How to pick a concrete PhD objective in this QFT/Gravity formalism?

[leo.]

I have a major in Mathematics and Mathematical Physics and I'm finishing a masters in Physics (just finishing to write down the dissertation really). I have also already enrolled the PhD course so that I need now to pick an advisor and a theme before june.

My main interest since the early days of the undergraduate course have always been in three major themes: quantum gravity (QG), general relativity (GR) and quantum field theory (QFT) as well as its variant in curved spacetimes.

Now, in my masters I decided to give a try to these new ideas of bringing quantum information and gravity together. Because of that I have worked on quantum information aspects of a free Klein-Gordon field on an eternal black hole background. It was nice but to be honest I decided that I don't feel like continuing with information theory on the PhD.

Since saying "QG, GR and QFT" is absurdly vague I tried to find something more concrete and found the paper "Lectures on the Infrared Structure of Gravity and Gauge Theories" by Andrew Strominger. I actually am interested in this since 2017 and I have reasons to believe this is a good idea for a PhD. Although I think this is highly subjective, a few "objective points" I have in mind are:

1. It brings together all the things I'm interested in, there's QG, GR and QFT as well as QFT in curved spacetimes, so I have the opportunity to work and gain experience with the three things I have interest and that I want to follow a carreer on;
2. Strominger says that the area is on "its infancy" and "there's a lot to be done". So surely this is good for starting a career;
3. Since it has so much to be done if one of these possibility fails there are several others; This makes me more comfortable since as far as I know having original results in a PhD is mandatory, so that not getting anything isn't an option;
4. There seems to be a large community working on this;

Now, I did talk to a professor on the department that has experience in QFT, has interest in gravity and is open for new ideas. He then told me to come up with a concrete thing that can be done with this formalism so that a research project can be written. He considers a "vague" project to be a bad idea and wants a concrete objective.

The issue is that I imagine that to be able to say: "well this has potential to be applied to this theoretical problem and I foresee that this is a possible result" requires a huge amount of experience that I don't have by now. In fact, I've enrolled a PhD course exactly to end with such a huge amount of experience in the involved themes!

For instance, Strominger wrote the section "Echoing triangles" showing a lot that can be done. I must be honest though that it is a bit overwhelming. In fact there seems to be many options (the black hole triangles, SUGRA, cosmology, superrotation symmetry, just to mention a few) and I actually don't know what is still open, what has already been exhausted and what can concretely be done.

So how could I come up with a "concrete objective" to write a research project? What are possible yet open questions fit for a PhD inside this formalism that I could consider?

Could someone point some viable research projects in this which lie in the intersection of quantum gravity, GR and QFT?

 

[Dale]

I need now to pick an advisor and a theme before june.

Pick your advisor first. Then have him advise you regarding the theme.

Your advisor is much more important for your success and happiness than your theme. Pick an advisor that works on generally interesting topics, but more importantly pick an advisor that impresses you on a personal level as being supportive, kind, and ethical.

Once you have a good advisor, be willing to be flexible on the topic. He or she likely has good reasons to steer you towards or away from certain topics and you likely may not appreciate the importance of those reasons.

 

[leo.]

Pick your advisor first. Then have him advise you regarding the theme.

I did that. The one I have already spoken to seems to be the only available advisor in the moment which has interest in QFT/gravity in the department. He asked me to come up with something concrete, however, so he asked for suggestion of some objective.

One remark is that on that department indeed there seems to be no experts working on the intersection QG/GR/QFT. There are professors with interest on that which agree to supervise work done in that area and so there are a few students that follow this route.

Once you have a good advisor, be willing to be flexible on the topic.

I think that it is not that I'm not being flexible. You see, I have just picked an (yet huge) area that I feel I can work with comfortably and start a career on. The professor agreed and said he has interest on it, but just asked me to come up with something concrete on that area. That is what I'm struggling to do, so that any help is highly appreciated!

By the way, of course one might say that I or the other students interested on those themes should simply move to another university where there are experts on that, but for my particular case that is not an option for several reasons, financial ones being central.

That said, I don't want to give up the theoretical physics career, nor work for 4 years on a PhD about something I don't believe in or don't want to work afterwards. To be honest, I've seem a few professors in the department trying to learn something different than what they did in their PhD's and because of their overall work load they simply never achieve it. I'm doing my best to not end up like that.

 

[Dale]

I did that. The one I have already spoken to seems to be the only available advisor in the moment which has interest in QFT/gravity in the department.

That is the exact opposite of the approach I am suggesting. Here you have chosen a topic first such that there is no choice in advisor remaining. It is a bad idea.

In the end you will be much happier working for an excellent advisor on a second-tier topic than for a poor advisor on a first-tier topic. Broaden your interests enough to look at three different professors and carefully consider them as people, not just as experts.

for my particular case that is not an option for several reasons, financial ones being central

Then for those same reasons I recommend that you consider a different topic. Given these constraints the odds of failure and frustration are very high if you follow your current course.