What, broadly speaking, is string theory, and how did this theory come about?

**Cvetic: **In understanding how nature works, we want to** **understand the origin of fundamental forces of nature. And in this context we explain particle physics in terms of quantum mechanical phenomena. Elementary particle physics is consistent with quantum mechanics, but we also have gravity theory that we want to describe in terms of quantum phenomena, and that’s where things get hard.

**Lin:** It’s like the people who invented gravity had a different language than people who invented quantum mechanics.

**Cvetic:** That’s the main motivation of string theory: Originally intended as a description of the strong nuclear force, people realized that it allows for a quantum description of gravity. The way we identify quantum particles in string theory, including quantum particles of gravity, is by vibrations, excitations of tiny strings. String theory as a consistent quantum theory does not live in three spatial/one time dimensions, but in 10 dimensions. So we are dealing with the idea of compactifying six extra dimensions, namely, shrinking them to small sizes. While unobservable to us, these dimensions can still be probed by the microscopic strings and affect how they behave.

But there is a byproduct here: The shrinking of extra dimensions allows us to start describing particle physics. We observe not only the quantum particle of gravity but also the quantum particle of, say, electromagnetic interactions, which we call a photon.

In some ways you say, “Oh gosh, extra dimensions, that’s trouble,” but these extra dimensions also naturally produce types of interactions in four dimensions other than gravity, which we did not ask for in the beginning. Depending on the geometric shapes of the extra dimensions, we may identify these interactions with other forces of nature, like electromagnetism and nuclear forces.

In our current understanding, these forces are described by the so-called standard model of particle physics, but this does not include gravity. And that’s where string theory becomes an interesting field of research.

What are the challenges of finally realizing Einstein’s dream of unifying the other forces with gravity?

**Lin: **If you think about music, it’s like someone invented the notation, but what we actually observe in an experiment is a particular piece. The problem is that we don’t have a** **good system that allows us to write down what we observe in experiments, or, to use that same analogy, what we listen to in a concert hall, using the system we have.

It’s like our sheet music can distinguish between half-tone steps, but there is other music that has finer intonational increments. So our current sheet music will never be able to capture that, and, if there’s a particular piece that has these kinds of changes, how do we capture these things?

String theory is trying to propose a new system of writing down music, a new system of writing down theories of quantum gravity. But it’s not just a system to write down what we know for our world because we don’t even know all the features that are worth writing down.

We have a few hints what specific features our system needs to provide, and what we are trying to do is explore more technical things, like do these kinds of mathematical tools actually help us in capturing features of the standard model.

Your paper relied on methods from the F-theory branch of string theory. What are the benefits of this approach, and what does having a quadrillion solutions really mean?

**Cvetic: **The beautiful thing about this regime of string theory is that we can describe its properties in terms of geometry: The shape of this additional compact space, how singular it is, how it determines properties of the particles in three space/one time dimension. So for certain properties, in particular to get the standard model particles out, the power of geometry helped us uncover examples where we can match it to the music of the standard model.

**Lin: **The quadrillion solutions are related to the question of how special is our universe, the standard model and the particle physics phenomena that we observe, in what we call the string landscape. From a particle physics perspective, people think that, if I change certain parameters of the standard model, our world would be very drastically different, so it is special in some sense.

In string theory we have this nice feature that everything comes in discrete numbers, so we can count how many solutions there are. What we show is that, yes, the standard model is special, but within string theory it has the potential to be realized in many different ways.

What are the challenges of your work, and where do you go next?

**Cvetic: **For consistency, the constructions from string theory rely on something called supersymmetry. We include supersymmetry because it’s a technical tool we need for deriving these properties, but it can be broken at large energies. This is an important issue because people would like to match, in all details, our constructions to experimental constraints where we don’t observe supersymmetry at low energies, so we would be required to address those things in more details.

**Lin: **That’s one of the conceptual problems of string theory. If someone builds a new detector and finds these additional particles, associated with supersymmetry, at some higher energies than what we are currently reaching in experiments, that would be an advance on the experimental side which could help us a lot. On the other hand, not observing supersymmetry in the near future does not mean that string theory is wrong. It just means that we need to develop new frameworks and methods to improve our toolkit.

In terms of what to do with these quadrillion examples, these are not just something to be put in a museum, but you can actually use these examples to test new conceptual frameworks and computational methods in string theory. Somebody else will maybe have some ideas, for example, how to break supersymmetry, and now that we have this huge ensemble to explore these ideas, and it’s so large that you could even think about using big data techniques.

It’s like you produce a bunch of cars, and, even if you just smash them into a wall to test if your airbags are working, they are still providing some usefulness.

What continues to excite you and inspire you about this area of research?

**Cvetic: **I think one of the strengths of the Penn effort is that we ask questions from theory that are relevant to our colleagues in experimental high energy physics. So on one side, the questions we are asking are questions related to things that high energy experimentalists are testing in colliders, and on the other hand we are using techniques of formal string theory that tie us closely to our math department colleagues.

**Lin:** What I find interesting about what we do, and more broadly what string theory provides, is the idea of dual descriptions for the same phenomena that suddenly makes certain aspects much easier to grasp. There have been these sorts of ideas floating around in theoretical physics, but it’s string theory that has made this notion of dualities much more present. These ideas have, for example, influenced works in condensed matter which have no immediate connection to string theory.

And if one thinks from the mathematician’s perspective, what’s also very intriguing is that suddenly, after centuries where mathematicians provided tools for physicists, we’re now at a stage where we can use our intuition to tell mathematicians what to do. That’s unprecedented throughout the history of science, that physics is now guiding math.

**Liu: **This interplay between physics and math is particularly fascinating to me in F-theory. The powerful dictionary between concepts in fundamental theoretical physics and beautiful abstract math allows us to translate many demanding questions that intrigue physicists into solvable questions in geometry. Conversely, our physical intuition can uncover novel theorems which are tough to prove under pure mathematical circumstances.

**Cvetic:** I think F-theory is amazing. But to understand on a deeper level it’s like uncovering something beyond quantum gravity or beyond string theory. I think that, specifically, the important role of geometry in string theory and more generally in theoretical physics, has led to tremendous conceptual progress, and we may be just scratching the tip of the iceberg of some of these fundamental ideas.