Non-linear integral equation and finite volume spectrum of minimal models perturbed by Φ(1,3)

Feverati, Giovanni; Ravanini, Francesco; Takács, Gábor

doi:10.1016/s0550-3213(99)00771-3

Cited by 26 publications

(32 citation statements)

References 33 publications

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“…Setting ζ = β 2 /(8π−β 2 ), it can be shown that for ζ = p/(q−p) and α = 1/p, the ground-state energy of the φ 13 perturbation of a general minimal model M p,q is also matched [23,24,[27][28][29]. (Note that this definition of ζ is thus in line with the one given in the introduction.)…”

Section: The Nonlinear Integral Equationmentioning

confidence: 62%

“…The previously-studied sequence (1.1), (1.2) is picked out by the monotonicity of the function c eff as a function of r. In all other cases, somewhat to our surprise, we found that the effective central charge undergoes a number of oscillations as it interpolates between its short and long distance limits. Our approach differs from the TBA method, and is much closer to that of the papers [20][21][22][23][24][25][26], in that a single nonlinear integral equation (NLIE) is proposed to describe infinitely-many different perturbed conformal field theories, each being picked out by an appropriate choice of certain parameters. For massless flows, the one previous example of such an equation was found by Al.…”

Section: Introductionmentioning

confidence: 99%

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New families of flows between two-dimensional conformal field theories

2000

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We present evidence for the existence of infinitely-many new families of renormalisation group flows between the nonunitary minimal models of conformal field theory. These are associated with perturbations by the φ 21 and φ 15 operators, and generalise a family of flows discovered by Martins. In all of the new flows, the finitevolume effective central charge is a non-monotonic function of the system size. The evolution of this effective central charge is studied by means of a nonlinear integral equation, a massless variant of an equation recently found to describe certain massive perturbations of these same models. We also observe that a similar nonmonotonicity arises in the more familiar φ 13 perturbations, when the flows induced are between nonunitary minimal models.

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Section: The Nonlinear Integral Equationmentioning

confidence: 62%

Section: Introductionmentioning

confidence: 99%

New families of flows between two-dimensional conformal field theories

2000

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“…For the sine-Gordon model, naturally associated with the φ 13 perturbing operator [30,31], it has been observed both analytically and numerically [11,15,16,32,33] that reduction is implemented at the level of finite-size effects and the non-linear integral equation via a particular choice of the chemical potential. The similarity between our equations and those in [15,16] suggests that the same should be true here.…”

Section: A Link With Perturbed Conformal Field Theorymentioning

confidence: 99%

Differential equations and integrable models: the SU(3) case

2000

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We exhibit a relationship between the massless a Ž2. integrable quantum field theory and a 2 certain third-order ordinary differential equation, thereby extending a recent result connecting the massless sine-Gordon model to the Schrodinger equation. This forms part of a more general correspondence involving A -related Bethe ansatz systems and third-order differential equations. IntroductionA curious connection between certain integrable quantum field theories and the w x theory of the Schrodinger equation has been the subject of some recent work 1-4 . In this paper we extend these results by establishing a link between functional relations for Ž w x. A -related Bethe ansatz systems see, for example, Refs. 5,6 and third-order differen-2 tial equations. Most of our analysis concerns a certain specialisation of the model, a w x particularly symmetric case that can also be related to the dilute A-model of 7 . 0550-3213r00r$ -see front matter q 2000 Elsevier Science B.V. All rights reserved.Ž . PII: S 0 5 5 0 -3 2 1 3 9 9 0 0 7 9 1 -9 Dorey, R. Tateo r Nuclear Physics B 571 PM 2000 583-606 584 w x In the cases studied in 1-4 , the most general differential equation was a radial Schrodinger problem with 'angular momentum' l and homogeneous potential x 2 M , Ž . initially defined on the positive real axis x g 0,`:The relevant integrable quantum field theories were the massless twisted sine-Gordon models or, equivalently, the twisted XXZr6-vertex models in their thermodynamic limits, and their reductions. It is worth noting that these models are all related to the Lie Ž . w x algebra A . Spectral functions associated with 1.1 satisfy functional relations 8-11 , 1 and these were mapped into functional equations appearing in the context of integrable w x quantum field theory in 1-4 . We will follow a similar strategy here, taking a simple third-order ordinary differential equation as our starting-point and showing that the Stokes multipliers and certain spectral functions for this equation together satisfy relations which are essentially the analogues, for the Bethe ansatz systems treated in w x 6,7 , of the T-Q systems which arise in the context of the integrable quantum field w x theories related to A 12,13 . This is the subject of Section 2, while in Section 3 we 1 borrow some other ideas from integrable quantum field theory in order to derive a non-linear integral equation for the spectral functions, an equation which is put to the test in a simple example in Section 4. Duality properties are discussed in Section 5, Ž . allowing us to find the equivalent of the angular-momentum term in 1.1 for the third-order equation. Connections with various perturbed conformal field theories are discussed and tested in Section 6. Finally, Section 7 discusses the most general A -related BA equations that arise in this context, and Section 8 contains our conclu-2 sions. The differential equationWe begin with the following third-order ordinary differential equation:3 M Ž . and initially restrict ourselves to purely homoge...

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“…Based on earlier results [15,16,17,18,8] it is expected that the NLIE (2.8) at appropriate values of the twist angle α can describe the finite volume spectrum of the supersymmetry preserving perturbation Φ 13 of the N = 1 superminimal models. In this section we confirm this expectation.…”

mentioning

confidence: 92%

“…The NLIE is derived for the lattice model, then tuning appropriately the lattice constant and the inhomogeneity parameter one gets the NLIE for the continuum sine-Gordon model [5]. This NLIE was shown to describe the full finite size spectrum of the sine-Gordon model [6,7], and moreover considering twisted versions of the NLIE one can describe finite size effects of massive integrable perturbations of Virasoro minimal models (unitary and non-unitary) [8].…”

Section: Introductionmentioning

confidence: 99%