We come to the conclusion of Section 1.2 in Polchinski's textbook. In this note we'll discuss how there are two possible modifications that we can make to the Polyakov action (see last note) that preserve Poincaré invariance. The first is a cosmological constant term on the worldsheet. The second modification involves the scalar curvature $latex …

# Notes on string theory #4: Polyakov action

In our ongoing read through of Polchinski's textbook, we left off on page 12 having studied the first principle Nambu-Goto action $latex {S_{NG}}&fg=000000$ for the string. We have glimpsed early on why string theory is a generalisation - or, one could also say, deformation - of point particle theory. The generalisation from point particles to …

# Holiday reading list 2022

The end of term is here, and with that comes a much needed winter break. One thing that I enjoy prior to Christmas break is compiling a list of books for my holiday reading. It gets me excited for the holiday season. I also enjoy sharing books, and have grown to like the idea of …

# A rare glimpse of climate debate within the finer margins of reason

https://www.youtube.com/watch?v=5Gk9gIpGvSE It seems in the last decade especially narratives about climate have become increasingly saturated with a certain distinguishable hysteria, which, I would argue, is detrimental to rational discourse on what is undoubtedly an important issue of our time. It doesn't help that popular media coverage on climate science is generally poor, if not altogether …

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# Tameness and Quantum Field Theory

A paper by Michael R. Douglas, Thomas W. Grimm, and Lorenz Schlechter appeared on the archive yesterday. Admittedly, I haven't had time yet to properly work through it. From what I quickly skimmed last night, the paper mainly concentrates on the notion of tameness and how tame classes of functions can be applied in the …

# Number theory in physics

This summer I was expecting to be working mainly on an extended field theory and geometry project as well as pushing toward the conclusion of a study on double sigma models. But somewhat unexpectedly I've found myself also working on some interesting things at the interface of number theory and physics. It has to do …

# Generalised geometry #3: Symmetries

When doing generalised linear algebra, we want to study transformations that preserve the canonical pairing from the last note (of signature $latex {O(d,d)}&fg=000000$): $latex \displaystyle O(V \oplus V^{\star}) = \{A \in GL(V \oplus V^{\star}): \langle A_v, A_w \rangle = \langle v, w \rangle \ \text{for all} \ v,w \in V \oplus V^{\star}. \} \ \ …

# Book review: Fantastic numbers and where to find them

My PhD supervisor, Tony, has published a book. It's titled, Fantastic Numbers and Where to Find Them: A Cosmic Quest from Zero to Infinity. Full disclosure: I read one of the earliest drafts, which must have been about two years ago. It was quite enjoyable witnessing the book develop, hearing about new chapter plans, and …

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# Generalised geometry #2: Generalised vector space and bilinear form

Generalised linear algebra In the first note we introduced one of the fundamental structures of generalised geometry, namely the generalised tangent bundle $latex {E \simeq TM \oplus T^{\star}M}&fg=000000$. In the extension of the standard tangent bundle $latex {TM}&fg=000000$ to $latex {TM \oplus T^{\star}M}&fg=000000$, we are simultaneously extending linear algebra to some notion of generalised linear …

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# Notes on string theory #3: Nambu-Goto action

1. Introduction I haven't been keeping up with this as much as I would like, mainly because I have been busy. But I am committed to continuing to reupload many of my notes on Polchinski's textbooks. It is fun for me to go through it all again in my spare time, and I've noticed that …

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