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Register a new userFinite Volume Spectrum of Sine-Gordon Model and its Restrictions
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Authors
G. Feverati
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In this thesis, we review recent progresses on Nonlinear Integral Equation approach to finite size effects in two dimensional integrable quantum field theories, with emphasis to Sine-Gordon/Massive Thirring model and restrictions to minimal models perturbed by $Phi_{1,3}$. Exact calculations of the dependence of energy levels on the size are presented for vacuum and many excited states.
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We examine the connection between the nonlinear integral equation (NLIE) derived from light-cone lattice and sine-Gordon quantum field theory, considered as a perturbed c=1 conformal field theory. After clarifying some delicate points of the NLIE deduction from the lattice, we compare both analytic and numerical predictions of the NLIE to previously known results in sine-Gordon theory. To provide the basis for the numerical comparison we use data from Truncated Conformal Space method. Together with results from analysis of infrared and ultraviolet asymptotics, we find evidence that it is necessary to change the rule of quantization proposed by Destri and de Vega to a new one which includes as a special case that of Fioravanti et al. This way we find strong evidence for the validity of the NLIE as a description of the finite size effects of sine-Gordon theory.
We present an expression for the generating function of correlation functions of the sine-Gordon integrable field theory on a cylinder, with compact space. This is derived from the Destri-De Vega integrable lattice regularization of the theory, formulated as an inhomogeneous Heisenberg XXZ spin chain, and from more recent advances in the computations of spin form factors in the thermodynamic limit.
The semi-classical spectrum of the Homogeneous sine-Gordon theories associated with an arbitrary compact simple Lie group G is obtained and shown to be entirely given by solitons. These theories describe quantum integrable massive perturbations of Gepners G-parafermions whose classical equations-of-motion are non-abelian affine Toda equations. One-soliton solutions are constructed by embeddings of the SU(2) complex sine-Gordon soliton in the regular SU(2) subgroups of G. The resulting spectrum exhibits both stable and unstable particles, which is a peculiar feature shared with the spectrum of monopoles and dyons in N=2 and N=4 supersymmetric gauge theories.
Extending our previous construction in the sine-Gordon model, we show how to introduce two kinds of fermionic screening operators, in close analogy with conformal field theory with c<1.
We study one-point functions of the sine-Gordon model on a cylinder. Our approach is based on a fermionic description of the space of descendent fields, developed in our previous works for conformal field theory and the sine-Gordon model on the plane. In the present paper we make an essential addition by giving a connection between various primary fields in terms of yet another kind of fermions. The one-point functions of primary fields and descendants are expressed in terms of a single function defined via the data from the thermodynamic Bethe Ansatz equations.
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