A Unified Conformal Field Theory Description of Paired Quantum Hall States

The wave functions of the Haldane-Rezayi paired Hall state have been previously described by a non-unitary conformal field theory with central charge c=-2. Moreover, a relation with the c=1 unitary Weyl fermion has been suggested. We construct the complete unitary theory and show that it consistently describes the edge excitations of the Haldane-Rezayi state. Actually, we show that the unitary (c=1) and non-unitary (c=-2) theories are related by a local map between the two sets of fields and by a suitable change of conjugation. The unitary theory of the Haldane-Rezayi state is found to be the same as that of the 331 paired Hall state. Furthermore, the analysis of modular invariant partition functions shows that no alternative unitary descriptions are possible for the Haldane-Rezayi state within the class of rational conformal field theories with abelian current algebra. Finally, the known c=3/2 conformal theory of the Pfaffian state is also obtained from the 331 theory by a reduction of degrees of freedom which can be physically realized in the double-layer Hall systems.Comment: Latex, 42 pages, 2 figures, 3 tables; minor corrections to text and reference

Study of Apollo water impact. Volume 8 - Unsymmetric shells of revolution analysis Final report

Numerical analysis of static, and dynamic shell response to water impact load

(2+1)-Gravity with Moving Particles in an Instantaneous Gauge

By defining a regular gauge which is conformal-like and provides instantaneous field propagation, we investigate classical solutions of (2+1)-Gravity coupled to arbitrarily moving point-like particles. We show how to separate field equations from self-consistent motion and we provide a solution for the metric and the motion in the two-body case with arbitrary speed, up to second order in the mass parameters.Comment: 16 pages, LaTeX, no figure

Non-Perturbative Particle Dynamics

We construct a non-perturbative, single-valued solution for the metric and the motion of two interacting particles in ($2+1$)-Gravity, by using a Coulomb gauge of conformal type. The method provides the mapping from multivalued ( minkowskian ) coordinates to single-valued ones, which solves the non-abelian monodromies due to particles's momenta and can be applied also to the general N-body case.Comment: 11 pages, LaTeX, no figure

The W_N minimal model classification

We first rigourously establish, for any N, that the toroidal modular invariant partition functions for the (not necessarily unitary) W_N(p,q) minimal models biject onto a well-defined subset of those of the SU(N)xSU(N) Wess-Zumino-Witten theories at level (p-N,q-N). This permits considerable simplifications to the proof of the Cappelli-Itzykson-Zuber classification of Virasoro minimal models. More important, we obtain from this the complete classification of all modular invariants for the W_3(p,q) minimal models. All should be realised by rational conformal field theories. Previously, only those for the unitary models, i.e. W_3(p,p+1), were classified. For all N our correspondence yields for free an extensive list of W_N(p,q) modular invariants. The W_3 modular invariants, like the Virasoro minimal models, all factorise into SU(3) modular invariants, but this fails in general for larger N. We also classify the SU(3)xSU(3) modular invariants, and find there a new infinite series of exceptionals.Comment: 25 page

't Hooft Anomaly Matching Conditions for Generalized Symmetries in 2D

The 't Hooft anomaly matching conditions are a standard tool to study and test non-perturbative issues in quantum field theory. We give a new, simple proof of the anomaly matching conditions in 2D Poincare` invariant theories. We consider the case of invariance under a large class of generalized symmetries, which include abelian and non-abelian internal symmetries, space-time symmetries generated by the stress tensor, and W-type of symmetries generated by higher spin currents.Comment: 10 pages, TeX, corrected minor misprints in text and reference

A new class of Matrix Models arising from the W-infinity Algebra

We present a new class of hermitian one-matrix models originated in the W-infinity algebra: more precisely, the polynomials defining the W-infinity generators in their fermionic bilinear form are shown to expand the orthogonal basis of a class of random hermitian matrix models. The corresponding potentials are given, and the thermodynamic limit interpreted in terms of a simple plasma picture. The new matrix models can be successfully applied to the full bosonization of interesting one-dimensional systems, including all the perturbative orders in the inverse size of the system. As a simple application, we present the all-order bosonization of the free fermionic field on the one-dimensional lattice.Comment: 8 pages, 1 figur

Quantum Field Theory Anomalies in Condensed Matter Physics

We give a pedagogical introduction to quantum anomalies, how they are calculated using various methods, and why they are important in condensed matter theory. We discuss axial, chiral, and gravitational anomalies as well as global anomalies. We illustrate the theory with examples such as quantum Hall liquids, Fermi liquids, Weyl semi-metals, topological insulators and topological superconductors. The required background is basic knowledge of quantum field theory, including fermions and gauge fields, and some familiarity with path integral and functional methods. Some knowledge of topological phases of matter is helpful, but not necessary.Comment: Lecture notes. 142 pages, 24 figures. Please send comment

Thermal broadening of the Coulomb blockade peaks in quantum Hall interferometers

We demonstrate that the differential magnetic susceptibility of a fractional quantum Hall disk, representing a Coulomb island in a Fabry--Perot interferometer, is exactly proportional to the island's conductance and its paramagnetic peaks are the equilibrium counterparts of the Coulomb blockade conductance peaks. Using as a thermodynamic potential the partition functions of the edge states' effective conformal field theory we find the positions of the Coulomb blockade peaks, when the area of the island is varied, the modulations of the distance between them as well as the thermal decay and broadening of the peaks when temperature is increased. The finite-temperature estimates of the peak's heights and widths could give important information about the experimental observability of the Coulomb blockade. In addition, the predicted peak asymmetry and displacement at finite temperature due to neutral multiplicities could serve to distinguish different fractional quantum Hall states with similar zero-temperature Coulomb blockade patterns.Comment: 6 pages, 6 figures; published versio

Chiral persistent currents and magnetic susceptibilities in the parafermion quantum Hall states in the second Landau level with Aharonov-Bohm flux

Using the effective conformal field theory for the quantum Hall edge states we propose a compact and convenient scheme for the computation of the periods, amplitudes and temperature behavior of the chiral persistent currents and the magnetic susceptibilities in the mesoscopic disk version of the Z_k parafermion quantum Hall states in the second Landau level. Our numerical calculations show that the persistent currents are periodic in the Aharonov-Bohm flux with period exactly one flux quantum and have a diamagnetic nature. In the high-temperature regime their amplitudes decay exponentially with increasing the temperature and the corresponding exponents are universal characteristics of non-Fermi liquids. Our theoretical results for these exponents are in perfect agreement with those extracted from the numerical data and demonstrate that there is in general a non-trivial contribution coming from the neutral sector. We emphasize the crucial role of the non-holomorphic factors, first proposed by Cappelli and Zemba in the context of the conformal field theory partition functions for the quantum Hall states, which ensure the invariance of the annulus partition function under the Laughlin spectral flow.Comment: 14 pages, RevTeX4, 7 figures (eps