String Conferences for the 2019/20 Academic Year

I’ve had to narrow my list of string conferences that I would like to attend during the 2019/20 academic year. In the best case, it is likely this year I will only be able to attend one more in person. So hopefully most, if not all, of the following conferences will be live streamed or recorded.

With the theme of my research this year, I’ve prioritised my list of conferences to be mainly on the topic of string geometry. That said, the Swampland conference in August 2020 organised by Eran Palti, Daniel Kläwer, Irene Valenzuela, and Timo Weigand is also one I have highlighted.

Here’s my current list along with links (where available), in order of date,

‘Geometry and Duality’ (2-6 Dec 2019) at the Max Planck Institute for Gravitational Physics in (Potsdam, Germany).

‘Supergeometry, Supersymmetry, and Quantisation’ (16-19 Dec 2019) at The University of Luxembourg (Esch-sur-Alzette, Luxembourg).

‘Strings and Geometry’ (28 April – 12 May 2020) at Utrecht University (Utrecht, The Netherlands).

‘Strings 2020’ (29 June – 03 July 2020) at the University of Cape Town (Cape Town, South Africa).

‘Eurostrings 2020’ (24 – 28 August) at the University of Oxford (Oxford, England).

‘Mathematical Foundations of the Swampland’ (17 August – 4 Sept 2020) at the Mainz Institute for Theoretical Physics, Johannes Gutenberg University (Mainz, Germany). This is the Swampland conference being organised by Eran Palti alongside Daniel Kläwer, Irene Valenzuela, and Timo Weigand.

I may add or subtract from this list over the coming weeks, depending on ongoing research commitments and a number of other variables. As things stand, it looks to be an exciting year.

A poster from 2005 promoting a pure spinor workshop.

Pure Spinor Formalism

In recent days, pure spinors have become my life. And that is by no means a bad thing.

I don’t want to divulge too much at this time. The short of it is that I’ve been looking into the pure spinor formalism for a possible research project. Whether the project comes to fruition or not has yet to be determined. Regardless of the outcome, the time will have been well spent as I’ve immensely enjoyed learning the topic. What is intriguing is the power of the formalism when studying superstrings on different curved backgrounds. It is also useful when studying multiloop amplitudes. More personally, I have also found it nice to work through and think about because there is some connection with my interests in twistor theory, among other things.

As it is quite a rich area, there is a lot to comment on. Given time, I will type and upload my own notes as a sort of tour through the formalism. For now I’ve put together a select list of preprint papers that give an overview, organised by date. I haven’t listed everything, and the reader may find other works that adequately study pure spinors. For me, I found it useful to simultaneously read [2, 3, 6] as review, having then marched on from there.

[1] N. Berkovits, ‘Super-Poincare Covariant Quantization of the Superstring’, (2000) preprint in arXiv [arXiv:hep-th/0001035 [hep-th]].

[2] N. Berkovits, ‘ICTP Lectures on Covariant Quantization of the Superstring’ [lecture notes], (2002) preprint in arXiv [arXiv:hep-th/0209059 [hep-th]].

[3] N. Berkovits and D. Z. Marchioro, ‘Relating the Green-Schwarz and Pure Spinor Formalisms for the Superstring’, (2004) preprint in arXiv [arXiv:hep-th/0412198 [hep-th]].

[4] N.I. Farahat and H.A. Elegla, ‘Path Integral Quantization of Brink-Schwarz Superparticle’, EJTP 5, No. 19 (2008) 57–64.

[5] C.R. Mafra, ‘Superstring Scattering Amplitudes with the Pure Spinor Formalism’, (2008) preprint in arXiv [arXiv:0902.1552v3 [hep-th]].

[6] O. A. Bedoya and N. Berkovits, ‘GGI Lectures on the Pure Spinor Formalism of the Superstring’, (2009) preprint in arXiv [arXiv:0910.2254v1 [hep-th]].

[7] T. Adamo and E. Casali,’Scattering equations, supergravity integrands, and pure spinors’, (2015) preprint in arXiv [arXiv:1502.06826v2 [hep-th]].

[8] N. Berkovits, ‘Untwisting the Pure Spinor Formalism to the RNS and Twistor String in a Flat and AdS_5 \times S^5 Background’, (2015) preprint in arXiv [arXiv:1604.04617v2 [hep-th]].

[9] N. Berkovits, ‘Origin of the Pure Spinor and Green-Schwarz Formalisms’, (2015) preprint in arXiv [arXiv:1503.03080 [hep-th]]

*Image: A 2005 poster by the IHES promoting a pure spinor workshop.

SiftS 2019

SiftS 2019 concluded on Friday. It was an enjoyable two weeks of study and discussion on topics in string theory and holography. Eran Palti and Kyriakos Papadodimas were for me the highlight of the event. This is not meant to take away from others, it is just that Palti and Papadodimas were one of the main reasons for my attending SiftS. I could sit and listen to Papadodimas talk physics for hours. And Palti’s lectures on the Swampland were outstanding, as expected.

