# Full Logarithmic Conformal Field theory - an Attempt at a Status Report

## TL;DR

This paper reviews recent advances in logarithmic conformal field theories, focusing on their algebraic structures, conformal blocks, and progress towards a derived modular functor, highlighting new insights into bulk and boundary fields.

## Contribution

It provides a comprehensive status report on the development of logarithmic CFTs, emphasizing recent progress in understanding their modular properties and boundary phenomena.

## Key findings

- New descriptions of conformal blocks via modular functors
- Progress in understanding boundary fields and boundary states
- Advances towards a derived modular functor

## Abstract

Logarithmic conformal field theories are based on vertex algebras with non-semisimple representation categories. While examples of such theories have been known for more than 25 years, some crucial aspects of local logarithmic CFTs have been understood only recently, with the help of a description of conformal blocks by modular functors. We present some of these results, both about bulk fields and about boundary fields and boundary states. We also describe some recent progress towards a derived modular functor. This is a summary of work with Terry Gannon, Simon Lentner, Svea Mierach, Gregor Schaumann and Yorck Sommerh\"auser.