Notes on string theory #5: Modifying the Polyakov action (cosmological constant and Ricci scalar)

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 …

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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 …

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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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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}. \} \ \ …

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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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