## Friday, 4 September 2020

### Does this covariant function belong to some 2d CFT?

In conformal field theory, correlation functions of primary fields are covariant functions of the fields’ positions. For example, in two dimensions, a correlation function of N diagonal primary fields must be such that
\begin{aligned} F(z_1,z_2,\cdots , z_N) = \prod_{j=1}^N {|cz_j+d|^{-4\Delta_j}} F\left(\tfrac{az_1+b}{cz_1+d},\tfrac{az_2+b}{cz_2+d},\cdots , \tfrac{az_N+b}{cz_N+d}\right) \ , \end{aligned}
where zj ∈ ℂ are the fields’ positions, Δj ∈ ℂ their conformal dimensions, and $\left(\begin{smallmatrix} a& b \\ c& d \end{smallmatrix}\right)\in SL_2(\mathbb{C})$ is a global conformal transformation. In addition, there are nontrivial relations between different correlation functions, such as crossing symmetry. But given just one covariant function, do we know whether it belongs to a CFT, and what can we say about that CFT?

In particular, in two dimensions, do we know whether the putative CFT has local conformal symmetry, and if so what is the Virasoro algebra’s central charge?

Since covariance completely fixes three-point functions up to an overall constant, we will focus on four-point functions i.e. N = 4. The stimulus for addressing these questions came from the correlation functions in the Brownian loop soup, recently computed by Camia, Foit, Gandolfi and Kleban. (Let me thank the authors for interesting correspondence, and Raoul Santachiara for bringing their article to my attention.)

#### Doesn’t any covariant function belong to multiple 2d CFTs?

In conformal field theory, any correlation function can be written as a linear combination of s-channel conformal blocks. These conformal blocks are a particular basis of smooth covariant functions, labelled by a conformal dimension and a conformal spin. (I will not try to say preciely what smooth means.) In two dimensions, we actually have a family of bases, parametrized by the central charge c, with the limit c = ∞ corresponding to global conformal symmetry rather than local conformal symmetry.

## Thursday, 27 August 2020

### (2/2) Open access mystery: why did ERC backstab Plan S?

In my first post about the ERC’s recent withdrawal from supporting Plan S, I tried to explain ERC’s announcement using publicly available information on the ERC, Plan S, and their recent news. The potential dangers of this approach were to miss relevant pieces of information, and to give too much weight to calendar coincidences.

We are still waiting for a detailed and convincing explanation from the ERC, and for a description of their open access strategy if they still have one. Meanwhile, I would like to complete the picture based on informal contacts with a few well-informed colleagues. There emerge two potential lines of explanation.

## Wednesday, 22 July 2020

### (1/2) Open access mystery: why did the ERC backstab Plan S?

The European Research Council (ERC) just announced that they would withdraw their support for Coalition S, the consortium of research funders behind Plan S. Plan S is the valiant but not universally welcome attempt to impose strong open access requirements to research articles, without paying more money to publishers.

The ERC is Europe’s most prestigious research funder, and a main backer of Plan S. Without Plan S, the ERC has no open access strategy, and without the backing of ERC, Coalition S may not be big enough for succeeding. Why would ERC make this U-turn? I do not know, but let me gather a few potentially relevant pieces of the puzzle. The pieces are of three types:
• some context on the ERC and more generally on Europe’s research plans,
• the recently announced rights retention strategy by Coalition S,
• ERC’s meager and not very credible justification for their withdrawal.

## Tuesday, 3 March 2020

### With open peer review, open is just the beginning

#### Abstract

Open peer review does not just mean publishing existing reviewer reports, but should also lead to writing reports primarily for the public. We make a specific proposal for structured reviewer reports, based on the three criteria validity, interest and clarity.
This post is partly based on a joint proposal with Anton Akhmerov for improving the structure of reviewer reports at SciPost. Feedback from Jean-Sébastien Caux on that proposal is gratefully acknowledged.

#### Benefits of open peer review: the obvious and the less obvious

In the traditional model of academic peer review, reviewers’ reports on the submitted article are kept confidential, and this is a big source of inefficiency and waste. If the article is published, the readers can neither assess how rigorous the process was, nor benefit directly from the reviewers’ insights. If it is rejected, the work has to start all over again at another journal.

Open peer review, defined here as making the reports public, could help journals remedy the penury of reviewers: if applied to rejected articles, by avoiding duplicating effort, and if coupled with naming reviewers, by giving them better incentives to do the work. However, the consequences of open peer review may be more far-reaching. Published reports can indeed be used for evaluating the article’s interest and quality. In aggregate, they could be used for evaluating journals and researchers. For these purposes, they would certainly be better than citation counts.