67 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
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
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.
Integrable flows between exact CFTs
We explicitly construct families of integrable -model actions
smoothly interpolating between exact CFTs. In the ultraviolet the theory is the
direct product of two current algebras at levels and . In the
infrared and for the case of two deformation matrices the CFT involves a coset
CFT, whereas for a single matrix deformation it is given by the ultraviolet
direct product theories but at levels and . For isotropic
deformations we demonstrate integrability. In this case we also compute the
exact beta-function for the deformation parameters using gravitational methods.
This is shown to coincide with previous results obtained using perturbation
theory and non-perturbative symmetries.Comment: 1+27 pages, text improvements, version published in JHE
The most general -deformation of CFTs and integrability
We show that the CFT with symmetry group consisting of WZW models based on the same group , but at
arbitrary integer levels, admits an integrable deformation depending on
continuous parameters. We derive the all-loop effective action of the
deformed theory and prove integrability. We also calculate the exact in the
deformation parameters RG flow equations which can be put in a particularly
simple compact form. This allows a full determination and classification of the
fixed points of the RG flow, in particular those that are IR stable. The models
under consideration provide concrete realizations of integrable flows between
CFTs. We also consider non-Abelian T-duality type limits.Comment: 27 page
Novel all loop actions of interacting CFTs: Construction, integrability and RG flows
We construct the all loop effective action representing, for small couplings,
simultaneously self and mutually interacting current algebra CFTs realized by
WZW models. This non-trivially generalizes our previous works where such
interactions were, at the linear level, not simultaneously present. For the two
coupling case we prove integrability and calculate the coupled RG flow
equations. We also consider non-Abelian T-duality type limits. Our models
provide concrete realisations of integrable flows between exact CFTs and
exhibit several new features which we discuss in detail.Comment: 33 pages, 4 figures, typos corrected in version 2, version published
in Nucl. Phys.
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