# Geometry, dualities and the string landscape

**A CNRS-Imperial joint PhD project conducted by:**

Prof Dan Waldram - Professor of Theoretical Physics and Coordinator of the Quantum Fields and Strings International Research Network (Imperial)

Dr Mariana Graña - Institut de Physique Théorique (CNRS)

Stephanie Baines - Imperial PhD Student

Veronica Collazuol - CNRS PhD student

Theoretical Physics attempts to answer some of the fundamental questions about the world around us: what causes us to stick to Earth’s surface? How did the observable universe begin? What is all this stuff made up of? Theoretical physicists use models or abstractions and mathematics to predict certain properties of physical phenomena, sometimes striking gold when their predictions later turn out to be measurably accurate in experiments. Einstein’s theory of relativity, formulated to explain gravity, describes a curved spacetime, in which space and time are warped by massive objects like stars, or blackholes, causing things like the formation of planets, solar systems and the expansion of the universe. Quantum mechanics, meanwhile, describes what exists at a subatomic level and how elemental particles interact with each other to form everything we see around us and plenty of things we don’t. Quantum mechanics does a good job at explaining all the really small stuff in the world, whilst gravity works really well at predicting most of the big things. Getting the two theories to marry up into a quantum gravity theory has historically caused a world of mathematical pain which was a problem because we live in a universe in which really big things AND really small things coexist.

## Voices of International Collaborations, Episode 3: Can you combine quantum gravity and quantum mechanics?

## Discover more about the project

### Open to read

**Quantum Gravity Project**

INTRO

What are the possibilities when scientists collaborate across borders?

*Enable great ideas to develop, Make new materials, revolutionise cancer treatment, unlock the secrets of the physical forces that shape our world.*

*Thee projects highlight some of the incredible collaborative science made possible by the International Research Centre, a joint venture between Imperial College London and the Centre National de Recherche Scientifique or CNRS in France.*

NARRATOR

Theoretical Physics attempts to answer some of the fundamental questions about the world around us: what causes us to stick to Earth’s surface? How did the observable universe begin? What is all this stuff made up of? Theoretical physicists use models or abstractions and mathematics to predict certain properties of physical phenomena, sometimes striking gold when their predictions later turn out to be measurably accurate in experiments. Einstein’s theory of relativity, formulated to explain gravity, describes a curved spacetime, in which space and time are warped by massive objects like stars, or blackholes, causing things like the formation of planets, solar systems and the expansion of the universe. Quantum mechanics, meanwhile, describes what exists at a subatomic level and how elemental particles interact with each other to form everything we see around us and plenty of things we don’t. Quantum mechanics does a good job at explaining all the really small stuff in the world, whilst gravity works really well at predicting most of the big things. Getting the two theories to marry up into a quantum gravity theory has historically caused a world of mathematical pain which was a problem because we live in a universe in which really big things AND really small things coexist.

PROF. WALDRAM

I'm Dan Waldram. I'm a professor in theoretical physics. So the biggest outstanding problem in theoretical physics is how you combine the ideas of quantum mechanics and Einstein's theory of gravity, which says that spacetime is curved and there's the curvature of space time that tells you why gravity exists.

NARRATOR

Professor Waldram is one of the Principle Investigators on this joint project. His areas of expertise span gravity, quantum field theory, as well as string theory and its relation to geometry. More on that later…

PROF. WALDRAM

And the project we're working on is about trying to really understand what quantum gravity is / to try and understand how combining these two things together, quantum mechanics and gravity, might restrict some of the things we see physically.

So our project is to try and understand how to do some of the maths and understanding some of the string theory which is sort of our only good quantum theory of gravity that we have.

We're interested in a particular set of fields, so that’s like certain types of particles. And we're interested in how their properties get constrained by the fact that quantum gravity's true. And to do that, we have to do a whole lot of mathematics that's associated to geometry, partly because gravity is about geometry.

NARRATOR

Fields in physics are basically a** way of quantifying the physical effects that different entities, from particles to planets, have on each other at a distance. **Think magnetic fields or force fields. And what does geometry have to do with gravity? Well imagine gravity warping one of these fields like a ball indenting a bed sheet. The shape of the sheet or field is dictated by geometrical principles.

PROF GRAÑA

I'm Mariana Graña, I work at the Institute of Theoretical Physics of CEA Saclay, and this is a mixed research institution between CEA, so the Comisaria Energia Atomic, and the CNRS. So we work in high energy physics, in particular string theory, which is one of the descriptions of quantum gravity, and there are certain conjectures on what an effective theory has to satisfy to be a good theory of quantum gravity. So at high energies, make it compatible with quantum gravity. And what we are trying to do is to show that this conjecture apply in a certain set, which is quite general. These conjectures are very hard to prove in general. So it just uses mathematics. We can show that one of these conjectures is true. So we don't need to use what's called construction in string theory.

NARRATOR

Fellow Principle Investigator Professor Graña is one of the leading thinkers on string theory, an idea proposed in the 60s as a unifying theory of everything. Instead of theorising elemental particles as dimension-less points, it defined them as loops of string, like 1 dimensional rubber bands which could vibrate in different energy states. Depending on how they vibrate in different dimensions the strings might be perceived in our world as matter, light or gravity. This explanation worked really well at low energy states. But up until recently, the maths fell apart at high energy states, failing to account for gravity. The other problem with String Theory is that generally it throws up a gargantuan number of possible models of the universe, or what theoretical physicists call conjectures. But after years of investigation by thousands of researchers, it appears that very few models of the universe are in fact plausible.

