Minimal string theories and their limits

This text is an introduction to recent work by Collier, Eberhardt, Mühlmann and Rodriguez:

• arXiv:2309.10846 – The Virasoro Minimal String

• arXiv:2409.18759 – The complex Liouville string: the worldsheet

• arXiv:2410.07345 – The complex Liouville string: the matrix integral

I am grateful to the authors for helpful discussions and correspondence, and to SciPost for invitations to review two of these articles. (As always with SciPost, the reviews are online.) I am also grateful to the string theory group at IPhT Saclay for inviting me to discuss this subject in their journal club.

 

Minimal string theories

In the worldsheet approach, a string theory may be constructed from a two-dimensional conformal field theory with the central charge c = 26, where we consider primary fields of conformal dimensions $\Delta=\bar{\Delta}=1$. These conditions on the central charge and conformal dimensions, called respectively criticality and marginality, are necessary for the string theory to be independent from the parametrization of the worldsheet. Alternatively, if we take the physical spacetime to be the worldsheet itself rather than the target space, we obtain a model of two-dimensional quantum gravity. In this interpretation, criticality allows gravity to remain topological at the quantum level.

Which conformal field theories give rise to string theories that are simple enough to be tractable, but complicated enough to be interesting? A simple recipe is to take a product of two theories: a theory called the matter CFT, which can in principle be arbitrary, and Liouville theory, which allows arbitrary complex values of c and Δ, allowing us to fulfill criticality and to build a marginal field from any diagonal field of the matter CFT. The resulting string theory is tractable provided the matter CFT is, given that Liouville theory is exactly solved.

A portrait of the blogger as a peer-reviewer

In a publish-or-perish system of scientific communication, large numbers of articles are written and submitted to journals. Editors face the challenge of finding peer reviewers for all these articles. Scientists who accept invitations to review, usually for free, play a vital role in the system. This gives them a lot of freedom to choose which invitations to accept, and to perform peer review as they wish. 

This blog post states my own current “code of conduct” as a peer reviewer: my answers to questions that arise whenever a researcher receives an invitation to review, or has an article to referee.

Should I review this article?

1. Only review for journals I would publish in. This means the publisher should not be Elsevier, the journal should be open access, should not have obnoxious formatting constraints, should not cost too much to the community, and should publish reviewer reports.

2. See the article’s full text before deciding. And the article should already be available on arXiv as a preprint.