54 research outputs found
Integrable deformations of the coset CFTs
We study the effective action for the integrable -deformation of the
coset CFTs. For unequal levels theses
models do not fall into the general discussion of -deformations of
CFTs corresponding to symmetric spaces and have many attractive features. We
show that the perturbation is driven by parafermion bilinears and we revisit
the derivation of their algebra. We uncover a non-trivial symmetry of these
models parametric space, which has not encountered before in the literature.
Using field theoretical methods and the effective action we compute the exact
in the deformation parameter -function and explicitly demonstrate the
existence of a fixed point in the IR corresponding to the
coset CFTs. The same result is verified
using gravitational methods for . We examine various limiting cases
previously considered in the literature and found agreement.Comment: 1+23 pages, Latex; v2: NPB version; v3: Correcting a typo in Eqs.
(2.21), (2.22
Weyl anomaly and the -function in -deformed CFTs
For a general -deformation of current algebra CFTs we compute the
exact Weyl anomaly coefficient and the corresponding metric in the couplings
space geometry. By incorporating the exact -function found in previous
works we show that the Weyl anomaly is in fact the exact Zamolodchikov's
-function interpolating between exact CFTs occurring in the UV and in the
IR. We provide explicit examples with the anisotropic case presented in
detail. The anomalous dimension of the operator driving the deformation is also
computed in general. Agreement is found with special cases existing already in
the literature.Comment: 1+19 pages, Latex, v2: NPB versio
All-loop anomalous dimensions in integrable -deformed -models
We calculate the all-loop anomalous dimensions of current operators in
-deformed -models. For the isotropic integrable deformation
and for a semi-simple group we compute the anomalous dimensions using two
different methods. In the first we use the all-loop effective action and in the
second we employ perturbation theory along with the Callan-Symanzik equation
and in conjunction with a duality-type symmetry shared by these models.
Furthermore, using CFT techniques we compute the all-loop anomalous dimensions
of bilinear currents for the isotropic deformation case and a general .
Finally we work out the cases of anisotropic and the two coupling,
corresponding to the symmetric coset and a subgroup , splitting of a
group .Comment: 1+26 pages, Latex; v2: minor corrections; v3: few minor changes, NPB
version; v4: clarifications in section 2.
All-loop correlators of integrable -deformed -models
We compute the 2- and 3-point functions of currents and primary fields of
-deformed integrable -models characterized also by an integer
. Our results apply for any semisimple group , for all values of the
deformation parameter and up to order . We deduce the OPEs and
equal-time commutators of all currents and primaries. We derive the currents'
Poisson brackets which assume Rajeev's deformation of the canonical structure
of the isotropic PCM, the underlying structure of the integrable
-deformed -models. We also present analogous results in two
limiting cases of special interest, namely for the non-Abelian T-dual of the
PCM and for the pseudodual model.Comment: 30 pages plus appendices; v2: few minor changes, NPB versio
The classical Yang-Baxter equation and the associated Yangian symmetry of gauged WZW-type theories
We construct the Lax-pair, the classical monodromy matrix and the
corresponding solution of the Yang--Baxter equation, for a two-parameter
deformation of the Principal chiral model for a simple group. This deformation
includes as a one-parameter subset, a class of integrable gauged WZW-type
theories interpolating between the WZW model and the non-Abelian T-dual of the
principal chiral model. We derive in full detail the Yangian algebra using two
independent methods: by computing the algebra of the non-local charges and
alternatively through an expansion of the Maillet brackets for the monodromy
matrix. As a byproduct, we also provide a detailed general proof of the Serre
relations for the Yangian symmetry.Comment: 1+32 pages, Latex, v2: few minor changes, NPB version, v3: A factor
of two corrected in (A.22
Integrable models based on non-semi-simple groups and plane wave target spacetimes
We initiate the construction of integrable -deformed WZW models
based on non-semisimple groups. We focus on the four-dimensional case whose
underlying symmetries are based on the non-semisimple group . The
corresponding gravitational backgrounds of Lorentzian signature are plane waves
which can be obtained as Penrose limits of the -deformed
background times a timelike coordinate for appropriate choices of the
-matrix. We construct two such deformations which we demonstrate to be
integrable. They both deform the Nappi-Witten plane wave and are inequivalent.
Nevertheless, they have the same underlying symmetry algebra which is a
Saletan-type contraction of that for the -deformed background
with a timelike direction. We also construct a plane wave from the Penrose
limit of the -deformation of the \nicefrac{SU(2)}{U(1)} coset CFT
times a timelike coordinate which represents the deformation of a logarithmic
CFT constructed in the past. Finally, we briefly consider contractions based on
the simplest Yang-baxter -models.Comment: v1:1+33 pages, Latex, v2:JHEP versio
Quantum aspects of doubly deformed CFTs
We study quantum aspects of the recently constructed doubly lambda-deformed
sigma-models representing the effective action of two WZW models interacting
via current bilinears. We show that although the exact beta-functions and
current anomalous dimensions are identical to those of the lambda-deformed
models, this is not true for the anomalous dimensions of generic primary field
operators in accordance with the fact that the two models differ drastically.
Our proofs involve CFT arguments, as well as effective sigma-model action and
gravity calculations.Comment: 1+26 pages, Late
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