, , satisfies , where is the
nearest-neighbor exchange constant, while `nearly-critical' quantum-disordered
ground states have a energy-gap, , towards excitations with spin-1,
which satisfies . Under these circumstances, we show that the
wavevector/frequency-dependent uniform and staggered spin susceptibilities, and
the specific heat, are completely universal functions of just three
thermodynamic parameters. Explicit results for the universal scaling functions
are obtained by a expansion on the quantum non-linear sigma model,
and by Monte Carlo simulations. These calculations lead to a variety of
testable predictions for neutron scattering, NMR, and magnetization
measurements. Our results are in good agreement with a number of numerical
simulations and experiments on undoped and lightly-doped .Comment: 81 pages, REVTEX 3.0, smaller updated version, YCTP-xxx
Phase Transitions and Mass Generation in 2+1 Dimensions
The possibility that the epsilon expansion can predict the order of phase
transitions in three dimensional field theories is examined. For a Hermitean
matrix-valued order parameter, the epsilon expansion predicts fluctuation
induced first order phase transitions. We analyze two 2+1-dimensional quantum
field theories which exhibit spontaneous symmetry breaking and have martix
order parameters. Using the large expansion, we show that these models
exhibit second order transitions and discuss the implications for the chiral
symmetry breaking transition in 2+1-dimensional QCD for a critical number of
quark flavors.Comment: published in Phys. Rev. D50, 1060 (1994