The symmetric space and homogeneous sine-Gordon theories

Fernández-Pousa, Carlos R.; Gallas, M. V.; Hollowood, Timothy J.; Miramontes, J. Luis

doi:10.1016/s0550-3213(96)00603-7

Cited by 103 publications

(273 citation statements)

References 35 publications

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“…In a previous paper [15], Sakai and the present authors pointed out that the TBA equations for the minimal surfaces with 2ñ cusps in AdS 3 coincide with those of the SU(ñ − 2) 2 /U(1)ñ −3 homogeneous sine-Gordon (HSG) model [16] with purely imaginary resonance parameters. Similarly, it was inferred there that the TBA equations for the minimal surfaces with n cusps in AdS 4 are those of the HSG model associated with SU(n − 4) 4 /U(1) n−5 .…”

Section: Introductionmentioning

confidence: 55%

“…The ratio of the rescaled remainder functions at strong coupling and at two loops is then 16) which is close to 1. By numerics, we also find that the two 6-point rescaled remainder functions are close to each other for all the scales as shown in figure 5 (a).…”

Section: Rescaled Remainder Functionmentioning

confidence: 69%

“…Since ρ 2 = k(k 2 − 1)/12, comparing (3.14) and (3.6) gives 16) up to field identifications. For example, the perturbing operator φ (1,1,adj) for the single-mass cases is labeled by 17) and has the dimension…”

Section: Jhep02(2013)067mentioning

confidence: 99%

“…where 16) and S F ab is defined in (2.25). The deforming factors Z |b,r;C a,s are non-trivial only in the case s = r, where they reduce to those for the minimal ATFT [19].…”

Section: Jhep02(2013)067mentioning

confidence: 99%

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Null-polygonal minimal surfaces in AdS4 from perturbed W minimal models

Hatsuda¹,

Ito

Satoh

2013

J. High Energ. Phys.

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Abstract:We study the null-polygonal minimal surfaces in AdS 4 , which correspond to the gluon scattering amplitudes/Wilson loops in N = 4 super Yang-Mills theory at strong coupling. The area of the minimal surfaces with n cusps is characterized by the thermodynamic Bethe ansatz (TBA) integral equations or the Y-system of the homogeneous sine-Gordon model, which is regarded as the SU(n − 4) 4 /U(1) n−5 generalized parafermion theory perturbed by the weight-zero adjoint operators. Based on the relation to the TBA systems of the perturbed W minimal models, we solve the TBA equations by using the conformal perturbation theory, and obtain the analytic expansion of the remainder function around the UV/regular-polygonal limit for n = 6 and 7. We compare the rescaled remainder function for n = 6 with the two-loop one, to observe that they are close to each other similarly to the AdS 3 case.

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Section: Introductionmentioning

confidence: 55%

Section: Rescaled Remainder Functionmentioning

confidence: 69%

Section: Jhep02(2013)067mentioning

confidence: 99%

“…where 16) and S F ab is defined in (2.25). The deforming factors Z |b,r;C a,s are non-trivial only in the case s = r, where they reduce to those for the minimal ATFT [19].…”

Section: Jhep02(2013)067mentioning

confidence: 99%

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Null-polygonal minimal surfaces in AdS4 from perturbed W minimal models

Hatsuda¹,

Ito

Satoh

2013

J. High Energ. Phys.

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“…This is equivalent to the statement that one can always diagonalize Φ and A at large |z| by a suitable gauge transformation into the following form 16) where m andm are constants.…”

Section: Hitchin Systemmentioning

confidence: 99%

Six-point gluon scattering amplitudes from $$ {\mathbb{Z}_4} $$ -symmetric integrable model

Hatsuda

Ito

Sakai

et al. 2010

J. High Energ. Phys.

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We study six-point gluon scattering amplitudes in N = 4 super Yang-Mills theory at strong coupling by investigating the thermodynamic Bethe ansatz equations of the underlying Z 4 -symmetric integrable model both analytically and numerically.By the conformal field theory (CFT) perturbation, we compute the free energy part of the remainder function with generic chemical potential near the CFT/small mass limit. Combining this with the expansion of the Y-functions, we obtain the remainder function near the small mass limit up to a function of the chemical potential, which can be evaluated numerically. We also find the leading corrections to the remainder function near the large mass limit. We confirm that these results are in good agreement with numerical computations.

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Revisiting the O(3) Non‐linear Sigma Model and Its Pohlmeyer Reduction

Pastras

2017

Fortschritte der Physik

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It is well known that sigma models in symmetric spaces accept equivalent descriptions in terms of integrable systems, such as the sine-Gordon equation, through Pohlmeyer reduction. In this paper, we study the mapping between known solutions of the Euclidean O(3) non-linear sigma model, such as instantons, merons and elliptic solutions that interpolate between the latter, and solutions of the Pohlmeyer reduced theory, namely the sinh-Gordon equation. It turns out that instantons do not have a counterpart, merons correspond to the ground state, while the class of elliptic solutions is characterized by a two to one correspondence between solutions in the two descriptions.

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The symmetric space and homogeneous sine-Gordon theories

Cited by 103 publications

References 35 publications

Null-polygonal minimal surfaces in AdS4 from perturbed W minimal models

Null-polygonal minimal surfaces in AdS4 from perturbed W minimal models

Six-point gluon scattering amplitudes from $$ {\mathbb{Z}_4} $$ -symmetric integrable model

Revisiting the O(3) Non‐linear Sigma Model and Its Pohlmeyer Reduction

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