My first exposure to physics was A Brief History of Time by Stephen Hawking, which I first picked up when I was around 8 or 9. It didn’t spawn an immediate infatuation with physics, but it did sow a dormant interest that I would only fully appreciate later on. This was primarily because I did not know of any introductory physics resources, so my knowledge of “actual physics” was only school-level until around 9th grade - although I was, and will always remain, a huge science enthusiast. This was when I found a solid book on Newtonian mechanics, and on completing it, decided to pick up Griffiths’ Introduction to Quantum Mechanics to put my multivariable calculus skills to the test. It was probably midway through this book that it dawned on me that I wanted to pursue a degree at least partly in physics.
My current interests primarily lie in theoretical high energy physics, broadly spanning quantum field theory, gauge theories, particle physics, supersymmetry and string theory. That said, I absolutely love solving classical mechanics and electrodynamics problems, they’re great fun and they keep your mind sharp too. Since I’m an avid programmer too, I often try to create simulations and visualisations related to or inspired by my physics learning. Some of my favourite topics in physics include:
- 2+1D Quantum Gravity and the AdS3/CFT2 correspondence
- Quantum Anomalies
- Non-perturbative phenomena like solitons and D-branes
- Holography and Black Hole Thermodynamics
- Topological String Theory
- Chiral Perturbation Theory and Large N QCD
On this blog I’ll be writing both technical and non-technical accounts of a wide range of physics topics that I find interesting.
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We get a little computational 08 Jun 2022
Hi, I’m back again, returning after a somewhat extended hiatus from physics. For one thing I’ve been doing a lot of competitive programming practice (Leetcode, Codeforces, Google Code Jam Archives - dynamic programming is a favourite), which honestly deserves a whole post of its own. Back in the realm of physics, a lot of my current exploration is in computational phys/chem, something which I hadn’t looked into much until now. Here’s what I’ve been working...
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What is ... superconductivity? (Part I) 19 Oct 2021
You’ve probably heard of superconductivity - isn’t it the phenomenon where a material has zero resistance, usually at very low temperatures? It sounds simple, but it actually requires the full force of quantum mechanics to describe it, and this is what Bardeen, Cooper and Schreiffer did in their Nobel-prize winning work, 60 years ago. In this two part series, I’ll aim to describe the physics behind superconductors, which will involve interesting detours into solid state...
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What is ... the muon $g-2$ experiment? (Part I) 01 Oct 2021
Definitions and History
Let’s talk about electrons. Classically, you can model them as a ball of charge whose radius is determined by equating the electrostatic potential energy that it generates with its rest mass energy. Now interestingly we find that an electron interacts with a magnetic field - something that we would expect from a rotating charged body. But the magnitude of angular momentum that is consistent with experimental observations of the electrons in magnetic...
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cond-mat and hep-th, the best of friends 14 Sep 2021
Lately, as you may have noticed from my previous posts, I have become increasingly interested in learning condensed matter physics (side-by-side with some high energy physics). It’s incredible - something as simple as a linear chain of spins (say $\vert\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow…\rangle$) exhibits a wonderful range of phenomena, including duality, phase transitions, emergent phenomena, spinon waves, and can describe even paramagnets and ferromagnets! Indeed, the appeal of these statistical models to me lay not only their ability...
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Color charge is not the analogue of electric charge 14 Sep 2021
Let’s say it loud and clear one more time for the people at the back: “Color charge is not the analogue of electric charge”.
This is one of those misconceptions which is spawned from annoying terminology: “color charge” as referred to in popular science accounts (red, green, blue) doesn’t refer to a charge in the conventional sense. There are a couple of places you may have noticed this: firstly, how come electric charge is observable...
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An Introduction to QCD 10 Sep 2021
This post mostly serves to describe a few preliminary concepts in quantum chromodynamics as an introduction to a few more in-depth QCD posts that I have planned. Later on in this series I’ll aim to illustrate analogues between a few phenomena from gauge theory in the context of condensed matter and other low energy phenomena.
Introduction
Electrical charge is a reasonably simple concept to understand: electrons have a charge of $-e$, positrons (anti-electrons) and protons...
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A Tale of $(\mathcal N =)$ 2 Supersymmetries 14 Aug 2021
I didn’t know much supersymmetry a couple of weeks ago - only as far as supermultiplets and superfields. In particular, I didn’t know how to construct supersymmetric gauge theories and the like, so that was my starting point. Also, I’ve found the new exotic territory (that I describe in this post) extremely appealing: I love the way that SUSY gauge theories can be lifted to string theory, the way that statistical field theoretic notions like...
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Baryons, Skyrmions and Topological Twists 07 Jul 2021
In my previous learning journey, I’d mentioned about baryons being topological twists in the pion field. By popular request, I will be giving a lightning review of what this construction, known as the Skyrmion model.
Before the QCD model of quarks and gluons was definitively established, the leading model for nuclear interactions was the pion model. A number of different pion fields packaged neatly into a larger, composite field (using the generators of $\mathfrak{su}(N_f)$) interacted...
