502 research outputs found
Curvature formula for the space of 2-d conformal field theories
We derive a formula for the curvature tensor of the natural Riemannian metric
on the space of two-dimensional conformal field theories and also a formula for
the curvature tensor of the space of boundary conformal field theories.Comment: 36 pages, 1 figure; v2 references adde
Conformal Moduli and b-c Pictures for NSR Strings
We explore the geometry of the superconformal moduli of the NSR superstring
theory in order to construct the consistent sigma-model for the NSR strings,
free of picture-changing ambiguities. The sigma-model generating functional is
constructed by the integration over the bosonic and anticommuting moduli,
corresponding to insertions of the vertex operators in scattering amplitudes.
In particular, the integration over the bosonic moduli results in the
appearance of picture-changing operators for the b-c system. Important example
of the b-c pictures involves the unintegrated and integrated forms of the
vertex operators. We derive the BRST-invariant expressions for the b-c
picture-changing operators for open and closed strings and study some of their
properties. We also show that the superconformal moduli spaces of the NSR
superstring theory contain the global singularities, leading to the appearance
of non-perturbative solitonic D-brane creation operators.Comment: 22 pages, references adde
Entropy flow in near-critical quantum circuits
Near-critical quantum circuits are ideal physical systems for asymptotically
large-scale quantum computers, because their low energy collective excitations
evolve reversibly, effectively isolated from the environment. The design of
reversible computers is constrained by the laws governing entropy flow within
the computer. In near-critical quantum circuits, entropy flows as a locally
conserved quantum current, obeying circuit laws analogous to the electric
circuit laws. The quantum entropy current is just the energy current divided by
the temperature. A quantum circuit made from a near-critical system (of
conventional type) is described by a relativistic 1+1 dimensional relativistic
quantum field theory on the circuit. The universal properties of the
energy-momentum tensor constrain the entropy flow characteristics of the
circuit components: the entropic conductivity of the quantum wires and the
entropic admittance of the quantum circuit junctions. For example,
near-critical quantum wires are always resistanceless inductors for entropy. A
universal formula is derived for the entropic conductivity:
\sigma_S(\omega)=iv^{2}S/\omega T, where \omega is the frequency, T the
temperature, S the equilibrium entropy density and v the velocity of `light'.
The thermal conductivity is Real(T\sigma_S(\omega))=\pi v^{2}S\delta(\omega).
The thermal Drude weight is, universally, v^{2}S. This gives a way to measure
the entropy density directly.Comment: 2005 paper published 2017 in Kadanoff memorial issue of J Stat Phys
with revisions for clarity following referee's suggestions, arguments and
results unchanged, cross-posting now to quant-ph, 27 page
Fluid Dynamics of NSR Strings
We show that the renormalization group flows of the massless superstring
modes in the presence of fluctuating D-branes satisfy the equations of fluid
dynamics.In particular, we show that the D-brane's U(1) field is related to the
velocity function in the Navier-Stokes equation while the dilaton plays the
role of the passive scalar advected by the turbulent flow. This leads us to
suggest a possible isomorphism between the off-shell superstring theory in the
presence of fluctuating branes and the fluid mechanical degrees of freedom.Comment: 24 pages Dedicated to the memory of Ian Koga
Interplay of the Scaling Limit and the Renormalization Group: Implications for Symmetry Restoration
Symmetry restoration is usually understood as a renormalization group induced
phenomenon. In this context, the issue of whether one-loop RG equations can be
trusted in predicting symmetry restoration has recently been the subject of
much debate. Here we advocate a more pragmatic point of view and expand the
definition of symmetry restoration to encompass all situations where the
physical properties have only a weak dependence upon an anisotropy in the bare
couplings. Moreover we concentrate on universal properties, and so take a
scaling limit where the physics is well described by a field theory. In this
context, we find a large variety of models that exhibit, for all practical
purposes, symmetry restoration: even if symmetry is not restored in a strict
sense, physical properties are surprisingly insensitive to the remaining
anisotropy.