If I had one minor personal grief about the summer school as a whole, it’s that there wasn’t enough pure string theory. But it is very likely that I would say this at a number of different engagements, with the exception perhaps of Strings 2019 and String-Math 2019, two of the main string conferences. So it is unfair to make any such complaint formal, and one must also be mindful that while string theory was the theme, the engagement wasn’t necessarily meant to serve pure stringy discussion.

All of this is to say that I am both thrilled and honoured to have had the privilege of attending SiftS 2019. To mark its conclusion, I want to take a moment to congratulate the SiftS organisers for putting together a terrific summer school. I also want to take a moment to thank everyone at the Universidad de Autonomous Madrid for their hospitality and support throughout my stay. My impression of the university before arriving was that it was one of the best in Europe, and I left the campus and the Instituto de Física Teórica UAM/CSIC with the same view. I can say with honesty that I very much look forward to my return at some point in the future.

***

Now that SiftS is over for the year, and with the conclusion of my admittedly brief holiday during the weekend, I have returned to my research and studies at the University of Nottingham. There is a lot to discuss and catch up on with Prof. Padilla, with a number of possibly interesting ideas percolating. My return to Nottingham also means that I will start actively blogging again. In addition to covering some interesting topics from SiftS 2019, I am also working on a number of research projects which will be nice to write about in the coming days, weeks, and months. I will also be continuing my series of string notes, where the reader and I are on our way to covering the whole of textbook bosonic and superstring theory. We will start from where we left off, namely an introduction to conformal field theory. (In the background, I am going to continue working on my blog to fix the LaTeX of older posts as a result the move).

With regards to SiftS 2019 in particular. I will not write about all of the lecture series and topics covered. Instead, I will focus on sharing my notes and thoughts from the lectures by Palti on the Swampland and by Papadodimas on the Black Hole Interior. This will serve as a nice opportunity to also reflect on some of their respective papers, and to summarise key arguments.

Some papers I’ve recently read, including a new one from Susskind (12/05/19)

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.

Polchinski_string theory_tracingcurves blog

Reading Polchinski: Notes on string theory – First entry, including a list of supplementary texts

As part of my Scattering Amplitudes blog, I would like to begin a project of sharing and explaining my own notes on string theory. These notes have a bit of a story. They were developed while self-studying string theory as a first-year undergraduate student, prior to my formal academic acceleration to post-graduate school in the same year. They are a product of a rigorous examination and review, organised around the central motivation to rederive the whole of bosonic and then superstring theory from first principles, or, where appropriate, at least from as close to first principles as possible.

The set of notes uploaded on this blog will, I suspect, be tailored to fit a more ‘blog friendly’ format. I cannot profess to be certain of the intended reader at this time, other than I would like to try to present my notebooks in a pedagogical way that also does not dilute the maths/physics. However vague sounding this may be, over time I am sure the structure of the notes will clarify.

As a first entry it is worth mentioning that my string theory notes, which I will upload to this blog over time, my also be updated from time to time to take on new views or clarified understanding. Such is the method of reason.

I should also like to add that the main structure on which my notes are based are primarily focused on reading Joseph Polchinski’s much celebrated two-volume text, ‘String Theory‘. That is to say, Polchinski is my default – the scaffold on which my studies are based. But while Polchinski’s approach defines the essential structure to my notes, the following list of supplementary texts have also proved useful. Various ideas, motivations and pedagogical approaches have been drawn from this list of texts, sometimes inspired word-for-word. This list of texts includes (in order of last name):

Katrin Becker, Melanie Becker, John H. Schwarz. (2006). ‘String Theory and M-Theory: A Modern Introduction‘.

Michael Dine. (2007). ‘Supersymmetry and String Theory: Beyond the Standard Model‘.

Michael B. Green, John H. Schwarz, and Edward Witten. (1987). ‘Superstring Theory‘ (Volume 1 and 2).

David Tong. (2009). ‘String Theory‘ [lecture notes].

Timo Weigand. (2015/16). ‘Introduction to String Theory‘ [lecture notes].

Kevin Wray. (2009). ‘An Introduction to String Theory’ [lecture notes].

Barton Zwiebach. (2009). ‘A First Course in String Theory‘.

I am not yet an expert in string theory. Perhaps one day that may be the case, as it seems increasingly clear that pure string theory is my future. For now, I am merely a humble student of the subject and thus humble correspondent. My hope is that by sharing these notes (and updating them over time, where necessary) another individual may find use in them in their own learning.

I close with one final comment. String theory is currently one of my favourite subjects, along with quantum field theory. To any readers who find interest, my hope is that you enjoy the maths and physics as much as I. Thanks for reading.

*Edited 20/04/19.