In a recent article, Perlmutter investigated closed-form expressions for Virasoro conformal blocks. As a complement to that article, let me discuss what is known on such expressions, and what they are good for.

The definition of conformal blocks is the subject of an interesting discussion at Physics.StackExchange. Basically, conformal blocks are the universal building blocks of correlation functions, and are determined by conformal symmetry.

# Research Practices and Tools

## Friday, 13 March 2015

## Wednesday, 11 March 2015

### Conformal blocks at Physics.StackExchange

I realized that the first Gogle hit for "conformal blocks" was a discussion at Physics.StackExchange about "A pedestrian explanation of conformal blocks".

This discussion is quite interesting and there are a number of good quality answers. But these answers were written in the span a few days, and they do not amount to a complete or satisfactory explanation of conformal blocks.

Such an explanation should probably be written as a Wikipedia article. But before writing it, one should probably rewrite the article on conformal field theory, and more generally build a decent set of articles on that subject. So, as a quick fix, I just added my own explanation of conformal blocks to the discussion in question.

This discussion is quite interesting and there are a number of good quality answers. But these answers were written in the span a few days, and they do not amount to a complete or satisfactory explanation of conformal blocks.

Such an explanation should probably be written as a Wikipedia article. But before writing it, one should probably rewrite the article on conformal field theory, and more generally build a decent set of articles on that subject. So, as a quick fix, I just added my own explanation of conformal blocks to the discussion in question.

## Wednesday, 8 October 2014

### Reality of three-point structure constants in CFT, unitary or not

The reality of three-point structure constants in unitary CFT is a crucial ingredient of the numerical bootstrap in more than two dimensions. But what are the precise meaning and the proof of this property? Surely not all operators can have real three-point structure constants, since rescaling an operator by a complex scalar destroys this property. And the proof is not necessarily obvious, because the definition of unitarity as the existence of a positive definite scalar product is not directly related to three-point structure constants.

Fortunately I have received some explanations on these questions from Slava Rychkov. So here is what I understood from his arguments on unitary CFT, plus speculations of my own on non-unitary CFT.

Fortunately I have received some explanations on these questions from Slava Rychkov. So here is what I understood from his arguments on unitary CFT, plus speculations of my own on non-unitary CFT.

## Sunday, 28 September 2014

### Modular invariance in non-rational CFT

Modular invariance of the torus partition function is often the first -- and sometimes the only -- thing people check about a proposed CFT. There is a good reason for this: computing the torus partition function only requires knowing the characters of the representations which appear in the spectrum, whereas other consistency checks, such as crossing symmetry of the sphere four-point function, involve much more complicated conformal blocks.

However, modular invariance is neither sufficient, nor necessary for a CFT to be consistent.

However, modular invariance is neither sufficient, nor necessary for a CFT to be consistent.

## Wednesday, 24 September 2014

### Les critères d'inscription à l'HDR en Physique à l'université Paris-Sud

Bien que le dossier d'inscription à l'HDR soit décrit en détail sur la page de l'université, rien n'indique selon quels critères un candidat sera autorisé à s'inscrire ou non. Le dossier comprend naturellement une liste de publications et des indications sur les étudiants déjà suivis, mais combien faut-il de publications? et quelle expérience d'encadrement est nécéssaire? J'ai reçu récemment quelques explications à ce sujet de Réza Ansari, le correspondant HDR pour la physique théorique entre autres.

## Monday, 23 June 2014

### Bourses doctorales de l'ED PIF: quelques précisions

L'École Doctorale Physique en Île-de-France (ED PIF) vient de procéder à son premier concours de recrutement des doctorants. Ayant présenté un candidat (malheureux) à ce concours, et ayant eu des échanges avec certains membres du jury, je peux donner quelques éléments sur le fonctionnement du concours, dans le but d'informer les candidats potentiels aux prochaines éditions.

## Saturday, 7 June 2014

### Positive feedback loops in research funding

Funding research should mean sending money where it is most useful, considering the strength of the researchers to be funded, the interest of their projects, and how much these projects need money. However, in practice, already being well-funded or belonging to a well-funded institution is helpful, and sometimes even necessary, for a researcher to obtain funding. So there are positive feedback loops in research funding, which should be distinguished from other mechanisms that tend to concentrate research funding -- such as some people being better than others at getting money. (That these people are not necessarily the best researchers is not our subject here.)

Let's discuss some positive feedback loops:

Let's discuss some positive feedback loops:

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