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Strings Conference 2021 04 Jul 2021
I recently attended the Strings 2021 conference! An annual conference, it takes place over a span of two weeks, in a different country across the globe each year, with the pre-eminent names in high-energy physics being invited to speak in front of hundreds of graduate students, postdocs and faculty. It’s always been in-person - until this year. For the first time ever, the Strings conference has been organised online, which meant that participation has shot...
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At the Confluence of HEP and LEP 30 Jun 2021
I’ve found myself exploring some really intriguing and novel (at least to me) topics recently. In particular, an underlying theme of many of these is that they are topics at the crossroads of advanced field theory and elements from other areas of physics:
The instanton fluid model The thermodynamics and bulk propagation in the chiral condensate The XY model and the Kosterlitz-Thouless transition - it’s a statistical model which exhibits duality with magnetic fields. It...
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The Many Faces of String Theory (Part IV) 15 Jun 2021
String Dualities
The five superstring theories that we’ve been constructing are all beautiful, but the fact that there are five of them in the first place is somewhat mysterious. This puzzled string theorists long past the first superstring revolution, but the second superstring revolution brought with it a radical idea - what if all these ostensibly different theories were really related, and so incarnations of a deeper, more fundamental theory?
Let us motivate the nature...
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The Many Faces of String Theory (Part III) 12 Jun 2021
In the previous post, we looked at the construction of superstring theory, but to our surprise, found two slightly different methods of constructing it! Now we will explore what the difference between the two is, and whether they are consistent. Be prepared for a couple of surprises along the way.
Superstring theories!?
But first, a detour into spin. To this date, spin remains the most misleading piece of terminology since nothing is actually spinning in...
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The Many Faces of String Theory (Part II) 12 Jun 2021
In the last post, I described bosonic string theory and its limitations. A natural method to augment the theory is to introduce supersymmetry, an established idea from quantum mechanics.
A Foray into Supersymmetry
It is imperative to take a momentary step back and describe supersymmetry in general, unrestricted to the confines of stringy physics. The premise is straightforward: supersymmetry posits the existence of one (or more!) particles corresponding to each existing particle in the model....
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The Many Faces of String Theory (Part I) 12 Jun 2021
Everybody has heard of string theory. Depending on your other interests and prior beliefs, you may either see it a mystical, unattainable orb-like existence atop a fortress, the one true, elegant theory of everything, or a colossal drainage on the worlds’ intellectual resources.
Regardless of the physical ramifications, it is undeniably a mathematically beautiful construction. In this post, I’ll attempt to illustrate, non-technically, some of the aspects and history of string theory. The only thing...
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The Great Gravitational Paradigm Shift 07 Jun 2021
Physics-wise I’ve enjoyed reading about instantons, large N gauge theories, topological string theory (I definitely recomomend the review by Vafa, it delves into toric geometry) and some superstring theory (RNS formalism, GSO projection, black hole microstates). Some other cool stuff is viewing the string B-field as a cohomology class, and probing the geometrical structure of CFTs (the sort of thing they teach mathematicians about QFT and CFT). That said, I feel like my current interests...
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Who Doesn't Love D-Branes and Anomalies? 20 Apr 2021
String theory (and indeed AdS/CFT) in itself is a huge vortex that one gets sucked into, so I am cautious about spending too much time there - besides, there is something entirely unsatisfying about learning something at the pinnacle of physics research as AdS/CFT from distilled lecture notes without a sufficiently strong background in strings, and indeed, an appreciation of other fields of HEP. That said, I am very fond of D-brane dynamics.
Gauge theories:...
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String Theory Again (gone mathematical) 25 Jan 2021
I’ve primarily been exploring mathematical physics these days, following a breakthrough in my understanding of classifying spaces - this opened up a lot of doors to interesting stuff like K-theory, Chern-Weil theory, Yang-Mills instantons (BPST for now, the nLab pages are fantastic) and geometric quantisation, which looks amazing so far. I’m continuing with bosonic string theory, and topological string theory also struck me as elegant, so I picked that up too - on the mathematical...
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String Theory! 05 Jan 2021
My current course of action has inevitably led me to the grand culmination that is string theory. Rather than poring over lecture notes (not really that terse, introductory string theory lecture notes are surprisingly some of the most accessible ones I’ve seen), I opted for reviews and talks on the string theory and M-theory scene by some of the legends - Polchinski, Schwarz, Witten (actually I was reading his paper on 2+1D topological gravity -...
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Return of the King™ 26 Dec 2020
Hey everyone, I’m back after a short hiatus. I’ve decided to change the format a little: instead of documenting a complete learning journey (which, honestly, was quite strenuous), I’ll be giving a weekly (fortnightly?) summary of the things I’ve been working on/reading up on.
Since October, I’ve been doing a lot of physics, not much mathematics or programming at all - but this has changed recently after I started proper differential geometry: fibre bundles and...