Although we have adopted an expanded notion of symmetry restoration, we
nonetheless emphasize that the scaling limit also has implications for symmetry
restoration as a renormalization group induced phenomenon. In all the models we
considered, the scaling limit turns out to only permit bare couplings which are
nearly isotropic and small. Then the one-loop beta-function should contain all
the physics and higher loop orders can be neglected. We suggest that this
feature generalizes to more complex models. We exhibit a large class of
theories with current-current perturbations (of which the SO(8) model of
interest in two-leg Hubbard ladders/armchair carbon nanotubes is one) where the
one-loop beta-functions indicates symmetry restoration and so argue that these
results can be trusted within the scaling limit.Comment: 20 pages, 11 figures, RevTe
Lattice Models with N=2 Supersymmetry
We introduce lattice models with explicit N=2 supersymmetry. In these
interacting models, the supersymmetry generators Q^+ and Q^- yield the
Hamiltonian H={Q^+,Q^-} on any graph. The degrees of freedom can be described
as either fermions with hard cores, or as quantum dimers. The Hamiltonian of
our simplest model contains a hopping term and a repulsive potential, as well
as the hard-core repulsion. We discuss these models from a variety of
perspectives: using a fundamental relation with conformal field theory, via the
Bethe ansatz, and using cohomology methods. The simplest model provides a
manifestly-supersymmetric lattice regulator for the supersymmetric point of the
massless 1+1-dimensional Thirring (Luttinger) model. We discuss the
ground-state structure of this same model on more complicated graphs, including
a 2-leg ladder, and discuss some generalizations.Comment: 4 page
Semi-Lorentz invariance, unitarity, and critical exponents of symplectic fermion models
We study a model of N-component complex fermions with a kinetic term that is
second order in derivatives. This symplectic fermion model has an Sp(2N)
symmetry, which for any N contains an SO(3) subgroup that can be identified
with rotational spin of spin-1/2 particles. Since the spin-1/2 representation
is not promoted to a representation of the Lorentz group, the model is not
fully Lorentz invariant, although it has a relativistic dispersion relation.
The hamiltonian is pseudo-hermitian, H^\dagger = C H C, which implies it has a
unitary time evolution. Renormalization-group analysis shows the model has a
low-energy fixed point that is a fermionic version of the Wilson-Fisher fixed
points. The critical exponents are computed to two-loop order. Possible
applications to condensed matter physics in 3 space-time dimensions are
discussed.Comment: v2: Published version, minor typose correcte
Conformal Invariance in Percolation, Self-Avoiding Walks and Related Problems
Over the years, problems like percolation and self-avoiding walks have
provided important testing grounds for our understanding of the nature of the
critical state. I describe some very recent ideas, as well as some older ones,
which cast light both on these problems themselves and on the quantum field
theories to which they correspond. These ideas come from conformal field
theory, Coulomb gas mappings, and stochastic Loewner evolution.Comment: Plenary talk given at TH-2002, Paris. 21 pages, 9 figure
Lie superalgebras and irreducibility of A_1^(1)-modules at the critical level
We introduce the infinite-dimensional Lie superalgebra and
construct a family of mappings from certain category of -modules
to the category of A_1^(1)-modules of critical level. Using this approach, we
prove the irreducibility of a family of A_1^(1)-modules at the critical level.
As a consequence, we present a new proof of irreducibility of certain
Wakimoto modules. We also give a natural realizations of irreducible quotients
of relaxed Verma modules and calculate characters of these representations.Comment: 21 pages, Late
Spin-singlet hierarchy in the fractional quantum Hall effect
We show that the so-called permanent quantum Hall states are formed by the
integer quantum Hall effects on the Haldane-Rezayi quantum Hall state. Novel
conformal field theory description along with this picture is deduced. The odd
denominator plateaux observed around are the permanent states if the
plateau is the Haldane-Rezayi state. We point out that there is no
such hierarchy on other candidate states for . We propose experiments
to test our prediction.Comment: RevTex,4 pages, v2:typo,one reference adde
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