Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Logarithmic conformal field theory, log-modular tensor categories and
  modular forms   The two pillars of rational conformal field theory and rational vertex
operator algebras are modularity of characters on the one hand and its
interpretation of modules as objects in a modular tensor category on the other
one. Overarching these pillars is the Verlinde formula.
  In this paper we consider the more general class of logarithmic conformal
field theories and $C_2$-cofinite vertex operator algebras. We suggest that
their modular pillar are trace functions with insertions corresponding to
intertwiners of the projective cover of the vacuum, and that the categorical
pillar are finite tensor categories $\mathcal C$ which are ribbon and whose
double is isomorphic to the Deligne product $\mathcal C\otimes \mathcal
C^{opp}$.
  Overarching these pillars is then a logarithmic variant of Verlinde's
formula. Numerical data realizing this are the modular $S$-matrix and modified
traces of open Hopf links.
  The representation categories of $C_2$-cofinite and logarithmic conformal
field theories that are fairly well understood are those of the $\mathcal
W_p$-triplet algebras and the symplectic fermions. We illustrate the ideas in
these examples and especially make the relation between logarithmic Hopf links
and modular transformations explicit.

15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph