27 research outputs found
On the Integrability of the Bukhvostov-Lipatov Model
The integrability of the Bukhvostov-Lipatov four-fermion model is
investigated. It is shown that the classical model possesses a current of
Lorentz spin 3, conserved both in the bulk and on the half-line for specific
types of boundary actions. It is then established that the conservation law is
spoiled at the quantum level -- a fact that might indicate that the quantum
Bukhvostov-Lipatov model is not integrable, contrary to what was previously
believed.Comment: 11 pages, 1 figure, LaTeX2e, AMS; new references adde
On the Beta Function for Anisotropic Current Interactions in 2D
By making use of current-algebra Ward identities we study renormalization of
general anisotropic current-current interactions in 2D. We obtain a set of
algebraic conditions that ensure the renormalizability of the theory to all
orders. In a certain minimal prescription we compute the beta function to all
orders.Comment: 7 pages, 6 figures. v2: References added and typos corrected; v3:
cancellation of finite parts more accurately state
Freezing transitions and the density of states of 2D random Dirac Hamiltonians
Using an exact mapping to disordered Coulomb gases, we introduce a novel
method to study two dimensional Dirac fermions with quenched disorder in two
dimensions which allows to treat non perturbative freezing phenomena. For
purely random gauge disorder it is known that the exact zero energy eigenstate
exhibits a freezing-like transition at a threshold value of disorder
. Here we compute the dynamical exponent which
characterizes the critical behaviour of the density of states around zero
energy, and find that it also exhibits a phase transition. Specifically, we
find that (and ) with for and
for . For a finite system size we find large
sample to sample fluctuations with a typical .
Adding a scalar random potential of small variance , as in the
corresponding quantum Hall system, yields a finite noncritical whose scaling exponent exhibits two transitions, one
at and the other at . These transitions are shown
to be related to the one of a directed polymer on a Cayley tree with random
signs (or complex) Boltzmann weights. Some observations are made for the strong
disorder regime relevant to describe transport in the quantum Hall system
Generalized sine-Gordon/massive Thirring models and soliton/particle correspondences
We consider a real Lagrangian off-critical submodel describing the soliton
sector of the so-called conformal affine Toda model coupled to
matter fields (CATM). The theory is treated as a constrained system in the
context of Faddeev-Jackiw and the symplectic schemes. We exhibit the parent
Lagrangian nature of the model from which generalizations of the sine-Gordon
(GSG) or the massive Thirring (GMT) models are derivable. The dual description
of the model is further emphasized by providing the relationships between
bilinears of GMT spinors and relevant expressions of the GSG fields. In this
way we exhibit the strong/weak coupling phases and the (generalized)
soliton/particle correspondences of the model. The case is also
outlined.Comment: 22 pages, LaTex, some comments and references added, conclusions
unchanged, to appear in J. Math. Phy
Spacetimes for λ-deformations
We examine a recently proposed class of integrable deformations to two-dimensional conformal field theories. These {\lambda}-deformations interpolate between a WZW model and the non-Abelian T-dual of a Principal Chiral Model on a group G or, between a G/H gauged WZW model and the non-Abelian T-dual of the geometric coset G/H. {\lambda}-deformations have been conjectured to represent quantum group q-deformations for the case where the deformation parameter is a root of unity. In this work we show how such deformations can be given an embedding as full string backgrounds whose target spaces satisfy the equations of type-II supergravity. One illustrative example is a deformation of the Sl(2,R)/U(1) black-hole CFT. A further example interpolates between the SU(2)ĂSU(2)SU(2)ĂSL(2,R)ĂSL(2,R)SL(2,R)ĂU(1)4 gauged WZW model and the non-Abelian T-dual of AdS3ĂS3ĂT4 supported with Ramond flux
Renormalization and redundancy in 2d quantum field theories
We analyze renormalization group (RG) flows in two-dimensional quantum field
theories in the presence of redundant directions. We use the operator picture
in which redundant operators are total derivatives. Our analysis has three
levels of generality. We introduce a redundancy anomaly equation which is
analyzed together with the RG anomaly equation previously considered by
H.Osborn [8] and D.Friedan and A.Konechny [7]. The Wess-Zumino consistency
conditions between these anomalies yield a number of general relations which
should hold to all orders in perturbation theory. We further use conformal
perturbation theory to study field theories in the vicinity of a fixed point
when some of the symmetries of the fixed point are broken by the perturbation.
We relate various anomaly coefficients to OPE coefficients at the fixed point
and analyze which operators become redundant and how they participate in the RG
flow. Finally, we illustrate our findings by three explicit models constructed
as current-current perturbations of SU(2)_k WZW model. At each generality level
we discuss the geometric picture behind redundancy and how one can reduce the
number of couplings by taking a quotient with respect to the redundant
directions. We point to the special role of polar representations for the
redundancy groups.Comment: 59 pages, 5 pdf figures; V3: version equivalent to the version
published in JHEP (up to an additional footnote
Yang Baxter and anisotropic sigma and lambda models, cyclic RG and exact S-matrices
Integrable deformation of SU(2) sigma and lambda models are considered at the classical and quantum levels. These are the Yang-Baxter and XXZ-type anisotropic deformations. The XXZ type deformations are UV safe in one regime, while in another regime, like the Yang-Baxter deformations, they exhibit cyclic RG behaviour. The associated affine quantum group symmetry, realised classically at the Poisson bracket level, has q a complex phase in the UV safe regime and q real in the cyclic RG regime, where q is an RG invariant. Based on the symmetries and RG flow we propose exact factorisable S-matrices to describe the scattering of states in the lambda models, from which the sigma models follow by taking a limit and non-abelian T-duality. In the cyclic RG regimes, the S-matrices are periodic functions of rapidity, at large rapidity, and in the Yang-Baxter case violate parity