27 research outputs found
Representations of affine Lie algebras, elliptic r-matrix systems, and special functions
There were some errors in paper hep-th/9303018 in formulas 6.1, 6.6, 6.8,
6.11. These errors have been corrected in the present version of this paper.
There are also some minor changes in the introduction.Comment: 33 pages, no figure
Character Expansion Methods for Matrix Models of Dually Weighted Graphs
We consider generalized one-matrix models in which external fields allow
control over the coordination numbers on both the original and dual lattices.
We rederive in a simple fashion a character expansion formula for these models
originally due to Itzykson and Di Francesco, and then demonstrate how to take
the large N limit of this expansion. The relationship to the usual matrix model
resolvent is elucidated. Our methods give as a by-product an extremely simple
derivation of the Migdal integral equation describing the large limit of
the Itzykson-Zuber formula. We illustrate and check our methods by analyzing a
number of models solvable by traditional means. We then proceed to solve a new
model: a sum over planar graphs possessing even coordination numbers on both
the original and the dual lattice. We conclude by formulating equations for the
case of arbitrary sets of even, self-dual coupling constants. This opens the
way for studying the deep problem of phase transitions from random to flat
lattices.Comment: 22 pages, harvmac.tex, pictex.tex. All diagrams written directly into
the text in Pictex commands. (Two minor math typos corrected.
Acknowledgements added.
Disorder Effects in Two-Dimensional d-wave Superconductors
Influence of weak nonmagnetic impurities on the single-particle density of
states of two-dimensional electron systems with a conical
spectrum is studied. We use a nonperturbative approach, based on replica trick
with subsequent mapping of the effective action onto a one-dimensional model of
interacting fermions, the latter being treated by Abelian and non-Abelian
bosonization methods. It is shown that, in a d-wave superconductor, the density
of states, averaged over randomness, follows a nontrivial power-law behavior
near the Fermi energy: . The exponent
is calculated for several types of disorder. We demonstrate that the
property is a direct consequence of a {\it continuous} symmetry
of the effective fermionic model, whose breakdown is forbidden in two
dimensions. As a counter example, we consider another model with a conical
spectrum - a two-dimensional orbital antiferromagnet, where static disorder
leads to a finite due to breakdown of a {\it discrete}
(particle-hole) symmetry.Comment: 24 pages, 3 figures upon request, RevTe
Effective action of gauged WZW model and exact string solutions
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 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 the gauge invariant non-local
effective action of the gauged WZW model. The two terms (corresponding to the
group and subgroup) which appear with the same coefficients in the classical
action get different -dependent coefficients in the effective one. The
procedure of integrating out the gauge field is considered in detail for the
model and the exact expressions for the metric and the
dilaton (originally found in the conformal field theory approach) are
reproduced.Comment: 26 pages, harvmac, Imperial/TP/92-93/10 (misprints corrected and some
explanations added
On gauge theories for non-semisimple groups
We consider analogs of Yang-Mills theories for non-semisimple real Lie
algebras which admit invariant non-degenerate metrics. These 4-dimensional
theories have many similarities with corresponding WZW models in 2 dimensions
and Chern-Simons theories in 3 dimensions. In particular, the quantum effective
action contains only 1-loop term with the divergent part that can be eliminated
by a field redefinition. The on-shell scattering amplitudes are thus finite
(scale invariant). This is a consequence of the presence of a null direction in
the field space metric: one of the field components is a Lagrange multiplier
which `freezes out' quantum fluctuations of the `conjugate' field. The
non-positivity of the metric implies that these theories are apparently
non-unitary. However, the special structure of interaction terms (degenerate
compared to non-compact YM theories) suggests that there may exist a unitary
`truncation'. We discuss in detail the simplest theory based on 4-dimensional
algebra E^c_2. The quantum part of its effective action is expressed in terms
of 1-loop effective action of SU(2) gauge theory. The E^c_2 model can be also
described as a special limit of SU(2) x U(1) YM theory with decoupled
ghost-like U(1) field.Comment: 22 pages, harvma
Modeling of graphene-based NEMS
