arXiv subjects

F. Ravanini

Publications and source records attributed to F. Ravanini.

16 recordsLinked to original sources

arXiv2004

Excited Boundary TBA in the Tricritical Ising Model

By considering the continuum scaling limit of the $A_{4}$ 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 $ξ$ which plays the role of the perturbing boundary field $ϕ_{1,3}$ and induces the renormalization group flow between boundary fixed points. The boundary TBA equations determining the RG flows are derived in the $\mathcal{B}_{(1,2)}\to \mathcal{B}_{(2,1)}$ 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.

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arXiv2003

Exact $ϕ_{1,3}$ boundary flows in the tricritical Ising model

We consider the tricritical Ising model on a strip or cylinder under the integrable perturbation by the thermal $ϕ_{1,3}$ 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 $A_4$ 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 $ϕ_{1,3}$. 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.

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arXiv1999

Nonlinear Integral Equation and Finite Volume Spectrum of Minimal Models Perturbed by $Φ_{(1,3)}$

We describe an extension of the nonlinear integral equation (NLIE) method to Virasoro minimal models perturbed by the relevant operator $Φ_{(1,3)$. Along the way, we also complete our previous studies of the finite volume spectrum of sine-Gordon theory by considering the attractive regime and more specifically, breather states. For the minimal models, we examine the states with zero topological charge in detail, and give numerical comparison to TBA and TCS results. We think that the evidence presented strongly supports the validity of the NLIE description of perturbed minimal models.

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arXiv1998

Nonlinear Integral Equation and Finite Volume Spectrum of Sine-Gordon Theory

We examine the connection between the nonlinear integral equation (NLIE) derived from light-cone lattice and sine-Gordon quantum field theory, considered as a perturbed c=1 conformal field theory. After clarifying some delicate points of the NLIE deduction from the lattice, we compare both analytic and numerical predictions of the NLIE to previously known results in sine-Gordon theory. To provide the basis for the numerical comparison we use data from Truncated Conformal Space method. Together with results from analysis of infrared and ultraviolet asymptotics, we find evidence that it is necessary to change the rule of quantization proposed by Destri and de Vega to a new one which includes as a special case that of Fioravanti et al. This way we find strong evidence for the validity of the NLIE as a description of the finite size effects of sine-Gordon theory.

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arXiv1998

Scaling Functions in the Odd Charge Sector of Sine-Gordon/Massive Thirring Theory

A non-linear integral equation (NLIE) governing the finite size effects of excited states of even topological charge in the sine-Gordon (sG) / massive Thirring (mTh) field theory, deducible from a light-cone lattice formulation of the model, has been known for some time. In this letter we conjecture an extension of this NLIE to states with odd topological charge, thus completing the spectrum of the theory. The scaling functions obtained as solutions to our conjectured NLIE are compared successfully with Truncated Conformal Space data and the construction is shown to be compatible with all other facts known about the local Hilbert spaces of sG and mTh models. With the present results we have achieved a full control over the finite size behaviour of energy levels of sG/mTh theory.

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arXiv1998

Truncated Conformal Space at c=1, Nonlinear Integral Equation and Quantization Rules for Multi-Soliton States

We develop Truncated Conformal Space (TCS) technique for perturbations of c=1 Conformal Field Theories. We use it to give the first numerical evidence of the validity of the non-linear integral equation (NLIE) derived from light-cone lattice regularization at intermediate scales. A controversy on the quantization of Bethe states is solved by this numerical comparison and by using the locality principle at the ultra- violet fixed point. It turns out that the correct quantization for pure hole states is the one with half-integer quantum numbers originally proposed by Mariottini et al. Once the correct rule is imposed, the agreement between TCS and NLIE for pure hole states turns out to be impressive.

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arXiv1996

Excited State Destri - De Vega Equation for Sine-Gordon and Restricted Sine-Gordon Models

We derive a generalization of the Destri - De Vega equation governing the scaling functions of some excited states in the Sine-Gordon theory. In particular configurations with an even number of holes and no strings are analyzed and their UV limits found to match some of the conformal dimensions of the corresponding compactified massless free boson. Quantum group reduction allows to interpret some of our results as scaling functions of excited states of Restricted Sine-Gordon theory, i.e. minimal models perturbed by phi_13 in their massive regime. In particular we are able to reconstruct the scaling functions of the off-critical deformations of all the scalar primary states on the diagonal of the Kac-table.

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arXiv1996

Infrared Behaviour of Massless Integrable Flows entering the Minimal Models from phi_31

It is known that any minimal model M_p receives along its phi_31 irrelevant direction *two* massless integrable flows: one from M_{p+1} perturbed by phi_{13}, the other from Z_{p-1} parafermionic model perturbed by its generating parafermion field. By comparing Thermodynamic Bethe Ansatz data and ``predictions'' of infrared Conformal Perturbation Theory we show that these two flows are received by M_p with opposite coupling constants of the phi_31 irrelevant perturbation. Some comments on the massless S matrices of these two flows are added.

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arXiv1994

Integrable perturbations of CFT with complex parameter: the $M_{3/5}$ model and its generalizations

We give evidence, by use of the Thermodynamic Bethe Ansatz approach, of the existence of both massive and massless behaviours for the $ϕ_{2,1}$ perturbation of the $M_{3,5}$ non-unitary minimal model, thus resolving apparent contradictions in the previous literature. The two behaviours correspond to changing the perturbing bare coupling constant from real values to imaginary ones. Generalizations of this picture to the whole class of non-unitary minimal models $M_{p,2p\pm 1}$, perturbed by their least relevant operator lead to a cascade of flows similar to that of unitary minimal models perturbed by $ϕ_{1,3}$. Various aspects and generalizations of this phenomenon and the links with the Izergin-Korepin model are discussed.

