*money*and

*goods and services*.

In the debate about the carbon footprint of cryptocurrencies, Nature has recently published a one-page correspondence titled “Cryptocurrency mining is neither wasteful nor uneconomic”. This counter-intuitive claim provoked me to read the text in search of a non-trivial idea. To my shock and horror, the only basis for the claim is the trivial wordplay of using the same term “wealth” for both *money* and *goods and services*.

In its negotiations with Springer, the consortium Couperin that was in charge of most French researchers’ subscriptions had been modestly asking that Springer renounce “double dipping”, i.e. does not get paid twice for the same articles – once via subscriptions, once via open access APCs. But this would have meant decreasing subscription prices by 15%, while Springer has been used to yearly increases of the order of 3-5%.

Today’s news are that negotiations have broken down, and most French researchers are set to lose legal access to most articles published by Springer on April 1st. (See CNRS’s note on the subject, in French.) In such a conflict, researchers can stand up against the publisher by

**Update on April 3rd: **According to an email from Couperin, access to Springer journals has in fact not been cut off. It seems that Couperin got away with rejecting Springer's latest offer, and saying that they were willing to continue negotiating. So Springer was bluffing, and does not dare take a hard line against Couperin. If such a weak and ill-prepared consortium, with little support from researchers (who else is boycotting Springer?) can defeat Springer, pretty much anyone can.

**Update on April 11th: **There is now a petition called "Springer, we can do without".

Today’s news are that negotiations have broken down, and most French researchers are set to lose legal access to most articles published by Springer on April 1st. (See CNRS’s note on the subject, in French.) In such a conflict, researchers can stand up against the publisher by

- not complaining when they lose access to journals, and getting the articles elsewhere (which nowadays mostly means at Sci-Hub),
- boycotting the publisher, i.e. not submitting articles to its journals, and not working for them as a referee or editor.

Most French research institutions are set to lose access to Springer journals on April 1st. I am aware that this does not affect access to JHEP, which is covered by SCOAP3, and that in our field all articles are on arXiv anyway. However, as a matter of principle, I would like to protest Springer’s extortionate commercial practices, and to show solidarity with colleagues who will lose access to their own work. Therefore, I am suspending all new collaboration with JHEP, and I am declining to review this article.

If you only think of arXiv as a tool for making articles openly accessible, consider this: in 2007, a study showed that papers appearing near the top of the daily listing of new papers on arXiv, will eventually be more cited than papers further down the list – about two times more cited. And there is a daily scramble for submitting papers as soon as possible after the 14:00 EDT deadline, in order to appear as high as possible on the listing. The effect is not as perverse as it seems, as there is no strong causal relation between appearing near the top and getting more citations. (More likely, better papers are higher in the listing because their authors want to advertise them.)

The consequences of arXiv’s systematic use in some communities are actually so deep that a speciation event has occurred among researchers, and a new species of**arXivers** has appeared. Here I will try to explain how arXivers live, in order to help non-arXivers understand arXivers, and have an idea of what could happen to them if the currently proliferating clones of arXiv gained widespread use.

The consequences of arXiv’s systematic use in some communities are actually so deep that a speciation event has occurred among researchers, and a new species of

The original definition of Liouville theory by Polyakov in the 1980s was written in terms of a Lagrangian, motivated by applications to two-dimensional quantum gravity. In the 1990s however, Liouville theory was reformulated and solved in the conformal bootstrap approach. In this approach, the theory is characterized by a number of assumptions, starting with conformal symmetry. In order to actually define the theory, the assumptions have to be restrictive enough for singling out a unique consistent theory.

