Isomorphism of critical and off-critical operator spaces in two-dimensional quantum field theory

Delfino, Gesualdo; Niccoli, Giuliano

doi:10.1016/j.nuclphysb.2008.01.019

Cited by 19 publications

(24 citation statements)

References 33 publications

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“…This expectation was confirmed in many cases by explicit comparison of the space of solutions to the spectrum of local operators as described by the ultraviolet limiting conformal field theory [8,9,10,11,12,13,14,15]; the mathematical foundation is provided by the local commutativity theorem stating that operators specified by solutions of the form factor bootstrap are mutually local [5]. Another important piece of information comes from correlation functions.…”

Section: Introductionmentioning

confidence: 89%

Sine-Gordon multisoliton form factors in finite volume

2012

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Section: Introductionmentioning

confidence: 89%

Sine-Gordon multisoliton form factors in finite volume

2012

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“…This question turns out to be rather nontrivial in other approaches starting from the pioneer work [27]. An important understanding concerning the equivalence of the operator contents of conformal models and their massive perturbations was achieved in [28][29][30].…”

Section: Conserved Currentsmentioning

confidence: 99%

The complex sinh-Gordon model: form factors of descendant operators and current-current perturbations

Lashkevich

Pugai

2019

J. High Energ. Phys.

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We study quasilocal operators in the quantum complex sinh-Gordon theory in the form factor approach. The free field procedure for descendant operators is developed by introducing the algebra of screening currents and related algebraic objects. We work out null vector equations in the space of operators. Further we apply the proposed algebraic structures to constructing form factors of the conserved currents T k and Θ k . We propose also form factors of current-current operators of the form T k T −l . Explicit computations of the four-particle form factors allow us to verify the recent conjecture of Smirnov and Zamolodchikov about the structure of the exact scattering matrix of an integrable theory perturbed by a combination of irrelevant operators. Our calculations confirm that such perturbations of the complex sinh-Gordon model and of the Z N symmetric Ising models result in extra CDD factors in the S matrix. * Mailing address.

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“…However, great efforts were made to find form factors of other operators, which are descendant operators from the point of view of conformal field theory [11,12,[18][19][20][21][22][23][24]. In particular, counting procedures were invented, which reproduce the characters of representations of the Virasoro algebra even outside the conformal points [25][26][27][28]. Recently, a novel approach was proposed [29][30][31], which allows identifying some descendant operators (modulo commutators with integrals of motion) by means of a fermion algebra.…”

Section: Jhep04(2015)126mentioning

confidence: 99%

Form factors of descendant operators: reduction to perturbed M (2, 2s + 1) models

Lashkevich

Pugai

2015

J. High Energ. Phys.

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In the framework of the algebraic approach to form factors in two-dimensional integrable models of quantum field theory we consider the reduction of the sine-Gordon model to the Φ 13 -perturbation of minimal conformal models of the M (2, 2s + 1) series. We find in an algebraic form the condition of compatibility of local operators with the reduction. We propose a construction that make it possible to obtain reduction compatible local operators in terms of screening currents. As an application we obtain exact multiparticle form factors for the compatible with the reduction conserved currents T ±2k , Θ ±(2k−2) , which correspond to the spin ±(2k − 1) integrals of motion, for any positive integer k. Furthermore, we obtain all form factors of the operators T 2k T −2l , which generalize the famous TT operator. The construction is analytic in the s parameter and, therefore, makes sense in the sine-Gordon theory.

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Isomorphism of critical and off-critical operator spaces in two-dimensional quantum field theory

Abstract: For the simplest quantum field theory originating from a non-trivial fixed point of the renormalization group, the Lee-Yang model, we show that the operator space determined by the particle dynamics in the massive phase and that prescribed by conformal symmetry at criticality coincide.

Cited by 19 publications

References 33 publications

Sine-Gordon multisoliton form factors in finite volume

Sine-Gordon multisoliton form factors in finite volume

The complex sinh-Gordon model: form factors of descendant operators and current-current perturbations

Form factors of descendant operators: reduction to perturbed M (2, 2s + 1) models

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