The Big Picture

Why is Quantum Gravity special?

When people think of quantum gravity, people think of a mystery, something we do not understand or is not within our reach. Quantum gravity is special in the sense that the tools we have to undertstand physics fail to help with QG. Imagine you have a tool box with many different tools but I give  you project that none of these tools help you with, if the screw driver does not fit in the screw you can't make it work or you cannot use a hammer for it. Now imagine you have no store nearby, what would you do? Well firstly you would do everything possible to make your current tools work, be creative or even create a new tool. Well that is what we are trying to do. Our tools do not exactly fit and we had to have a new idea for quantum gravity. 

There are many ways to explain why quantum gravity is hard but the is easiest and most intuitive is that the  tools we have are mainly based on scale separation. We usually define a theory and study it within a range of distance, by the distance I mean small to large with small being subatomic particles and large being the solar system. In that way we split our physics on the study of subfield based on the distances they study. An easy way to think about this is that if you want to study the trajectory of a rolling ball you just need to know its velocity and time travelled to determine its trajectory and in your calculation you did not consider what electrons do. This just means that whatever the particles inside the atoms of the ball are doing they do not play a role into determining its trajectory. Therefore, a doctor can understand what is wrong with you without needing to study your individual particles. Just imagine how chaotic that would be? So in a sense it is a gift that our universe has given us. 

But distance is not the only way to understand scale separartion but also in terms of energy and how fast an object is moving. For example, we know that when something is very fast relativistic effects start being important. 

The idea described here is that of UV/IR decoupling. This is something that gravity does not like. Black hole physics and their thermodynamic properties suprise us by telling us that gravity does not like UV/IR decoupling.

There are actually many different approaches to Quantum gravity by many smart people trying to tackle the problem from different points of view. All of them face difficulties and problems, some more severe than others which I will not pretend to fully understand but I can tell you about one, String Theory. String theory is very successful because it unifies the Standard Model with Quantum gravity and in principle it can be predictive at any energy scale. Although, that does not mean that we actually understand string theory at any energy level. But we can understand few fundamental principles which we will outline below.

String  Universality

The question is simple; Is it true that every quantum gravity comes from String Theory? This question is important to address because the answer can shed light on whether conclusions we draw from String Theory are right or incomplete. So is String theory helping us understand quantum gravity or misleading us? 

Let us try to address this question by looking at the easier cases i.e. theories with some supersymmetry. It is rather easy to see that the maximal theories with 32 supercharges all come from String Theory, these are just M-theory and IIB with their circle compactifications. The amount of supersymmetry is restricting enough to not allow many choices.

The next case would be 16 Supercharges. In 10 dimensions the answer is simple and chiral anomalies are helping us see that indeed the only possibilities are coming from String theory, these are the two Heterotic Strings.  How about other dimensions ? 

This question needs to be addressed in stages. Firstly, is the number of massless modes bounded? From String theory and the finiteness of Calabi-Yau conjecture (Reid's Fantasy) we would expect the answer to be yes. Next can we set exact bounds on the number of gauge fields and matter fields and do these match what we expect ? Next do the type of gauge groups and type of representations match? Do the exact theories match?

The more specific the question, the harder is to give a definite answer. But as we saw the increased amount of supersymmetry can be helpful to attempt to asnwer some of these questions. In a paper we wrote with Cumrun Vafa and Hee-Cheol Kim we found a bound on the number of vectors in any dimension d with 16 supercharges, the bound is r<26-d. This magically exactly matches the expectation from String theory and this success ignited fruitful research to further answer all the above questions. Here is a table that summarizes few of the results:

To reach these conclusions ingredients were combined as simple as unitarity and anomaly cancellation to more intricate like various Swampland Conditions. Let us open our cards and dive into the winning hand that was used to arrive at these results.

The Swampland Conditions are conditions formulated with the sole purpose to distinguish between low energy effective theories consistent with Quantum Gravity(Landscape) versus those that are not(Swampland). In other words they are fundamental statements about quantum gravity that we believe to be true. Some are inspired by String theory but their validity stands on arguments independent of String theory, for example based on Black Hole arguments. Some of the arguments are stronger than others and some more useful, in the sense of excluding theories that could never be coupled to gravity. Therefore, the Swampland Program has a dual purpose; Firstly. one wants to exctract clear conditions/conjectures about quantum gravity and working more focused to come closer to a proof. Secondly, one can use the conjectures to understand what do they actually teach us about quantum gravity and whether they can make concrete predictions about the possible Landscape. Therefore, one could think of the Swampland as a torch helpful to navigate the Landscape and provide direction for where to look for our universe as well as giving explanations for open questions in particle physics.