Fermionic structure in the sine-Gordon model: Form factors and null-vectors

We are developing the algebraic construction for form factors of local operators in the sinhGordon theory proposed in [1]. We show that the operators corresponding to the null vectors in this construction are given by the degenerate Macdonald polynomials with rectangular partitions and the parameters t = −q on the unit circle. We obtain an integral representation for the null vectors and discuss its simple applications.

Section: Resultsmentioning

confidence: 99%

“…In the particular case of the Lee-Yang model a simple proof was proposed in [19,20]. Some promising steps towards finding the explicit correspondence has been made in [21,22]. The importance of resonances for understanding this problem was noted in [5,23] for the Lee-Yang model and in [24,25] for the Z N Ising model.…”

Section: Introductionmentioning

confidence: 99%

On form factors and Macdonald polynomials

Lashkevich

Pugai

2013

“…Beyond our approach, there is another approach to the form-factors of the SG model in cylindrical geometry [65][66][67][68][69][70][71]. We close the paper with some discussion concerning the comparison of our method with that of the series of papers [65][66][67][68][69][70][71].…”

Section: Jhep03(2018)047mentioning

confidence: 99%

“…We close the paper with some discussion concerning the comparison of our method with that of the series of papers [65][66][67][68][69][70][71]. In [65][66][67][68][69][70][71] the hidden Grassmannian structure of the XXZ model was exploited to determine the finite temperature 1-point functions [70] and ratios of infinite volume form-factors [71] of the local operators of the SG theory. In this approach the compactified direction is time and the compactification length corresponds to the inverse temperature.…”

Section: Jhep03(2018)047mentioning

confidence: 99%

Exact finite volume expectation values of $$ \overline{\varPsi}\varPsi $$ in the massive Thirring model from light-cone lattice correlators

Hegedűs

2018

In this paper, using the light-cone lattice regularization, we compute the finite volume expectation values of the composite operatorΨΨ between pure fermion states in the Massive Thirring Model. In the light-cone regularized picture, this expectation value is related to 2-point functions of lattice spin operators being located at neighboring sites of the lattice. The operatorΨΨ is proportional to the trace of the stress-energy tensor. This is why the continuum finite volume expectation values can be computed also from the set of non-linear integral equations (NLIE) governing the finite volume spectrum of the theory. Our results for the expectation values coming from the computation of lattice correlators agree with those of the NLIE computations. Previous conjectures for the LeClair-Mussardotype series representation of the expectation values are also checked.

“…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

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.