scholarly journals INTEGRABLE PERTURBATIONS OF CFT WITH COMPLEX PARAMETER: THE M3/5 MODEL AND ITS GENERALIZATIONS

1996 ◽  
Vol 11 (04) ◽  
pp. 677-697 ◽  
Author(s):  
F. RAVANINI ◽  
M. STANISHKOV ◽  
R. TATEO
Keyword(s):  
Bethe Ansatz ◽  
Minimal Model ◽  
Previous Literature ◽  
Coupling Constant ◽  
Minimal Models ◽  
Thermodynamic Bethe Ansatz ◽  
Bare Coupling ◽  
Bare Coupling Constant ◽  
Ansatz Approach ◽  
Relevant Operator

By using the thermodynamic Bethe ansatz approach, we give evidence of the existence of both massive and massless behaviors for the ϕ2,1 perturbation of the M3,5 nonunitary minimal model, thus resolving apparent contradictions in the previous literature. The two behaviors correspond to changing the perturbing bare coupling constant from real values to imaginary ones. Generalizations of this picture to the whole class of nonunitary minimal models Mp,2p±1, perturbed by their least relevant operator, lead to a cascade of flows similar to that of unitary minimal models perturbed by ϕ1,3. Various aspects and generalizations of this phenomenon and the links with the Izergin–Korepin model are discussed.

scholarly journals THERMODYNAMIC BETHE ANSATZ AND THREE-FOLD TRIANGULATIONS

1996 ◽  
Vol 11 (22) ◽  
pp. 4051-4064 ◽  
Author(s):  
F. GLIOZZI ◽  
R. TATEO
Keyword(s):  
Bethe Ansatz ◽  
Unknown Function ◽  
Functional Equations ◽  
Simple Solution ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Thermodynamic Bethe Ansatz ◽  
Ansatz Approach ◽  
General Explanation

In the thermodynamic Bethe ansatz approach to 2D integrable, ADE-related quantum field theories, one derives a set of algebraic functional equations (a Y system) which play a prominent role. This set of equations is mapped onto the problem of finding finite triangulations of certain 3D manifolds. This mapping allows us to find a general explanation of the periodicity of the Y system. For the AN related theories, and more generally for the various restrictions of the fractionally supersymmetric sine—Gordon models, we find an explicit, surprisingly simple solution of such functional equations in terms of a single unknown function of the rapidity. The recently found dilogarithm functional equations associated to the Y system simply express the invariance of the volume of a manifold for deformations of its triangulations.

scholarly journals STAIRCASE MODELS FROM AFFINE TODA FIELD THEORY

1993 ◽  
Vol 08 (05) ◽  
pp. 873-893 ◽  
Author(s):  
PATRICK DOREY ◽  
FRANCESCO RAVANINI
Keyword(s):  
Field Theory ◽  
Elastic Scattering ◽  
Lie Algebras ◽  
Bethe Ansatz ◽  
Minimal Model ◽  
Coupling Constants ◽  
Field Theories ◽  
Thermodynamic Bethe Ansatz ◽  
Group Flow ◽  
Toda Field Theory

We 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 (TBA) equations, we give analytic arguments in support of a conjectured renormalisation group flow visiting the neighbourhood of each Wg minimal model in turn.

scholarly journals Thermodynamic Bethe Ansatz past turning points: the (elliptic) sinh-Gordon model

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Lucía Córdova ◽  
Stefano Negro ◽  
Fidel I. Schaposnik Massolo
Keyword(s):  
Bethe Ansatz ◽  
Bound States ◽  
Turning Point ◽  
Central Charge ◽  
Continuation Method ◽  
Complex Conjugate ◽  
Minimal Models ◽  
Thermodynamic Bethe Ansatz ◽  
New Family ◽  
The Difference

Abstract We analyze the Thermodynamic Bethe Ansatz (TBA) for various integrable S-matrices in the context of generalized T$$ \overline{\mathrm{T}} $$ T ¯ deformations. We focus on the sinh-Gordon model and its elliptic deformation in both its fermionic and bosonic realizations. We confirm that the determining factor for a turning point in the TBA, interpreted as a finite Hagedorn temperature, is the difference between the number of bound states and resonances in the theory. Implementing the numerical pseudo-arclength continuation method, we are able to follow the solutions to the TBA equations past the turning point all the way to the ultraviolet regime. We find that for any number k of resonances the pair of complex conjugate solutions below the turning point is such that the effective central charge is minimized. As k → ∞ the UV effective central charge goes to zero as in the elliptic sinh-Gordon model. Finally we uncover a new family of UV complete integrable theories defined by the bosonic counterparts of the S-matrices describing the Φ1,3 integrable deformation of non-unitary minimal models $$ \mathcal{M} $$ M 2,2n+3.

SINE–GORDON THEORY IN THE REPULSIVE REGIME, THERMODYNAMIC BETHE ANSATZ AND MINIMAL MODELS

2012 ◽  
Vol 26 (27n28) ◽  
pp. 1243011
Author(s):  
H. ITOYAMA
Keyword(s):  
Bethe Ansatz ◽  
Central Charge ◽  
Thirring Model ◽  
Minimal Models ◽  
Massless Limit ◽  
Thermodynamic Bethe Ansatz ◽  
Massive Thirring Model ◽  
Conformal Theory

Neutral excitations present in the repulsive regime (1/2 < β2/8π < 1) of the sine–Gordon/massive–Thirring model and its study of the massless limit by the thermodynamic Bethe ansatz is revisited. At β2/8π = 1-1/(p+1) the solitons become infinitely heavy, forcing truncation to the neutral excitations alone. The central charge in this limit is calculated to be c = 1-6/p(p+1); the mass and S-matrices of the truncated theories are identified as those of the minimal conformal theory Mp perturbed by the ϕ(1, 3) operator.

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