After assuming conformal symmetry, it is natural to make assumptions on the theory’s spectrum, i.e. its space of states. For any complex value of the central charge \(c\), the spectrum of Liouville theory is

\[\mathcal{S} = \int_{\frac{c-1}{24}}^{\frac{c-1}{24}+\infty} d\Delta\ \mathcal{V}_\Delta \otimes \bar{\mathcal{V}}_\Delta\ ,\]

After assuming conformal symmetry, it is natural to make assumptions on the theory’s spectrum, i.e. its space of states. For any complex value of the central charge \(c\), the spectrum of Liouville theory is

\[\mathcal{S} = \int_{\frac{c-1}{24}}^{\frac{c-1}{24}+\infty} d\Delta\ \mathcal{V}_\Delta \otimes \bar{\mathcal{V}}_\Delta\ ,\]

Historically, the French consortium Couperin has obtained poor results in negotiating with predatory publishers, mostly consenting to their high and increasing prices. This is not necessarily Couperin’s fault, although it does not help that Couperin’s leadership appears weak and ill-informed. Rather, this is a consequence of the basic economics of scientific publishing, with publishers systematically abusing their strong position. Even the Finnish consortium FinELib, which was determined to seek a good deal and enjoyed a fair amount of support from researchers, recently consented to one more extortionate deal with Elsevier.

However, recent developments suggest that Couperin could fare better in current and upcoming negotiations:

However, recent developments suggest that Couperin could fare better in current and upcoming negotiations:

Earlier this week, there was a mini-workshop in Paris called Couperin’s open science days 2018. (Original title in French: JournÃ©es sciences ouverte 2018.) I followed most of it via webcast, and I will now summarize some of the salient points. The videos are available online, but most of them are in French.

####
The German way: Horst Hippler and Ralf Schimmer

####

The most important messages came from Germany: the country whose academic institutions have thought seriously about scientific publishing, and have organized themselves so as to drive the needed reforms. The most salient manifestation so far has been the standoff with Elsevier, and it was nice to have further details on the strategy.

The English language has inherited many scientifc words from Latin: a *spectrum*, an *index*, a *torus*, a *formula*. Then which plural forms should we use: the Latin plurals two *spectra*, two *indices*, two *tori*, two *formulae*? Or the English plurals two *spectrums*, two *indexes*, two *toruses*, two *formulas*? The Latin and the English plurals of these words are both considered correct, but the Latin plurals are more widespread. I will nevertheless argue that using Latin plurals is impractical and illogical, and should often be avoided.

This post is about the issue of solving a nonlinear matrix equation that I raised on MathOverflow. This matrix equation determines the existence of single-valued solutions of certain meromorphic differential equations. The motivating examples are the BPZ differential equations that appear in two-dimensional CFT. For more details on these examples, see my recent article with Santiago Migliaccio on the analytic bootstrap equations of non-diagonal two-dimensional CFT.

While the ongoing “Cost of knowledge” boycott of Elsevier may not be very effective, the likely “no deal” hard exit of Germany from Elsevier subscriptions renews the boycott’s relevance, and maybe its urgency. It is indeed likely that most German universities and research institutions will lose access to Elsevier articles in 2018.

As a researcher, why would I continue publishing in journals that are in principle inaccessible to most of my German colleagues? Universal access to the literature via Sci-Hub is under increasing legal assault and should not be taken for granted. In these circumstances, boycotting Elsevier is no longer only a matter of fighting an obnoxious publisher, but also a basic necessity of ensuring that articles are accessible to their intended audience. (Unless one thinks that the intended audience is not the scientific community, but the paying Elsevier subscribers.)

Now it turns out that if I boycott Elsevier because of Germany, I may have to boycott Springer because of France.

As a researcher, why would I continue publishing in journals that are in principle inaccessible to most of my German colleagues? Universal access to the literature via Sci-Hub is under increasing legal assault and should not be taken for granted. In these circumstances, boycotting Elsevier is no longer only a matter of fighting an obnoxious publisher, but also a basic necessity of ensuring that articles are accessible to their intended audience. (Unless one thinks that the intended audience is not the scientific community, but the paying Elsevier subscribers.)

Now it turns out that if I boycott Elsevier because of Germany, I may have to boycott Springer because of France.

