Daniel Harlow's webpage

Welcome! I am a professor of physics at MIT, where I work on quantum gravity and quantum field theory. My long term goal is to understand the fundamental laws of nature, with a particular focus on how they affect the universe at the largest scales and inside of black holes. I am also an avid hiker and pianist. I grew up in some combination of suburbs near Cincinnati, Boston, and Chicago, and I went to Columbia University for college and Stanford University for graduate school. The goals of this website are to provide some information about me and to give some resources and guidance to aspiring physicists.

Research

You can find my publications on Inspire. My papers tend to be somewhat long, because I like to explain things from the beginning and avoid requiring readers to consult many other references. Some papers I'm particularly proud of are:

• Bulk locality and quantum error correction in AdS/CFT In this paper we explain that the natural mathematical language for understanding the emergence of spacetime in the AdS/CFT correspondence is that of quantum error correction, which is a formalism that was originally invented to describe protocols to protect quantum computers from noise. See here for a relatively accessible description.
• Wormholes, emergent gauge fields, and the weak gravity conjecture In this paper I explain how the factorization property of quantum field theory on a disconnected space requires any gauge fields in the dual gravitational description to have objects that are charged under them. I also explain how this happens naturally when the gauge field is emergent, and suggest that the same is true for gravity.
• The Ryu-Takayanagi formula from quantum error correction In this paper I show that any quantum error correcting code has a version of the holographic entropy formula originally proposed by Ryu and Takayanagi and eventually refined into the quantum extremal surface formula of Engelhardt and Wall.
• Symmetries in quantum field theory and quantum gravity In this paper we develop a general understanding of what is meant by gauge and global symmetries in field theory and gravity. We then use this understanding to argue that in quantum gravity there are no global symmetries. Along the way we found many other interesting things, for example a better understanding of the decay of the neutral pion in the standard model of particle physics, examples of field theories with continuous symmetries that do not lead to conserved Noether currents, and a new order parameter for diagnosing confinement in situations with dynamical quarks.
• Covariant phase space with boundaries In this paper we present a fully covariant version of Lagrangian and Hamiltonian field theory, building off of the covariant phase space formalism popularized by Iyer and Wald but systematically including total derivatives and boundary terms. The latter are particularly crucial in gravity, as the Hamiltonian itself is a boundary term, so not treating them properly rendered the whole formalism imprecise. Our approach works for theories with arbitrary (finite) numbers of derivatives appearing in the Lagrangian, and gauge constraints are incorporated automatically.
• The black hole interior from non-isometric codes and complexity In this paper we argue that the essence of Hawking's black hole information problem can be resolved if the quantum error-correcting code that describes the emergence of the spacetime inside the black hole has the unusual feature of being "non-isometric". This means that it deletes many of the states which naively would be valid configurations of the interior degrees of freedom. This seems to be a massive violation of locality, but we argue that this non-locality cannot be detected unless you do an operation which is exponentially complex in the entropy of the black hole. See here for a relatively accessible description.

Teaching

I have written a fair number of lecture notes and reviews on various topics. These include:

• Jerusalem lectures on black holes and quantum information These give a general overview to the black hole information problem, focusing on understanding the origin of Hawking radiation, black holes in the AdS/CFT correspondence, and the infamous "firewall" paradoxes. Now somewhat dated. Lectures originally given at the Hebrew University of Jerusalem in January 2014.
• TASI lectures on the emergence of the bulk in AdS/CFT An overview on the quantum-error-correction approach to understanding the emergence of bulk spacetime in AdS/CFT. Lectures originally given at the University of Colorado Boulder in June 2017, also at the Institute for Advanced Study in July 2018.
• Lecture notes for first-year undergraduate electromagnetism These are my lecture notes for teaching 8.022 at MIT, which is an introductory electromagnetism class aimed at potential physics majors. The mathematical level is relatively high, with the goal being to give a self-consistent logical development of the subject.
• Lecture notes for quantum field theory I These are my lecture notes for teaching 8.323 at MIT, which is the first semester of relativistic quantum field theory. The focus is on understanding the general non-perturbative structure of quantum field theory, with most applications deferred to later semesters.
• Lecture notes for quantum field theory II These are my lecture notes for teaching 8.324 at MIT, which is the second semester of relativistic quantum field theory. This semester introduces fermions, abelian gauge fields, spontaneous symmetry breaking, and the Higgs mechanism. Non-abelian gauge fields are left to the third semester.

Music

Here are some examples of me playing piano in various contexts:

• Body and Soul A live recording at the Stanford Coho in 2009, with Anthony Diamond on alto sax, Amrit Robbins on trumpet, Jazz Sawyer on drums, and a bassist who I can picture but whose name I can't remember.
• Minor Blues A live recording at the Stanford Coho in 2011. Piece by Kurt Rosenwinkel , performed with Amrit Robbins on trumpet, Benjamin Bautz on Sax, Carter Hunt on Bass, Ben Stanton on drums.
• Cold Fusion A studio recording from Brooklyn in 2012, with Princeton undergraduates. Piece by me, vocals by Charmaine Lee, and sax solo by Divya Farias.
• Hejira From the same studio recording, piece by Charmaine Lee
• First and second movements of Gaspard de la Nuit by Maurice Ravel. Recorded in the KITP lecture hall in 2018. I did learn the third movement as well, but unfortunately I don't have a good recording.

