105 research outputs found
A new tool in the classification of rational conformal field theories
No full textThe fact that in any rational conformal field theory (RCFT) four-point function on the sphere must satisfy an ordinary differential equation gives a simple condition on the conformal dimensions of primary fields. We discuss how this can help in the classification program of RCFT. As an example all associative fusion rules with less than four non-trivial primary fields and Nijk ≤ 1 are discussed. Another application to the classification of chiral algebras is briefly mentioned. © 1989
GNXGL/GN+L CONFORMAL FIELD-THEORIES AND THEIR MODULAR INVARIANT PARTITION-FUNCTIONS
No full textWe study a Feigin-Fuchs construction of conformal field theories based on a coset space, in terms of screened bosons and parafermions. This allows to get the formula for the conformal dimensions of primary operators. Lists of modular invariant partition functions for the , and Wess-Zumino-Witten models are given.
Besides the principal series of diagonal invariants, a complementary series exists for and , which is due to the outer
automorphism of the Kac-Moody algebra. Moreover, exceptional solutions appear at level 5, 9, 21 for , at level 3, 7, 12 for and at level 3, 4 for . From these modular invariants, those for the corresponding models are constructed
Generalising the staircase models
No full textSystems of integral equations are proposed which generalise those previously encountered in connection with the so-called staircase models. Under the assumption that these equations describe the finite-size effects of relatistic field theories via the thermodynamic Bethe ansatz, analytical and numerical evidence is given for the existence of a variety of new roaming renormalisation group trajectories. For each positive integer k and s = 0,...,k - 1, there is a one-parameter family of trajectories, passing close by the coset conformal field theories G(k) × G(nk+s)/G((n+1)(k+s) before finally flowing to a massive theory for s = 0, or to another coset model for s ≠ 0. © 1993
Staircase Models from Affine Toda Field Theory
No full textWe propose a class of purely elastic scattering theories generalising the staircase model of Al. B. Zamolodchikov, based on the affine Toda field theories for simply-laced Lie algebras g=A,D,E at suitable complex values of their coupling constants. Considering their Thermodynamic Bethe Ansatz equations, we give analytic arguments in support of a conjectured renormalisation group flow visiting the neighbourhood of each W_g minimal model in turn
Excited Boundary TBA in the Tricritical Ising Model
No full textBy considering the continuum scaling limit of the RSOS lattice model of Andrews-Baxter-Forrester with integrable boundaries, we derive excited state TBA equations describing the boundary flows of the tricritical Ising model. Fixing the bulk weights to their critical values, the integrable boundary weights admit a parameter which plays the role of the perturbing boundary field and induces the renormalization group flow between boundary fixed points. The boundary TBA equations determining the RG flows are derived in the example. The induced map between distinct Virasoro characters of the theory are specified in terms of distribution of zeros of the double row transfer matrix
EUCLID - Integrable models and applications: from strings to condensed matter - Activity Year 2
No full textEUCLID is a Research Training Network funded by the European Commission's 5th Framework Improving Human Potential programme.
The central research objective is to deepen the understanding of the physics of integrability, identifying the fundamental mechanisms and developing applications in a variety of contexts, from string theory to condensed matter physics.
A copy of the network proposal is available as attachment. This provides details concerning the members of the collaboration together with a description of the proposed research and the training of young researchers.
The network contract (HPRN-CT-2002-00325) between the European Commission and network participants started on 1st October 2002 with a duration of 48 months.
The detailed work plan is also available as attachment.
2004 has been the second year of participation to this EU network.
A number of postdoctoral positions are appointed. In particular a two year position is appointed to Dr. Arpad Hegedus (hungarian) in Bologna beginning Oct 1, 2004.
Many conferences and schools have been organized, with partial support from the network. Up to Dec 2004, 1 workshop (6th Bologna workshop on CFT and Integrable Models) has been organized in Bologna and 1 official network meeting in Florence (2003) with participation of the Bologna group as organizer.
The coordinator is Prof. Ed Corrigan, of the Department of Mathematics of University of York, UK
Bologna participates as the coordinating site of a national node under the auspices of INFN, including also people in Firenze and Torino. This italian node has been coordinated by F. Ravanini.