PROF WALDRAM

Mariana Graña's a real expert in what kind of constraints you get from requiring gravity and quantum mechanics to fit together. So that goes under something called the landscape and the swampland. So the swampland are the theories where you try and put them together and they don't work, so you throw them away. And the landscape is the one where you put them together and they work. So, what we're trying to work out is what properties tell you that some theory is in the landscape or in the swampland.

NARRATOR

Think of a swamp, in which only very occasional patches of land emerge from the water. One of the patches of land represents our own observable universe. All other plausible theories that stick out as patches of land are termed Landscape theories. The vast majority, which do not marry up with gravity are called Swampland theories. PhD Students Stephanie and Veronica hope to make headway in some conjectures of quantum gravity during their joint PhD programme.

STEPHANIE

My name is Stephanie Baines. I'm a PhD student in the Theoretical Physics group at Imperial College. And the topic of my PhD is; I work on a couple of different things, but the one particular to CNRS is looking into understanding this idea of linking quantum mechanics and a theory of gravity, which is a theory of a curved spacetime.

I'm interested in working on the mathematical side, whereas my partner in France understands much better the string theory side and different models that can be used to understand this link between gravity and quantum mechanics. And we bring those two skill sets together and try and see if we can figure out something new.

The biggest thing for me has been the expertise of my counterpart in France. So I know much more about the mathematical side of things and the geometry side of things, which is really linked to the gravity side. And her expertise is very much more in understanding the Swampland program as a whole and how that links to string theory. So what the different conjectures are that might enable us to decide whether or not a theory is a good theory for linking a gravity theory to quantum mechanics or not. And so I can lean into her expertise and she can lean into mine and I've learned a lot through having that collaboration.

VERONICA

I'm Veronica Collazuola, and I'm doing a PhD in France at the Institute of Theoretical Physics. And with my supervisor, we are working on string theory, and in particular, on aspects of quantum gravity that could be potentially appearing in our world at low energies.

NARRATOR

In a highly esoteric discipline like theoretical physics, discussing and sharing ideas is vital for scientists to make progress. Stephanie and Veronica have been able to make excellent use of both in person and online meetings.

VERONICA

I've been to Imperial for two weeks last year and this has been very helpful because it was basically when we started to put together the project, to start a collaboration, being together physically. And being able to talk and just write on the blackboard and share ideas is very important.

I think that this has been a very fruitful collaboration because with two different perspectives on physics, on the one hand, one is more phenomenological, the one we are pursuing with Mariana, so more focused on low energy features of quantum gravity. While with the help of Dan and Stephanie, we could push this a bit further and give it a more mathematical and solid background.

Having two supervisors is very good. It's true that there may be some misunderstandings of notations and things like that, but especially when you are learning, having different views on the same topic is really helpful actually.

STEPHANIE

Yes, I do hope to go to France as well. Having that opportunity to be able to travel with the grant of course is hugely beneficial. And it's about meeting the student out there or her meeting me. But it's also about being able to mix the groups. So when she comes, she obviously interacts with my colleagues here and when I go there, I'll interact with hers. And a lot about theoretical physics is about talking to people and just getting expertise from a wide range of individuals. So it's even broader than just the two person collaboration.

Bringing those different ways of thinking and the different emphases in the education makes certain things maybe more important and bigger in some minds than in others. And being able to mix that, it broadens me as a person and, yeah, it gives me a much more, a much broader way of thinking about things, not just on your research, but on life, too. And Yeah, the personal development, I think is priceless.

NARRATOR

String Theory has not been able to account fully for all the physical properties of the world, but it is being improved upon and has led to breakthroughs in understandings of the Big Bang, and advances in pure mathematics.

PROF WALDRAM

The CNRS collaboration has been fantastic. This is an example, I think of where you take people with slightly different expertise or different approaches, and by putting them together, you get something extra.

We seem to be getting close to be able to prove a particular conjecture about being in the landscape versus in the swampland. So that's exciting. And if we do, then there's a whole load of further things we could do with it. So probably over the next two, three years, the project can definitely keep going.

So of course we're working in theoretical physics and it's somewhat abstract. I think what's amazing is I'm always struck by how excited people get by these ideas. Some of the things we're working on, although not directly, it's all about what happens inside a black hole, what really goes on when someone falls into a black hole, what happens really early in the universe right after the big bang.

We're part of this much bigger effort to understand quantum gravity, which is going to answer those questions. If we're a mature society, one of the things that we want to do is to understand the world. And that's, that's what we're trying to do.

NARRATOR

The most fundamental questions that humans have ever asked happen to be the hardest. If we want answers to what we’re made of and where our universe comes from, it’s going to take a proliferation of ideas, collaboration across borders, and an awful lot of maths.

OUTRO

*Thank you for listening. If you are interested in knowing more about this project or in the general partnership between the CNRS and Imperial, you can reach out to the International Research Office at Imperial College, and don't forget to look out for our next audio focusing on another brilliant piece of research.*