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arXiv1993

Integrable QFT(2) Encoded on Products of Dynkin Diagrams

A 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 $ADE\times ADE$ and a simple formula for the ultraviolet perturbing operator conformal dimensions only in terms of rank and Coxeter numbers of $ADE\times ADE$. We conclude with some remarks on the curious case $ADE\times D$. [Talk given by F.R. at the Cargese Workshop "New Developments in String Theory, Conformal Models and Topological Field Theory" (May 1993)]

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arXiv1992

A New Family of Diagonal Ade-Related Scattering Theories

We propose the factorizable S-matrices of the massive excitations of the non-unitary minimal model $M_{2,11}$ perturbed by the operator $Φ_{1,4}$. The massive excitations and the whole set of two particle S-matrices of the theory is simply related to the $E_8$ unitary minimal scattering theory. The counting argument and the Thermodynamic Bethe Ansatz (TBA) are applied to this scattering theory in order to support this interpretation. Generalizing this result, we describe a new family of NON UNITARY and DIAGONAL $ADE$-related scattering theories. A further generalization suggests the magnonic TBA for a large class of non-unitary $\G\otimes\G/\G$ coset models ($\G=A_{odd},D_n,E_{6,7,8}$) perturbed by $Φ_{id,id,adj}$, described by non-diagonal S-matrices.

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arXiv1992

Dynkin TBA's

We prove a useful identity valid for all $ADE$ minimal S-matrices, that clarifies the transformation of the relative thermodynamic Bethe Ansatz (TBA) from its standard form into the universal one proposed by Al.B.Zamolodchikov. By considering the graph encoding of the system of functional equations for the exponentials of the pseudoenergies, we show that any such system having the same form as those for the $ADE$ TBA's, can be encoded on $A,D,E,A/Z_2$ only. This includes, besides the known $ADE$ diagonal scattering, the set of all $SU(2)$ related {\em magnonic} TBA's. We explore this class sistematically and find some interesting new massive and massless RG flows. The generalization to classes related to higher rank algebras is briefly presented and an intriguing relation with level-rank duality is signalled.

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arXiv1992

Thermodynamic Bethe Ansatz for G_k x G_l / G_{k+l} Coset Models Perturbed by Their ϕ_{1,1,Adj} Operator

We propose a Thermodynamic Bethe Ansatz (TBA) for G_k x G_l / G_{k+l} conformal coset models (G any simply-laced Lie algebra) perturbed by their operator ϕ_{1,1,Adj}. An interesting adjacency structure appears and can be depicted in a sort of ``product'' of Dynkin diagrams of G and A_{k+l-1}. UV and IR limits are computed and reproduce the expected values for the central charges. For k->\infty, l fixed we obtain the TBA of the G_l WZW model perturbed by J_a\bar{J}_a, and for k,l->\infty, k-l fixed, that of Principal Chiral model with WZ term at level k-l.

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arXiv1991

Towards a Classification of Fusion Rule Algebras in Rational Conformal Field Theories

We review the main topics concerning Fusion Rule Algebras (FRA) of Rational Conformal Field Theories. After an exposition of their general properties, we examine known results on the complete classification for low number of fields ($\leq 4$). We then turn our attention to FRA's generated polynomially by one (real) fundamental field, for which a classification is known. Attempting to generalize this result, we describe some connections between FRA's and Graph Theory. The possibility to get new results on the subject following this ``graph'' approach is briefly discussed.

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arXiv1991

RG flows of non-diagonal minimal models perturbed by $ϕ_{1,3}$

Studying perturbatively, for large m, the torus partition function of both (A,A) and (A,D) series of minimal models in the Cappelli, Itzykson, Zuber classification, deformed by the least relevant operator $ϕ_{(1,3)}$, we disentangle the structure of $ϕ_{1,3}$ flows. The results are conjectured on reasonable ground to be valid for all m. They show that (A,A) models always flow to (A,A) and (A,D) ones to (A,D). No hopping between the two series is possible. Also, we give arguments that there exist 3 isolated flows (E,A)-->(A,E) that, together with the two series, should exhaust all the possible $ϕ_{1,3}$ flows. Conservation (and symmetry breaking) of non-local currents along the flows is discussed and put in relation to the A,D,E classification.

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arXiv1991

On the possibility of $Z_N$ exotic supersymmetry in two dimensional Conformal Field Theory

We investigate the possibility to construct extended parafermionic conformal algebras whose generating current has spin $1+\frac{1}{K}$, generalizing the superconformal (spin 3/2) and the Fateev Zamolodchikov (spin 4/3) algebras. Models invariant under such algebras would possess $Z_K$ exotic supersymmetries satisfying (supercharge)$^K$ = (momentum). However, we show that for $K=4$ this new algebra allows only for models at $c=1$, for $K=5$ it is a trivial rephrasing of the ordinary $Z_5$ parafermionic model, for $K=6,7$ (and, requiring unitarity, for all larger $K$) such algebras do not exist. Implications of this result for existence of exotic supersymmetry in two dimensional field theory are discussed.

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