See also How to become a Good Theoretical Physicist, by Gerard 't Hooft (Nobel laureate).

This particular web essay is intended for university students interested in doing a PhD in string theory in the Department of Physics at the University of Toronto, locally known as UofT

(pronounced you of tea

). Much of this information should also be useful to students interested in doing a PhD here in particle theory or early universe cosmology.

I created this web essay in order to cut down on the work involved in responding to every bright student who expresses interest in working in my research field or research group. Please respect the effort involved in writing this essay by reading it to the end before emailing me. Thanks!

Quick guide to emailing:-

**I do not have the power to admit you to our PhD program, so please do not ask me to do so. E-mail enquiries regarding admissions or general aspects of supervision should be directed to the Physics Graduate Office**, not to me.- Email questions which are
*specific to my expertise in gravitational string theory*are the ones to which I am happy to respond in detail. I always enjoy hearing from bright students who believe they have something to offer my specific research program. Give me a good physics reason to reply to your email, and I will respond.

If you are interested in coming to UofT for a PhD, then you should start by browsing our Physics Department web pages, especially our graduate programme section which contains important application information. Please ensure that you plan well enough in advance to submit your complete dossier before the **deadline of December 1st**. (Note: new students start our programme in Fall term only; there is no Winter/Spring intake.) The admissions committee will then review your dossier. In our high-energy theory group, we are always on the lookout for smart students interested in working with us.

Like other good departments worldwide, UofT Physics is strongly commited to excellence and equity and therefore has written policies and procedures that ensure fairness in graduate admissions. The basic principle is that every potential PhD student should have equitable merit-based access to potential PhD supervisors. Decisions on whom to admit to our programme are made by a committee of professors representing various areas of physics. Merit is decided from the three main components of the application: the transcript (grades and awards), the recommendation letters, and the statement of research interests. If you know one of our faculty members well enough for them to comment meaningfully on your abilities, then you should probably ask them to write you a recommendation letter.

In considering where to apply to PhD programmes, a good rule is that you should be interested in working with ** at least three **professors in the department of interest, and preferably more. It is unwise to set your heart on working with any one professor - here or anywhere else. For instance, through no fault of your own, your professor of choice may have zero new advisory capacity when you arrive. Equally, any professor may be different in real life than how they appear in the abstract or on the web.

You have clearly already found my home page. Note that we also have several other profs here doing forefront research in high-energy theory and experimental particle physics, among other fields. My closest colleagues are Prof. Erich Poppitz, a particle theorist who has also worked on string theory in the past, and particle theorists Prof. David Curtin, Prof. Michael Luke, and Prof. Bob Holdom. More generally, our physics department has tons of exciting and fascinating areas of research, and cognate departments and institutes are very strong: see also the Mathematics Department, the Fields Institute, the Canadian Institute for Theoretical Astrophysics (CITA), and the Astronomy Department home pages.

In our theoretical high-energy physics ("T-HEP") group, we do not expect Masters or Direct-Entry students to match up with thesis advisors before arriving. Our overall graduate programme structure is deliberately designed to allow you to think and learn for a bit before settling this all-important issue. That said, we also strongly encourage you to start discussing possibilities early in your first academic term here. Procrastination never pays off. Please see the *choosing your research advisor* section of our graduate handbook for details. (Students with offers to enter our 5-year programme at 2nd-year PhD level must find an advisor before arriving; this kind of match-up has not happened often in the T-HEP group.)

The basic point is that you need to have significant discussions with potential advisors - and their current students - so you can learn precisely what they research and how they work with research students. Any given potential advisor will also want to ask you some questions, e.g. about your physics and math background, so they can scope out your suitability for working with them. The overall idea of these discussions is, of course, to allow you *both* to figure out if you are a good fit for each other.

Before taking on any graduate student (MSc or PhD), I chat with them during substantial face-to-face discussions, in line with department policy. I also require prospective grad students to have significant discussions with my colleagues as well, to get a sense for how our research group works. In particular, I have prospective students talk to my current students. My colleagues in high-energy theory have similar principles. We do not find it wise for anyone - either us or the prospective student - to start the PhD relationship without substantial discussions face-to-face: it is just too important to skimp on!

Please note: if you are stuck far away, e.g. in another country, and therefore unable to drop by for crucial face-to-face discussions, then computer technology can help. If this applies to you, please ask me directly via email about having (say) a Skype video session at a mutually agreed-upon time.

String theory as a subject can be technically challenging, and very beautiful. It involves a lot of theoretical physics and some mathematics. As an undergraduate applying to do a PhD in particle/string theory, you must have a strong grasp of Lagrangian mechanics, electromagnetism, and quantum mechanics, as well as linear algebra, multivariable calculus, and partial differential equations. If you have the chance to learn particle physics, statistical mechanics, and fluid mechanics as an undergraduate as well, I recommend it. More advanced useful subjects to study before starting string theory research are general relativity, quantum field theory, supersymmetric field theories, and differential geometry. Take as many of these subjects as you can, as early as you can. The list of things to know as a researcher is neverending.

