Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some remarks on D-branes and defects in Liouville and Toda field
  theories   In this paper we analyze the Cardy-Lewellen equation in general diagonal
model. We show that in these models it takes simple form due to some general
properties of conformal field theories, like pentagon equations and OPE
associativity. This implies, that the Cardy-Lewellen equation has simple form
also in non-rational diagonal models. We specialize our finding to the
Liouville and Toda field theories. In particular we prove, that conjectured
recently defects in Toda field theory indeed satisfy the cluster equation. We
also derive the Cardy-Lewellen equation in all $sl(n)$ Toda field theories and
prove that the forms of boundary states found recently in $sl(3)$ Toda field
theory hold in all $sl(n)$ theories as well.

29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math