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Marco Rossi - One of the best experts on this subject based on the ideXlab platform.

  • large spin corrections in n 4 sym sl 2 still a Linear Integral Equation
    Nuclear Physics, 2009
    Co-Authors: Diego Bombardelli, Davide Fioravanti, Marco Rossi
    Abstract:

    Abstract Anomalous dimension and higher conserved charges in the sl ( 2 ) sector of N = 4 SYM for generic spin s and twist L are described by using a novel kind of non-Linear Integral Equation (NLIE). The latter can be derived under typical situations of the SYM sectors, i.e. when the scattering need not depend on the difference of the rapidities and these, in their turn, may also lie on a bounded range. Here the non-Linear (finite range) Integral terms, appearing in the NLIE and in the dimension formula, go to zero as s → ∞ . Therefore they can be neglected at least up to the O ( s 0 ) order, thus implying a Linear Integral Equation (LIE) and a Linear dimension/charge formula respectively, likewise the ‘thermodynamic’ (i.e. infinite spin) case. Importantly, these non-Linear terms go faster than any inverse logarithm power ( ln s ) − n , n > 0 , thus extending the Linearity validity.

  • Large spin corrections in N = 4 SYM sl(2): Still a Linear Integral Equation
    Nuclear Physics B, 2009
    Co-Authors: Diego Bombardelli, Davide Fioravanti, Marco Rossi
    Abstract:

    Abstract Anomalous dimension and higher conserved charges in the sl ( 2 ) sector of N = 4 SYM for generic spin s and twist L are described by using a novel kind of non-Linear Integral Equation (NLIE). The latter can be derived under typical situations of the SYM sectors, i.e. when the scattering need not depend on the difference of the rapidities and these, in their turn, may also lie on a bounded range. Here the non-Linear (finite range) Integral terms, appearing in the NLIE and in the dimension formula, go to zero as s → ∞ . Therefore they can be neglected at least up to the O ( s 0 ) order, thus implying a Linear Integral Equation (LIE) and a Linear dimension/charge formula respectively, likewise the ‘thermodynamic’ (i.e. infinite spin) case. Importantly, these non-Linear terms go faster than any inverse logarithm power ( ln s ) − n , n > 0 , thus extending the Linearity validity.

  • large spin corrections in cal n 4 sym sl 2 still a Linear Integral Equation
    Nuclear Physics, 2008
    Co-Authors: Diego Bombardelli, Davide Fioravanti, Marco Rossi
    Abstract:

    Anomalous dimension and higher conserved charges in the $sl(2)$ sector of ${\cal N}=4$ SYM for generic spin $s$ and twist $L$ are described by using a novel kind of non-Linear Integral Equation (NLIE). The latter can be derived under typical situations of the SYM sectors, i.e. when the scattering need not depend on the difference of the rapidities and these, in their turn, may also lie on a bounded range. Here the non-Linear (finite range) Integral terms, appearing in the NLIE and in the dimension formula, go to zero as $s\to \infty$. Therefore they can be neglected at least up to the $O(s^0)$ order, thus implying a Linear Integral Equation (LIE) and a Linear dimension/charge formula respectively, likewise the 'thermodynamic' (i.e. infinite spin) case. Importantly, these non-Linear terms go faster than any inverse logarithm power $(\ln s)^{-n}$, $n>0$, thus extending the Linearity validity.

  • Non-Linear Integral Equations in N = 4 SYM ∗
    arXiv: High Energy Physics - Theory, 2007
    Co-Authors: Diego Bombardelli, Davide Fioravanti, Marco Rossi
    Abstract:

    We survey and discuss the applications of the non-Linear Integral Equation in the framework of the Bethe Ansatz type Equations which are conjectured to give the eigenvalues of the dilatation operator in N = 4 SYM. Moreover, an original idea (different from that of [1]) to derive a non-Linear Integral Equation is briefly depicted in Section 4.

G Takacs - One of the best experts on this subject based on the ideXlab platform.

  • non Linear Integral Equation and finite volume spectrum of minimal models perturbed by φ 1 3
    Nuclear Physics, 2000
    Co-Authors: G Feverati, Francesco Ravanini, G Takacs
    Abstract:

    We describe an extension of the non-Linear 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.

  • non Linear Integral Equation and finite volume spectrum of sine gordon theory
    Nuclear Physics, 1999
    Co-Authors: G Feverati, Francesco Ravanini, G Takacs
    Abstract:

    We examine the connection between the non-Linear 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.

Diego Bombardelli - One of the best experts on this subject based on the ideXlab platform.

  • large spin corrections in n 4 sym sl 2 still a Linear Integral Equation
    Nuclear Physics, 2009
    Co-Authors: Diego Bombardelli, Davide Fioravanti, Marco Rossi
    Abstract:

    Abstract Anomalous dimension and higher conserved charges in the sl ( 2 ) sector of N = 4 SYM for generic spin s and twist L are described by using a novel kind of non-Linear Integral Equation (NLIE). The latter can be derived under typical situations of the SYM sectors, i.e. when the scattering need not depend on the difference of the rapidities and these, in their turn, may also lie on a bounded range. Here the non-Linear (finite range) Integral terms, appearing in the NLIE and in the dimension formula, go to zero as s → ∞ . Therefore they can be neglected at least up to the O ( s 0 ) order, thus implying a Linear Integral Equation (LIE) and a Linear dimension/charge formula respectively, likewise the ‘thermodynamic’ (i.e. infinite spin) case. Importantly, these non-Linear terms go faster than any inverse logarithm power ( ln s ) − n , n > 0 , thus extending the Linearity validity.

  • Large spin corrections in N = 4 SYM sl(2): Still a Linear Integral Equation
    Nuclear Physics B, 2009
    Co-Authors: Diego Bombardelli, Davide Fioravanti, Marco Rossi
    Abstract:

    Abstract Anomalous dimension and higher conserved charges in the sl ( 2 ) sector of N = 4 SYM for generic spin s and twist L are described by using a novel kind of non-Linear Integral Equation (NLIE). The latter can be derived under typical situations of the SYM sectors, i.e. when the scattering need not depend on the difference of the rapidities and these, in their turn, may also lie on a bounded range. Here the non-Linear (finite range) Integral terms, appearing in the NLIE and in the dimension formula, go to zero as s → ∞ . Therefore they can be neglected at least up to the O ( s 0 ) order, thus implying a Linear Integral Equation (LIE) and a Linear dimension/charge formula respectively, likewise the ‘thermodynamic’ (i.e. infinite spin) case. Importantly, these non-Linear terms go faster than any inverse logarithm power ( ln s ) − n , n > 0 , thus extending the Linearity validity.

  • large spin corrections in cal n 4 sym sl 2 still a Linear Integral Equation
    Nuclear Physics, 2008
    Co-Authors: Diego Bombardelli, Davide Fioravanti, Marco Rossi
    Abstract:

    Anomalous dimension and higher conserved charges in the $sl(2)$ sector of ${\cal N}=4$ SYM for generic spin $s$ and twist $L$ are described by using a novel kind of non-Linear Integral Equation (NLIE). The latter can be derived under typical situations of the SYM sectors, i.e. when the scattering need not depend on the difference of the rapidities and these, in their turn, may also lie on a bounded range. Here the non-Linear (finite range) Integral terms, appearing in the NLIE and in the dimension formula, go to zero as $s\to \infty$. Therefore they can be neglected at least up to the $O(s^0)$ order, thus implying a Linear Integral Equation (LIE) and a Linear dimension/charge formula respectively, likewise the 'thermodynamic' (i.e. infinite spin) case. Importantly, these non-Linear terms go faster than any inverse logarithm power $(\ln s)^{-n}$, $n>0$, thus extending the Linearity validity.

  • Non-Linear Integral Equations in N = 4 SYM ∗
    arXiv: High Energy Physics - Theory, 2007
    Co-Authors: Diego Bombardelli, Davide Fioravanti, Marco Rossi
    Abstract:

    We survey and discuss the applications of the non-Linear Integral Equation in the framework of the Bethe Ansatz type Equations which are conjectured to give the eigenvalues of the dilatation operator in N = 4 SYM. Moreover, an original idea (different from that of [1]) to derive a non-Linear Integral Equation is briefly depicted in Section 4.

H J De Vega - One of the best experts on this subject based on the ideXlab platform.

  • non Linear Integral Equation and excited states scaling functions in the sine gordon model
    arXiv: High Energy Physics - Theory, 1997
    Co-Authors: C Destri, H J De Vega
    Abstract:

    The NLIE (the non-Linear Integral Equation equivalent to the Bethe Ansatz Equations for finite size) is generalized to excited states, that is states with holes and complex roots over the antiferromagnetic ground state. We consider the sine-Gordon/massive Thirring model (sG/mT) in a periodic box of length $L$ using the light-cone approach, in which the sG/mT model is obtained as the continuum limit of an inhomogeneous six vertex model. This NLIE is an useful starting point to compute the spectrum of excited states both analytically in the large $L$ (perturbative) and small $L$ (conformal) regimes as well as numerically.

  • NON-Linear Integral Equation AND EXCITED-STATES SCALING FUNCTIONS IN THE SINE-GORDON MODEL
    Nuclear Physics B, 1997
    Co-Authors: C Destri, H J De Vega
    Abstract:

    Abstract The NLIE (the non-Linear Integral Equation equivalent to the Bethe ansatz Equations for finite size) is generalized to excited states, that is states with holes and complex roots over the antiferromagnetic ground state. We consider the sine-Gordon/massive Thirring model (sG/mT) in a periodic box of length L using the light-cone approach, in which the sG/mT model is obtained as the continuum limit of an inhomogeneous six-vertex model. This NLIE is an useful starting point to compute the spectrum of excited states both analytically in the large L (perturbative) and small L (conformal) regimes as well as numerically. We derive the conformal weights of the Bethe states with holes and non-string complex roots (close and wide roots) in the UV limit. These weights agree with the Coulomb gas description, yielding a UV conformal spectrum related by duality to the IR conformal spectrum of the six-vertex model.

G Feverati - One of the best experts on this subject based on the ideXlab platform.

  • non Linear Integral Equation and finite volume spectrum of minimal models perturbed by φ 1 3
    Nuclear Physics, 2000
    Co-Authors: G Feverati, Francesco Ravanini, G Takacs
    Abstract:

    We describe an extension of the non-Linear 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.

  • non Linear Integral Equation and finite volume spectrum of sine gordon theory
    Nuclear Physics, 1999
    Co-Authors: G Feverati, Francesco Ravanini, G Takacs
    Abstract:

    We examine the connection between the non-Linear 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.