I recommend that all string theory graduate students own copies of the classic textbooks *String Theory* by Joseph Polchinski (Cambridge, 2000) (both volumes), and *Superstring Theory* by Michael Green, John Schwarz and Edward Witten (Cambridge, 1988) (both volumes). A more introductory textbook, which is a beautifully constructed resource for beginners who want to learn the basic physics of relativistic [super]string theory, is *A First Course in String Theory*, by Barton Zwiebach (Cambridge, 2009 second edition). I also like *String Theory and M Theory: A Modern Introduction*, by Katrin Becker, Melanie Becker, and John Schwarz (Cambridge, 2007), which is more of a survey textbook.

One difficulty with picking string theory as a field to work in is that, like particle theory and a number of other highly abstract fields of physics, competition for academic jobs is fierce and there are very few jobs outside of academia which use its research skills directly. (The majority of horizontal job moves are made into financial mathematics.) String theory groups tend to be concentrated in research-intensive university physics departments offering doctoral degrees. In Canada, string theory groups are already established at UofT here in Toronto, at McGill in Montreal, at UBC in Vancouver, and at the Perimeter Institute in Waterloo.

Our group here benefits from an unusually strong Math department over the road, the Canadian Institute for Theoretical Astrophysics (CITA) upstairs, as well as the strong Astronomy department in the next building and the Fields Institute a hop skip and a jump away. Perimeter Insitute is also easy to visit for day trips.

If you have accepted an offer and are enrolled here, welcome!

The School of Graduate Studies (SGS) has a number of useful resources on its website, including Graduate Supervision Guidelines and Graduate Wellness Portal.

Tip: to get a decent, and humorously brief, description of professors' research be sure to attend the Physics Jamboree the day before classes start. The Beginning Of Term Party typically occurs straight afterwards.

Useful courses are plentiful on our Graduate menu, although it is worth noting that not all of the more specialized ones can be offered every year. In general, the best strategy is to use your opportunity to take interesting graduate courses to do two things: (a) to prepare for future PhD study in your specialized area of interest and (b) to fill in any important holes in your general physics knowledge.

If you are sure that you want to do research in high-energy theory at UofT, e.g. in my group, the following is my recommended set of courses, listed in order of priority. You should pick 3 per semester, or 4 if you would like to get all your coursework done in the first year.

Fall:

- PHY2403F
*Quantum Field Theory I* - PHY1483F
*Relativity Theory I* - PHY2315F
*Advanced Statistical Mechanics*or PHY1500F*Statistical Mechanics* - PHY1489F
*Introduction to High Energy Physics* - PHY1530F
*Fluid Mechanics*

Spring:

- PHY2404S
*Quantum Field Theory II* - PHY2406S
*Special Topics in High-Energy Theory*(if offered) - PHY1484S
*Relativity Theory II* - PHY1491S
*Current Interpretations of Quantum Mechanics* - PHY1600S
*Effective Communication of Science*

Generally, if you want to do a PhD in high-energy (particle/string) theory, in order to impress a potential PhD advisor at any university it helps to have good marks in your courses, especially in quantum field theory and relevant special topic courses. Independent initiative is also very carefully noted - for example, attending seminars, asking questions outside classes and course curricula, etc.

I normally take on one new PhD student about every two years. **Currently: I have two PhD students, and I am looking for a new student.** However, if a sufficiently outstanding candidate arises in an off

year, I will also consider taking them on, contingent on funds being available. In addition, I am always willing to give advice *face-to-face* to any student in high-energy theoretical physics looking for a graduate supervisor.

Graduate students in theoretical high-energy physics would be wise to plan on regularly attending our high-energy theory seminar series, to get to know our group members and to gain appreciation of the state of the art in research. If the level of seminars seems too high early on, you could take the initiative and start a pre-seminar meeting to discuss background material - try to find a senior grad student, postdoc or prof in the relevant sub-field to help explain jargon/technicalities. Mostly, we are delighted to respond to student initiative!

All graduate students, regardless of interest, would also be wise to make a habit of attending department colloquium on a regular basis. I strongly recommend that my own students attend colloquium every week, as matter of principle. The point of this is to develop well-roundedness as a physicist, and to open potential doors to multidisciplinary collaboration in future.

In addition, note that Teaching Assistantships are worthwhile because they help you learn how to teach, as well as earning you money. Getting TA experience during your PhD programme helps prepare for the rough-and-tumble of scholarly debate in your area of eventual expertise.

Finally: the Associate Chair for Graduate Studies Prof. William Trischuk and the Graduate Administrative Staff are a truly excellent resource, and I suggest that you get acquainted with them early in your time as a graduate student. The Graduate Office is on the third floor of the McLennan Physics (MP) building's Burton Tower, at the south-west corner. To get there, take the elevators to the 3rd floor, exit to the right, take another right turn, and keep going. Try not to bump into Krystyna Biel's desk!

I hope this was helpful for you.

-- Prof. Peet.