Do you want to come to MIT?

I often get emails from students at other universities who wish to come to MIT to do research. Unfortunately there are enough of these emails that for the most part I cannot respond to them. So I will instead give here some general advice about how you might be able to come here. The most important thing to emphasize is that you cannot come to do research at MIT if you do not apply to MIT. Our admissions process is very thorough, and you cannot avoid it just by sending me an email with a cv (the same is true for postdocs ). I also am not able to give you personalized advice or suggestions on your application: the admissions rate to our Center for Theoretical Physics is about one in fifty, so there are just too many applicants.

There are two ways that you can apply to come here to do research. The standard way is to apply to the PhD program in our physics department. If you want to be admitted you need to have a strong undergraduate course record, as well as substantial research experience. For the latter you need to have taken ownership of some task or project and carried it through - people who move around from project to project without committing tend to not do well. Your research experience doesn't need to be in the same field that you want to work on in graduate school: that you did it well is what counts. It is crucial that in your application you are as honest as possible about what you are interested in and who you hope to work with. Every year we have candidates who want to do theoretical physics, but make no mention of this in their application because they are told that it would make it harder for them to get in. This is academic dishonesty, and if you do it you are going to be disappointed when you arrive and find that the theory spots are filled by people who were more honest than you.

The second way you can apply to come to MIT is via our undergradaute summer research program, called MSRP. This program is designed to give undergraduates from US institutions that do not have strong research programs the opportunity to do research at MIT for the summer, with the goal of strengthening their graduate applications. MSRP applicants must satisfy additional eligibility criteria that you should carefully review before applying. MSRP is a great program, which I have worked closely with, and if you are eligible I encourage you to seriously consider applying!

How to succeed in graduate school in theoretical physics

The first thing to say is that there is no single path that works for everyone. There are many kinds of theoretical physicist, and there are many styles for doing theoretical physics. Some people like thinking about the big picture, while some people like doing detailed calculations. Some people like pencil and paper, while others like coding. Some people need to feel close to experiment, while other people like being close to mathematics. Your initial goal should be to figure out what kinds of questions you are curious about. Go to seminars, look at papers, talk to older students, listen to visitors, etc. You need to immerse yourself in what is going on at your institution, and figure out which topics are most exciting for you. After all if you aren't going to work on something you are excited about, you might as well get a real job and get paid for it. Once you know what you want to go for, there are two approaches for what to do next:

1. Jump into a project with your advisor and start doing things. These days this is the standard approach. There is nothing for learning something like doing it, and along the way you will understand more and more of what is going on and why. Your advisor will (or at least should) help keep you on track, and if you are lucky you'll see some publications in your first few years.
2. Spend a year or so studying the foundations of your chosen field before trying to work towards publishable results. This is the riskier approach, and the one which I myself took. It has the advantage that you develop more of your own picture for how things work and why, but the disadvantage that without the focus of a project you may not know what to work on day-to-day.

Regardless of which approach you take, there are a few essential points:

• You always need to be doing something, even if it isn't good. Doing research is very different from taking classes. When you are given a problem set in class, you know you will be able to solve it in a reasonable amount of time using the tools you learned about in class. When you encounter a research problem, at first you have no idea what tools might be needed to solve it, or even if it can be solved at all. Most of the time things are not working and you do not know why. The number one failure mode I have seen for theorists in graduate school is an unwillingness to take the next step because it may not be the right one. I'll save you the worry: your next step almost surely will not be the right one. That is part of the fun! What you need to do next is think about why it didn't work, and what other kind of step might work better instead. That one probably won't work either, but maybe it will fail for a different reason. So you'll have to try something else. Which will maybe work a little better, but then something else will break. And so on. A good research problem is like a good detective novel, where for most of the story you are acquiring data but you have little idea what is actually going on. Tolerating this uncertainty, or even better enjoying it, is an absolutely necessary skill to be a successful scientist.
• You need to learn to think for yourself. In theoretical physics, as in life, there is an all-too-human tendency to look to authority figures to do the difficult thinking so that we don't have to. Some level of this is perfectly sensible: why shouldn't we listen to people who have more experience in the field than we do? On the other hand those authority figures were educated in a different time to work on different problems, and if your field is at all an active one (and if it isn't then you should pick a different field) then those problems may no longer be the most interesting ones around. Your real goal should be to identify for yourself the next exciting problem, and senior people are there as resources for you to consult rather than oligarchs for you to follow.
• Sometimes you get lucky, and sometimes you don't. For better or for worse, luck plays a substantial role in determining scientific success. All the knowledge and persistence in the world will not help if you are working on the wrong problem, and depending where you are and who your advisor is you will be exposed to very different problems. Some people just happen to be in the right place at the right time, and some people face more obstacles by virtue of who they are and/or where they are from. You need to be ready to take advantage of good luck when you get it, and you need to be philosophical when you don't. Even though sometimes it really isn't fair.