When working on conformal field theory, your life is very different depending on whether the dimension is two or not. In \(d=2\) you have that infinite-dimensional symmetry algebra called the Virasoro algebra, and in some important cases such as minimal models you can classify your CFTs, and solve them analytically. In \(d\neq 2\), your symmetry algebra is finite-dimensional, and you mostly have to do with numerical results. This not only makes you code a lot, but also incites you to make technical assumptions that are physically restrictve, such as unitarity.

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Degenerate fields in \(d=2\) CFT

####

What makes \(d=2\) CFT solvable in many cases is the existence of degenerate primary fields.

What makes \(d=2\) CFT solvable in many cases is the existence of degenerate primary fields.

Three years and three major revisions after it first appeared on Arxiv and GitHub (why GitHub? see this blog post), my review article on two-dimensional conformal field theory may be mature enough for appearing in book form. But with which publisher?

To answer this question, I should first say why I would want to have a book in the first place, since the text is already on Arxiv.

To answer this question, I should first say why I would want to have a book in the first place, since the text is already on Arxiv.

In two-dimensional conformal field theory, correlation functions are partly (and sometimes completely) determined by the properties of the fields under symmetry transformations. In particular, correlation functions of primary fields are relatively simple, because by definition primary fields are killed by the annihilation modes of the symmetry algebra. On top of that, there exist degenerate primary fields that are killed not only by the annihilation modes, but also by some combinations of creation modes. As a result, correlation functions that involve degenerate primary fields sometimes obey nontrivial differential equations, for example BPZ equations. Usually, these equations are deduced from the relevant combinations of creation modes, called null vectors.

Determining null vectors in representations of a symmetry algebra is often complicated, as the algebraic structures of the relevant algebras and of their representations can themselves be complicated. Even in the case of the Virasoro algebra, it is not easy to explicitly determine null vectors. It is however much easier to determine which representations do have null vectors, using the fusion product. For example, if we know degenerate representations \(R_{(1,1)}\) and \(R_{(2,1)}\) with null vectors at levels \(1\) and \(2\) respectively, we can deduce that the fusion product \(R_{(2,1)}\times R_{(2,1)}\) is degenerate and contains \(R_{(1,1)}\). The remainder of \(R_{(2,1)}\times R_{(2,1)}\) must therefore be a degenerate representation, which can be identified as \(R_{(3,1)}\), and has a null vector at level \(3\). (See Section 2.3.1 of my review article for more details.)

An important idea is therefore that it is not the structures of the algebras and representations that matter, but rather the structure of the category of representations, in other words their fusion products. This idea has in particular been developed in the works of Fuchs, Runkel and Schweigert. But how does this help us compute correlation functions, and determine the differential equations that they obey? In other words, can we determine differential equations from fusion products, without computing null vectors?

Determining null vectors in representations of a symmetry algebra is often complicated, as the algebraic structures of the relevant algebras and of their representations can themselves be complicated. Even in the case of the Virasoro algebra, it is not easy to explicitly determine null vectors. It is however much easier to determine which representations do have null vectors, using the fusion product. For example, if we know degenerate representations \(R_{(1,1)}\) and \(R_{(2,1)}\) with null vectors at levels \(1\) and \(2\) respectively, we can deduce that the fusion product \(R_{(2,1)}\times R_{(2,1)}\) is degenerate and contains \(R_{(1,1)}\). The remainder of \(R_{(2,1)}\times R_{(2,1)}\) must therefore be a degenerate representation, which can be identified as \(R_{(3,1)}\), and has a null vector at level \(3\). (See Section 2.3.1 of my review article for more details.)

An important idea is therefore that it is not the structures of the algebras and representations that matter, but rather the structure of the category of representations, in other words their fusion products. This idea has in particular been developed in the works of Fuchs, Runkel and Schweigert. But how does this help us compute correlation functions, and determine the differential equations that they obey? In other words, can we determine differential equations from fusion products, without computing null vectors?

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