Finite size effects and the supersymmetric sine-Gordon models

“…We think that the quasi-local formulation of the mirror TBA equations is an important step towards the NLIE formulation of the AdS/CFT spectral problem since using it the application of techniques worked out for the relativistically invariant models [32,33,34,35,36] becomes possible.…”

Section: Resultsmentioning

confidence: 99%

Quasi-local formulation of the mirror TBA

Balog

Hegedűs

2012

J. High Energ. Phys.

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“…The source objects appearing in the NLIE are not arbitrary parameters, but they have to satisfy certain quantization conditions dictated by the analytic properties of the auxiliary functions (14)(15)(16)(17)(18)(19)(20)(21). These are as follows • For holes:…”

Section: The Nonlinear Integral Equationsmentioning

confidence: 99%

“…The NLIE technique was originally introduced in [12] where with the help of this technique the finite size effects of the ground states of the spin-1/2 and spin-1 XXZ chains were studied calculating analytically their central charges and in the spin-1 case the 2-string deviations in the ground state for the first time in a unified NLIE approach. Then the NLIE technique was successfully applied for describing finite size effects in various integrable spin chains and quantum field theories [14,15,16,17,18,19,20].Recently J. Suzuki [1] derived a set of NLIEs (different from the those of [12]) to describe the excited states of the integrable spin-1 XXZ chain in its repulsive regime…”

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confidence: 99%

Finite size effects and 2-string deviations in the spin-1 XXZ chains

Hegedűs

2007

J. Phys. A: Math. Theor.

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In an earlier work [1] J. Suzuki proposed a set of nonlinear integral equations (NLIE) to describe the excited state spectrum of the integrable spin-1 XXZ chain in its repulsive regime. In this paper we extend his equations for the attractive regime of the model, and calculate analytically the conformal spectrum of the spin chain. We also discuss the typical root configurations of the thermodynamic limit as well as the 2-string deviations of certain excited states of the model. Special objects appearing in the NLIE are also treated with special care.Recently spin-1 chains and quantum field theories related to the 19-vertex model [2] attract much attention. The spin-1 XXZ chains deducible from the 19-vertex model are interesting because on the one hand their Hamiltonian occurs in large N c QCD as the 1-loop anomalous dimension matrix of the single trace operators containing the self-dual components of the field strength tensor [3], and on the other hand the determination of correlation functions in these integrable higher spin chains is still an area of active research [4]. Furthermore it is known that in the context of light-cone approach [5] the inhomogeneous 19-vertex model with alternating inhomogeneities provides an integrable lattice regularization for the N = 1 supersymmetric sine-Gordon model [6,7].In this paper we investigate the finite size effects and 2-string deviations of the integrable spin-1 XXZ chain. It is well known that in the thermodynamic limit the anti-ferromagnetic ground state of the model is composed of quasi 2-strings, namely of pairs of complex roots having imaginary parts close to ± π 2 . The deviations of their imaginary parts from the values ± π 2 are called 2-string deviations. According to the string hypothesis these deviations should be exponentially small in N [8, 9, 10], but it turns out that these deviations are much larger; they are of order 1/N [11,12]. This is because the number of 2-strings is not of order one, but N/2 minus O(1) such that the centers of the outermost 2-strings tend to infinity as N tends to infinity. This is why these 2-string deviations are not negligible even in the large N limit calculations of the physical quantities. To treat correctly the technical difficulties coming from 2-string deviations one needs to use the so-called nonlinear integral equation technique (NLIE). The NLIE technique was originally introduced in [12] where with the help of this technique the finite size effects of the ground states of the spin-1/2 and spin-1 XXZ chains were studied calculating analytically their central charges and in the spin-1 case the 2-string deviations in the ground state for the first time in a unified NLIE approach. Then the NLIE technique was successfully applied for describing finite size effects in various integrable spin chains and quantum field theories [14,15,16,17,18,19,20].Recently J. Suzuki [1] derived a set of NLIEs (different from the those of [12]) to describe the excited states of the integrable spin-1 XXZ chain in its repulsive regime

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Finite size effects and the supersymmetric sine-Gordon models

Cited by 29 publications

References 60 publications

The finite size spectrum of the 2-dimensional nonlinear σ-model

The finite size spectrum of the 2-dimensional nonlinear σ-model

Quasi-local formulation of the mirror TBA

Finite size effects and 2-string deviations in the spin-1 XXZ chains

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