The possibility of designing nanoelectromechanical systems (NEMS) based on
relative motion or vibrations of graphene layers is analyzed. Ab initio and
empirical calculations of the potential relief of interlayer interaction energy
in bilayer graphene are performed. A new potential based on the density
functional theory calculations with the dispersion correction is developed to
reliably reproduce the potential relief of interlayer interaction energy in
bilayer graphene. Telescopic oscillations and small relative vibrations of
graphene layers are investigated using molecular dynamics simulations. It is
shown that these vibrations are characterized with small Q-factor values. The
perspectives of nanoelectromechanical systems based on relative motion or
vibrations of graphene layers are discussed.Comment: 19 pages, 4 figure
Low-Lying States of the Six-Dimensional Fractional Superstring
The fractional superstring Fock space is constructed in terms of
\bZ_4 parafermions and free bosons. The bosonization of the \bZ_4
parafermion theory and the generalized commutation relations satisfied by the
modes of various parafermion fields are reviewed. In this preliminary analysis,
we describe a Fock space which is simply a tensor product of \bZ_4
parafermion and free boson Fock spaces. It is larger than the Lorentz-covariant
Fock space indicated by the fractional superstring partition function. We
derive the form of the fractional superconformal algebra that may be used as
the constraint algebra for the physical states of the FSS. Issues concerning
the associativity, modings and braiding properties of the fractional
superconformal algebra are also discussed. The use of the constraint algebra to
obtain physical state conditions on the spectrum is illustrated by an
application to the massless fermions and bosons of the fractional
superstring. However, we fail to generalize these considerations to the massive
states. This means that the appropriate constraint algebra on the fractional
superstring Fock space remains to be found. Some possible ways of doing this
are discussed.Comment: 69 pages, LaTeX, CLNS 91/112
Free Boson Realization of
We construct a realization of the quantum affine algebra
of an arbitrary level in terms of free boson fields.
In the limit this realization becomes the Wakimoto
realization of . The screening currents and the vertex
operators(primary fields) are also constructed; the former commutes with
modulo total difference, and the latter creates the
highest weight state from the vacuum state of the boson
Fock space.Comment: 24 pages, LaTeX, RIMS-924, YITP/K-101
Chiral gauged WZNW models and heterotic string backgrounds
We construct new heterotic string backgrounds which are analogous to
superstring solutions corresponding to coset models but are not simply the
`embeddings'of the latter. They are described by the (1,0) supersymmetric
extension of the chiral gauged WZNW models. The `chiral gauged' WZNW
action differs from the standard gauged WZNW action by the absence of the
-term (and thus is not gauge invariant in the usual sense) but can
still be expressed as a combination of WZNW actions and is conformal invariant.
We explain a close relation between gauged and chiral gauged WZNW models and
prove that in the case of the abelian the chiral gauged theory is
equivalent to a particular gauged WZNW theory. In contrast to
the gauged WZNW model, the chiral gauged one admits a (1,0) supersymmetric
extension which is consistent at the quantum level. Integrating out the
gauge field we determine the exact (in ) form of the couplings of the
corresponding heterotic sigma model. While in the bosonic (superstring) cases
all the fields depend (do not depend) non-trivially on here the
metric receives only one correction while the antisymmetric tensor
and the dilaton remain semiclassical. As a simplest example, we discuss the
basic solution which is the heterotic string counterpart of the `black
string' background.Comment: 41 pages, harvmac, CERN-TH.6962, USC-93/HEP-S
On string cosmology and the RG flow in 2d field theory
Time-dependent solutions of bosonic string theory resemble renormalisation
group trajectories in the space of 2d field theories: they often interpolate
between repulsive and attractive static solutions. It is shown that the
attractive static solutions are those whose spatial sections are minima of
|\bar c-25|, where \bar c is the `c-function'. The size of the domain of
attraction of such a solution may be a measure of the probability of the
corresponding string vacuum. Our discussion has also an implication for the RG
flow in theories coupled to dynamical 2d gravity: the flow from models with
c>25 to models with c<25 is forbidden.Comment: 16 pages, Latex, BUTP-94/7, Imperial/TP/93-94/29 (some footnotes and
references added.