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

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

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

Lie superalgebras and irreducibility of A_1^(1)-modules at the critical level

We introduce the infinite-dimensional Lie superalgebra ${\mathcal A}$ and construct a family of mappings from certain category of ${\mathcal A}$-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 $\nu=5/2$ are the permanent states if the $\nu=5/2$ plateau is the Haldane-Rezayi state. We point out that there is no such hierarchy on other candidate states for $\nu=5/2$. We propose experiments to test our prediction.Comment: RevTex,4 pages, v2:typo,one reference adde