Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vacuum energy of the Bukhvostov-Lipatov model   Bukhvostov and Lipatov have shown that weakly interacting instantons and
anti-instantons in the $O(3)$ 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].

22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc