4 research outputs found
Vacuum energy of the Bukhvostov-Lipatov model
Bukhvostov and Lipatov have shown that weakly interacting instantons and
anti-instantons in the non-linear sigma model in two dimensions are
described by an exactly soluble model containing two coupled Dirac fermions. We
propose an exact formula for the vacuum energy of the model for twisted
boundary conditions, expressing it through a special solution of the classical
sinh-Gordon equation. The formula perfectly matches predictions of the standard
renormalized perturbation theory at weak couplings as well as the conformal
perturbation theory at short distances. Our results also agree with the Bethe
ansatz solution of the model. A complete proof the proposed expression for the
vacuum energy based on a combination of the Bethe ansatz techniques and the
classical inverse scattering transform method is presented in the second part
of this work [40].Comment: 28 pages, 10 figure
Bukhvostov-Lipatov model and quantum-classical duality
The Bukhvostov-Lipatov model is an exactly soluble model of two interacting
Dirac fermions in 1+1 dimensions. The model describes weakly interacting
instantons and anti-instantons in the non-linear sigma model. In our
previous work [arXiv:1607.04839] we have proposed an exact formula for the
vacuum energy of the Bukhvostov-Lipatov model in terms of special solutions of
the classical sinh-Gordon equation, which can be viewed as an example of a
remarkable duality between integrable quantum field theories and integrable
classical field theories in two dimensions. Here we present a complete
derivation of this duality based on the classical inverse scattering transform
method, traditional Bethe ansatz techniques and analytic theory of ordinary
differential equations. In particular, we show that the Bethe ansatz equations
defining the vacuum state of the quantum theory also define connection
coefficients of an auxiliary linear problem for the classical sinh-Gordon
equation. Moreover, we also present details of the derivation of the non-linear
integral equations determining the vacuum energy and other spectral
characteristics of the model in the case when the vacuum state is filled by
2-string solutions of the Bethe ansatz equations.Comment: 49 pages, 8 figure
Spectral Duality Between Heisenberg Chain and Gaudin Model
In our recent paper we described relationships between integrable systems
inspired by the AGT conjecture. On the gauge theory side an integrable spin
chain naturally emerges while on the conformal field theory side one obtains
some special reduced Gaudin model. Two types of integrable systems were shown
to be related by the spectral duality. In this paper we extend the spectral
duality to the case of higher spin chains. It is proved that the N-site GL(k)
Heisenberg chain is dual to the special reduced k+2-points gl(N) Gaudin model.
Moreover, we construct an explicit Poisson map between the models at the
classical level by performing the Dirac reduction procedure and applying the
AHH duality transformation.Comment: 36 page