scholarly journals Note on the thermodynamic Bethe ansatz approach to the quantum phase diagram of the strong coupling ladder compounds

2003 ◽  
Vol 5 ◽  
pp. 107-107 ◽  
Author(s):  
M T Batchelor ◽  
X-W Guan ◽  
A Foerster ◽  
H-Q Zhou
Keyword(s):  
Phase Diagram ◽  
Bethe Ansatz ◽  
Strong Coupling ◽  
Quantum Phase ◽  
Thermodynamic Bethe Ansatz ◽  
Ansatz Approach

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 GLUON SCATTERING AMPLITUDES FROM GAUGE/STRING DUALITY AND INTEGRABILITY

2013 ◽  
Vol 21 ◽  
pp. 1-21
Author(s):  
YUJI SATOH
Keyword(s):  
Perturbation Theory ◽  
Scattering Amplitudes ◽  
String Duality ◽  
Bethe Ansatz ◽  
Strong Coupling ◽  
Minimal Surfaces ◽  
Wilson Loops ◽  
Thermodynamic Bethe Ansatz ◽  
Yang Mills ◽  
Sine Gordon Model

We discuss gluon scattering amplitudes/null-polygonal Wilson loops of [Formula: see text] super Yang-Mills theory at strong coupling based on the gauge/string duality and its underlying integrability. We focus on the amplitudes/Wilson loops corresponding to the minimal surfaces in AdS3, which are described by the thermodynamic Bethe ansatz equations of the homogeneous sine-Gordon model. Using conformal perturbation theory and an interesting relation between the g-function (boundary entropy) and the T-function, we derive analytic expansions around the limit where the Wilson loops become regular-polygonal. We also compare our analytic results with those at two loops, to find that the rescaled remainder functions are close to each other for all multi-point amplitudes.

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 Quantum periods and TBA-like equations for a class of Calabi-Yau geometries

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bao-ning Du ◽  
Min-xin Huang
Keyword(s):  
Large Class ◽  
Bethe Ansatz ◽  
Difference Equations ◽  
The Other ◽  
Elementary Functions ◽  
Quantum Dilogarithm ◽  
Thermodynamic Bethe Ansatz ◽  
Dilogarithm Function ◽  
Quantum Operators

Abstract We continue the study of a novel relation between quantum periods and TBA(Thermodynamic Bethe Ansatz)-like difference equations, generalize previous works to a large class of Calabi-Yau geometries described by three-term quantum operators. We give two methods to derive the TBA-like equations. One method uses only elementary functions while the other method uses Faddeev’s quantum dilogarithm function. The two approaches provide different realizations of TBA-like equations which are nevertheless related to the same quantum period.

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