arXiv subjects

Davide Fioravanti

Publications and source records attributed to Davide Fioravanti.

64 records · Page 4Linked to original sources

arXiv2004

Geometrical Loci and CFTs via the Virasoro Symmetry of the mKdV-SG hierarchy: an excursus

We will describe the appearance of specific algebraic KdV potentials as a consequence of a requirement on a integro-differential expression. This expression belongs to a class generated by means of Virasoro vector fields acting on the KdV field. The ``almost'' rational KdV fields are described in terms of a geometrical locus of complex points. A class of solutions of this locus has recently appeared as a description of any conformal Verma module without degeneration.

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arXiv2003

Exact conserved quantities on the cylinder I: conformal case

The nonlinear integral equations describing the spectra of the left and right (continuous) quantum KdV equations on the cylinder are derived from integrable lattice field theories, which turn out to allow the Bethe Ansatz equations of a twisted ``spin -1/2'' chain. A very useful mapping to the more common nonlinear integral equation of the twisted continuous spin $+1/2$ chain is found. The diagonalization of the transfer matrix is performed. The vacua sector is analysed in detail detecting the primary states of the minimal conformal models and giving integral expressions for the eigenvalues of the transfer matrix. Contact with the seminal papers \cite{BLZ, BLZ2} by Bazhanov, Lukyanov and Zamolodchikov is realised. General expressions for the eigenvalues of the infinite-dimensional abelian algebra of local integrals of motion are given and explicitly calculated at the free fermion point.

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arXiv2003

Exact conserved quantities on the cylinder II: off-critical case

With the aim of exploring a massive model corresponding to the perturbation of the conformal model [hep-th/0211094] the nonlinear integral equation for a quantum system consisting of left and right KdV equations coupled on the cylinder is derived from an integrable lattice field theory. The eigenvalues of the energy and of the transfer matrix (and of all the other local integrals of motion) are expressed in terms of the corresponding solutions of the nonlinear integral equation. The analytic and asymptotic behaviours of the transfer matrix are studied and given.

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arXiv2001

Aspects of Symmetry in Sine-Gordon Theory

As a prototype of powerful non-abelian symmetry in an Integrable System, I will show the appearance of a Witt algebra of vector fields in the SG theory. This symmetry does not share anything with the well-known Virasoro algebra of the conformal $c=1$ unperturbed limit. Although it is quasi-local in the SG field theory, nevertheless it gives rise to a local action on $N$-soliton solution variables. I will explicitly write the action on special variables, which possess a beautiful geometrical meaning and enter the Form Factor expressions of quantum theory. At the end, I will also give some preliminary hints about the quantisation.

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arXiv2001

From the braided to the usual Yang-Baxter relation

Quantum monodromy matrices coming from a theory of two coupled (m)KdV equations are modified in order to satisfy the usual Yang-Baxter relation. As a consequence, a general connection between braided and {\it unbraided} (usual) Yang-Baxter algebras is derived and also analysed.

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arXiv2001

Hidden Virasoro Symmetry of the Sine Gordon Theory

In the framework of the Sine-Gordon (SG) theory we will present the construction of a dynamical Virasoro symmetry which has nothing to do with the space-time Virasoro symmetry of 2D CFT. Although, it is non-local in the SG field theory, nevertheless it gives rise to a local action on specific N-soliton solution variables. These {\it analytic} variables possess a beautiful geometrical meaning and enter the Form Factor expressions. At the end, we will also give some preliminary hints about the quantisation.

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arXiv2001

A braided Yang-Baxter Algebra in a Theory of two coupled Lattice Quantum KdV: algebraic properties and ABA representations

A generalization of the Yang-Baxter algebra is found in quantizing the monodromy matrix of two (m)KdV equations discretized on a space lattice. This braided Yang-Baxter equation still ensures that the transfer matrix generates operators in involution which form the Cartan sub-algebra of the braided quantum group. Representations diagonalizing these operators are described through relying on an easy generalization of Algebraic Bethe Ansatz techniques. The conjecture that this monodromy matrix algebra leads, {\it in the cylinder continuum limit}, to a Perturbed Minimal Conformal Field Theory description is analysed and supported.

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arXiv2000

Hidden local, quasi-local and non-local Symmetries in Integrable Systems

The knowledge of {\it non usual} and sometimes {\it hidden} symmetries of (classical) integrable systems provides a very powerful setting-out of solutions of these models. Primarily, the understanding and possibly the quantisation of intriguing symmetries could give rise to deeper insight into the nature of field spectrum and correlation functions in quantum integrable models. With this perspective in mind we will propose a general framework for discovery and investigation of local, quasi-local and non-local symmetries in classical integrable systems. We will pay particular attention to the structure of symmetry algebra and to the rôle of conserved quantities. We will also stress a nice unifying point of view about KdV hierarchies and Toda field theories with the result of obtaining a Virasoro algebra as exact symmetry of Sine-Gordon Model.

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arXiv1998

Non-Local Virasoro Symmetries in the mKdV Hierarchy

We generalize the dressing symmetry construction in mKdV hierarchy. This leads to non-local vector fields (expressed in terms of vertex operators) closing a Virasoro algebra. We argue that this algebra realization should play an important role in the study of 2D integrable field theories and in particular should be related to the Deformed Virasoro Algebra (DVA) when the construction is perturbed out of the critical theory.

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arXiv1995

Generalized KdV and Quantum Inverse Scattering Description of Conformal Minimal Models

We propose an alternative description of 2 dimensional Conformal Field Theory in terms of Quantum Inverse Scattering. It is based on the generalized KdV systems attached to $A_2^{(2)}$, yielding the classical limit of Virasoro as Poisson bracket structure. The corresponding T-system is shown to coincide with the one recently proposed by Kuniba and Suzuki. We classify the primary operators of the minimal models that commute with all the Integrals of Motion, and that are therefore candidates to perturb the model by keeping the conservation laws. For our $A_2^{(2)}$ structure these happen to be $ϕ_{1,2},ϕ_{2,1},ϕ_{1,5}$, in contrast to the $A_1^{(1)}$ case, studied by Bazhanov, Lukyanov and Zamolodchikov~\cite{BLZ}, related to $ϕ_{1,3}$.

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