The list of coordinators of the nodes of the network is:
* Ivan Todorov, INRNE-Sofia, Bulgaria
* Paul Sorba, CNRS-Annecy, France
* Jean-Michel Maillet, ENS-Lyon, France
* Vladimir Fateev, CNRS-Montpellier, France
* Michael Karowski, FU-Berlin, Germany
* Vladimir Rittenberg, University of Bonn, Germany
* László Palla, Eötvös Loránd University, Budapest, Hungary
* Francesco Ravanini, INFN-Bologna , Italy
* Giuseppe Mussardo, SISSA-Trieste, Italy
* J Luis Miramontes, University of Santiago de Compostela, Spain
* Patrick Dorey, Mathematical Sciences, University of Durham, UK
* Gérard Watts, Mathematics, King's College London, UK
In addition to these, some members of the following universities (contact names in brackets) are collaborating with the principal partners and are considered part of the above nodes:
* University of Mons-Hainaut (Jean Nuyts) with York
* CEN-Saclay (Denis Bernard) with CNRS-Annecy
* LPThE Paris VI University (Olivier Babelon) with ENS-Lyon
* University of Tours (Peter Forgacs) with CNRS-Montpellier
* University of Hannover (Michael Flohr) with Bonn
* University of Szeged (Laszlo Feher) and Nuclear and Particle Physics Research Laboratory of the Hungarian Academy of Sciences (Janos Balog) with Budapest
* University of Florence (Andrea Cappelli) and University of Torino (Michele Caselle), with Bologna
* University of Bilbao and IFT-Madrid (German Sierra) with Santiago
* Heriot-Watt University (Robert Weston) with Durham
* Universities of Cambridge (Jonathan Evans) and Swansea (Tim Hollowood) with KCL
* London - City University (Andreas Fring) with FU-Berlin
Further information about this activity can be found at the web site of the EUCLID network:
http://www-users.york.ac.uk/~ec9/fp5data.htm
Lattice approach to excited TBA boundary flows: Tricritical Ising model
No full textWe show how a lattice approach can be used to derive Thermodynamic Bethe Ansatz (TBA) equations describing all excitations for boundary flows. The method is illustrated for a prototypical flow of the tricritical Ising model by considering the continuum scaling limit of the A4 lattice model with integrable boundaries. Fixing the bulk weights to their critical values, the integrable boundary weights admit two boundary fields ξ and η which play the role of the perturbing boundary fields φ1,3 and φ1,2 inducing the renormalization group flow between boundary fixed points. The excitations are completely classified in terms of (m,n) systems and quantum numbers but the string content changes by certain mechanisms along the flow. For our prototypical example, we identify these mechanisms and the induced map between the relevant finitized Virasoro characters. We also solve the boundary TBA equations numerically to determine the flows for the leading excitations. © 2002 Elsevier Science B.V. All rights reserved
Exact phi_1,3 boundary flows in the tricritical Ising model
No full textWe consider the tricritical Ising model on a strip or cylinder under the integrable perturbation by the thermal 1,3 boundary field. This perturbation induces five distinct renormalization group (RG) flows between Cardy type boundary conditions labelled by the Kac labels (r,s). We study these boundary RG flows in detail for all excitations. Exact thermodynamic Bethe ansatz (TBA) equations are derived using the lattice approach by considering the continuum scaling limit of the A4 lattice model with integrable boundary conditions. Fixing the bulk weights to their critical values, the integrable boundary weights admit a thermodynamic boundary field ξ which induces the flow and, in the continuum scaling limit, plays the role of the perturbing boundary field 1,3. The excitations are completely classified, in terms of string content, by (m,n) systems and quantum numbers but the string content changes by either two or three well-defined mechanisms along the flow. We identify these mechanisms and obtain the induced maps between the relevant finitized Virasoro characters. We also solve the TBA equations numerically to determine the boundary flows for the leading excitations. © 2003 Elsevier B.V. All rights reserved
INTEGRABLE QFT(2) ENCODED ON PRODUCTS OF DYNKIN DIAGRAMS
No full textA large class of Thermodynamic Bethe Ansatz equations governing the Renormalization Group evolution of the Casimir energy of the vacuum on the cylinder for an integrable two-dimensional field theory, can often be encoded on a tensor product of two graphs. We demonstrate here that in this case the two graphs can only be of ADE type. We also give strong numerical evidence for a new large set of Dilogarithm sum Rules connected to ADE × ADE and a simple formula for the ultraviolet perturbing operator conformal dimensions only in terms of rank and Coxeter numbers of ADE × ADE . We conclude with some remarks on the curious case ADE × D
GROWTH-HORMONE, INSULIN-LIKE GROWTH-FACTOR-I AND SOMATOSTATIN IN HUMAN FETUS, NEWBORN, MOTHER PLASMA AND AMNIOTIC-FLUID.
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