Correlation functions along a massless flow

Delfino, Gesualdo; Mussardo, Giuseppe; Simonetti, P.

doi:10.1103/physrevd.51.r6620

Cited by 62 publications

(156 citation statements)

References 11 publications

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“…The Bethe ansatz stateΨ p (θ, u) was introduced in (8). At θ 1 = θ 2r + iπ, each of the r integration contours gets pinched at θ 2r , θ 2r ± iπ.…”

Section: Generalizationsmentioning

confidence: 99%

“…Let us note that the normalization of the form factors of the trace operator in (11) was chosen in order to match the effective Lagrangian [8]:…”

Section: Formmentioning

confidence: 99%

“…The form factors of the trace operator were first computed for a small number of particles in [8] in terms of symmetric polynomials. A formula valid for an arbitrary number of particles was then presented in [17].…”

Section: Formmentioning

confidence: 99%

“…In [8], using the S-matrix proposed in [7], a few form-factors 3 of some local and non local operators were constructed for the simplest model describing the flow [9][10][11] between the Tricritical Ising model (TIM) and the Ising model (IM), where the supersymmetry is spontaneously broken. Remarkably enough, the numerical results performed in [8] show that the knowledge of the form-factor with the lowest number of intermediate particles is enough to give quite an accurate approximation for the correlation function at almost all RG scale. Of course it is desirable to figure out whether these spectacular features remain valid in less trivial massless flows.…”

Section: Introductionmentioning

confidence: 99%

“…Finally, in sect. 3 we perform checks on the four particle form factor by making a numerical 3 We refer the reader to [8] for a discussion on form-factors in massless theories. …”

mentioning

confidence: 99%

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Form factors in the massless coset models

Grinza

Ponsot

2005

Nuclear Physics B

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IntroductionThe general problem of finding a suitable description of Renormalization Group (RG) flows between different non-trivial critical point in Quantum Field Theory is an open and appealing problem. In this respect 2d integrable QFTs provide a privileged framework where there is the actual possibility of finding a detailed description of such flows. As a matter of fact, one of the remarkable consequences of integrability is the knowledge of the exact S-matrix which allows to calculate exact form-factors [1][2][3]. From the latter one can reconstruct correlators by means of the spectral expansion which provides a non-perturbative representation of them. Such a representation has often been very accurate in the past -though it was noticed some time ago in [4] that this common belief, even for massive theories, is too optimistic in general-and allows, for example, to recover the conformal data using the c-theorem sum rule [5,6] which gives the difference between the central charges of the UV and IR fixed points. Integrable RG flows which limit in the infrared is a non-trivial CFT can be described by massless excitations, for which an exact scattering matrix can be found. More precisely, we deal with right and left movers and three different types of scatterings, associated to right-right, left-left, and right-left interactions. The right-right and left-left S-matrices, whose definition is formal, are independent of the RG scale, and are solely characterized by the properties of the IR fixed point CFT. On the contrary, the right-left scattering is quite rigorously defined [7]. It becomes trivial in the IR limit, thus the left and right movers decouple, and we obtain the IR CFT. In [8], using the S-matrix proposed in [7], a few form-factors 3 of some local and non local operators were constructed for the simplest model describing the flow [9][10][11] between the Tricritical Ising model (TIM) and the Ising model (IM), where the supersymmetry is spontaneously broken. Remarkably enough, the numerical results performed in [8] show that the knowledge of the form-factor with the lowest number of intermediate particles is enough to give quite an accurate approximation for the correlation function at almost all RG scale. Of course it is desirable to figure out whether these spectacular features remain valid in less trivial massless flows. In this respect, one has to take into account results obtained recently in [12] about the calculation of form factors in a massive integrable model of QFT called the SS model [13], as well as in its RSOS restrictions. The numerical checks performed in [12] show in particular the two-particles approximation of the c-theorem sum rule fails to give the usual good approximation of the exact results, showing instead large discrepancies (about 20-25%, see below).In this article we will consider the construction of form factors of the trace operator for an arbitrary number of intermediate particles in the family of massless flows [14] between the UV coset models [15] su(2) k+1 ⊗ su(2) k /su(...

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“…The Bethe ansatz stateΨ p (θ, u) was introduced in (8). At θ 1 = θ 2r + iπ, each of the r integration contours gets pinched at θ 2r , θ 2r ± iπ.…”

Section: Generalizationsmentioning

confidence: 99%

“…Let us note that the normalization of the form factors of the trace operator in (11) was chosen in order to match the effective Lagrangian [8]:…”

Section: Formmentioning

confidence: 99%

Section: Formmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Finally, in sect. 3 we perform checks on the four particle form factor by making a numerical 3 We refer the reader to [8] for a discussion on form-factors in massless theories. …”

mentioning

confidence: 99%

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Form factors in the massless coset models

Grinza

Ponsot

2005

Nuclear Physics B

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Kinks and Particles in Non-integrable Quantum Field Theories

Mussardo

2009

New Trends in Mathematical Physics

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Lectures on Non Perturbative Field Theory and Quantum Impurity Problems: Part II

Saleur

2001

New Theoretical Approaches to Strongly Correlated Systems

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These are notes of lectures given at The NATO Advanced Study Institute/EC Summer School on "New Theoretical Approaches to Strongly Correlated Systems", (Newton Institute, April 2000). They are a sequel to the notes I wrote two years ago for the Summer School, "Topological Aspects of Low Dimensional Systems", (Les Houches, July 1998). In this second part, I review the formfactors technique and its extension to massless quantum field theories. I then discuss the calculation of correlators in integrable quantum impurity problems, with special emphasis on point contact tunneling in the fractional quantum Hall effect, and the two-state problem of dissipative quantum mechanics.

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Correlation functions along a massless flow

Abstract: A non-perturbative method based on the Form Factor bootstrap approach is proposed for the analysis of correlation functions of 2-D massless integrable theories and applied to the massless flow between the Tricritical and the Critical Ising Models.

Cited by 62 publications

References 11 publications

Form factors in the massless coset models

Form factors in the massless coset models

Kinks and Particles in Non-integrable Quantum Field Theories

Lectures on Non Perturbative Field Theory and Quantum Impurity Problems: Part II

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