Vacuum Instability in Chern-Simons Theory, Null Vectors and Two-Dimensional Logarithmic Operators

A new relation between two-dimensional conformal field theories and three-dimensional topologically massive gauge theories is found, where the dynamical nature of the 3d theory is ultimately important. It is shown that the those primary states in CFT which have non-unitary descendants correspond in the 3d theory to supercritical charges and cause vacuum instability. It is also shown that logarithmic operators separating the unitary sector from a non-unitary one correspond to an exact zero energy ground state in which case the 3d Hamiltonian naturally has a Jordan structure.Comment: 12 pages, Latex. 1 figur

Hagedorn transition, vortices and D0 branes: Lessons from 2+1 confining strings

We study the behaviour of Polyakov confining string in the Georgi-Glashow model in three dimensions near confining-deconfining phase transition described in hep-th/0010201. In the string language, the transition mechanism is the decay of the confining string into D0 branes (charged W bosons of the Georgi-Glashow model). In the world-sheet picture the world-lines of heavy D0 branes at finite temperature are represented as world-sheet vortices of a certain type, and the transition corresponds to the condensation of these vortices. We also show that the ``would be'' Hagedorn transition in the confining string (which is not realized in our model) corresponds to the monopole binding transition in the field theoretical language. The fact that the decay into D0 branes occurs at lower than the Hagedorn temperature is understood as the consequence of the large thickness of the confining string and finite mass of the $D0$ branes.Comment: 31 pages, Late

Gauge Dressing of 2D Field Theories

By using the gauge Ward identities, we study correlation functions of gauged WZNW models. We show that the gauge dressing of the correlation functions can be taken into account as a solution of the Knizhnik-Zamolodchikov equation. Our method is analogous to the analysis of the gravitational dressing of 2D field theories.Comment: 13 pages, Late

Vacuum Instability in Topologically Massive Gauge Theory

We find the critical charge for a topologically massive gauge theory for any gauge group, generalising our earlier result for SU(2). The relation between critical charges in TMGT, singular vectors in the WZNW model and logarithmic CFT is investigated.Comment: 14 pages, Late

Deconfining Phase Transition in 2+1 D: the Georgi-Glashow Model

We analyze the finite temperature deconfining phase transition in 2+1 dimensional Georgi-Glashow model. We show explicitly that the transition is due to the restoration of the magnetic $Z_2$ symmetry and that it is in the Ising universality class. We find that neglecting effects of the charged $W$ bosons leads to incorrect predictions for the value of the critical temperature and the universality class of the transition, as well as for various correlation functions in the high temperature phase. We derive the effective action for the Polyakov loop in the high temperature phase and calculate the correlation functions of magnetic vortex operators.Comment: 26 pages, 1 figure, discussion about spatial Wilson loops added, to appear in JHE