I thought I would experiment with a new type of weekly post. The premise is simple: I collect and describe some of the papers that I have read that are my favourite or that standout for whatever reason. The papers could be from the last calender week or fortnight (we’re working with loosely defined parameters). Or they could simply be papers I read some time ago that have been on my mind as of late.

I imagine these posts will be primarily research based. There will be heavy focus in string theory, and certainly on new research. But I am also one for obscure papers, and for reading across other areas, which means that one should expect an occasional mixture. Within this mixture, also expect some pedagogical literature to be flagged. The papers listed will be old and new. I am also still trying to figure out the balance between specialist and pedagogical language as a blogging principle, so I imagine these posts will be a product of trial and error during the fledgling stage production.

Without further ado, and in no particular order:

Complexity and Newton’s Laws – Leonard Susskind

Last week Leonard Susskind uploaded a new paper to the archive. It is was originally forwarded to me by my Professor, as it relates to some interesting questions which may form the basis of a future research project in holography theory.

In this paper, Susskind follows recent efforts to explore the holographic origin of gravitational attraction with a study of the size-momentum correspondence. We’re working in the SYK model here, which simplifies things rather nicely. Susskind argues that Newton’s laws are a consequence of, or can be retrieved from, this improved version of the size-momentum correspondence.

A theory of gravity on the boundary is something I’ve started thinking about in recent time. So this paper was enjoyable to read. I take inspiration from the Susskind’s efforts here, and also from the surrounding literature, insofar that I have more or less being intuiting my way to the same domain of enquiry. That is always nice. I will have to dig a bit deeper into some of the background literature (like on the CV correspondence, etc.). The notion and treatment of complexity in this paper is also intriguing (I had a time where I was obsessed with complex systems, generally, and I maintain interest in the study of their evolution).

One last thing before moving on: the notion that entropy may behave like observables over a code space is super intriguing.

Modular invariance and orbifolds – Stefan Huber

This paper offers a survey of the some of key tools and ideas pertaining to
modular invariance in string theory. It uses Di Francesco et al., “Conformal Field Theory” (1997), as its main resource. The contents of discussion are also those covered by Polchinski in Volume 1. In any case, the paper offers a useful review of modular transformations on the torus, focusing particularly on the constraints of modular invariance in the context of CFTs defined on the torus.

Lectures on Two-Loop Superstrings – Eric D’Hoker and D.H. Phong

Lecture notes by D’Hoker and Phong from 2002. Though some time has passed, I’ve found these notes helpful. The main attraction is their review, and treatment of, multiloop superstring perturbation theory. The emphasis to start is a first principles construction of a two-loop superstring measure on moduli space. Much of the discussion, and certainly also the techniques on display, are useful to review. The section on the vanishing of the cosmological constant (CC) is interesting, as is the chapter on compactifications and the CC. The subtlties of chiral splitting is something I need to look into more thoroughly. In fact, this paper is filled with facts and assumptions that I need to still need think about.

Graviton Dominance in Ultra-High-Energy Scattering – G. ‘t Hooft

I’ve been thinking a lot about graviton scattering and more generally about the uniqueness of solutions in string theory. There is actually a lengthy story to be told here, including a motivating discussion with my professor, which relates to what is below.

In this paper from 1987, ‘t Hooft studies high-energy scattering of two particles in which the energy is so great that the gravitational field of the particle comes into direct focus. Here, ‘t Hooft describes how this field consists of a “shock wave”. The physics and the calculations are interesting, and I recommend going through it. But the main reason I was thinking about this paper again in recent days can be found on p.62. ‘t Hooft notes that there is a rather striking similarity between the scattering amplitude computed and the well-known Veneziano amplitudes. Anyone familiar with string theory will know about the Veneziano amplitudes or will be on course to become familiar with them. The similarity is most curious, indeed! It is interesting to think about from a number of perspectives.

Anything by ‘t Hooft is brilliant. He’s one of my favourite physicists, and I’ve said before that I hope I will get to meet him one day.

Magic: The Gathering is Turing Complete – Alex Churchill, Stella Biderman, and Austin Herrick

To end with something off track, and also quite fun, a new paper was uploaded to the archive which seeks to argue that optimal play in Magic: The Gathering (MTG) is at least as hard as the Halting Problem. As an avid player, one thing that stands out about Magic is that the gameplay has incredibly high variance. This high variance almost renders the notion of optimal play to be a sort of platonic and not quite attainable concept which one nevertheless continuously strives to achieve. It is generally what makes MTG thrilling. One strives for optimal gameplay through a mixture of logical and well-reasoned decision making. Each choice, or play, tends to matter. Pattern recognition is essential. However, even the best of players, who, at any given time, may be playing one of the more optimally constructed decks given the format and the current meta, will inevitably suffer a series of loses. One reason, as the linked paper argues, is that deterministic outcomes in MTG are essentially non-computable. In some sense, as one necessarily strives for as optimal of gameplay as possible, there is some definite limit to which one can effectively configure a logical and well-reasoned structure for decision making; because, by design, the game is configured to produce a complex and even mildly chaotic system of variables and inconsistencies.

As I have yet to dissect the paper, including the methodology, I will reserve further comment on the author’s study. Given some free time, it will be intriguing to go through it systemically.