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**Interviewer: How did you get interested in physics?**

**JUAN:** I was interested in understanding how things work, how the TV works, how the radio works, how technological things work. Then that led me to trying to understand the laws of electricity, and then I was interested in reading about the basic laws of physics. Then I was trying to understand the laws of more fundamental levels in the sense of what are the smallest things that govern the behavior of bigger things.

**Interviewer: Why is there a need for string theory and Extra dimensions?**

**JUAN:** We need to describe space-time in a quantum mechanical way because the classical laws in which we describe space-time are not valid in certain cases. We know that space-time is dynamical from the theories of Einstein. Einstein said that gravity is due to the dynamics of space-time, and why we know that the universe is expanding.

Now, if we go back in time, the universe, at some point, was very, very small and when it was very small the density was so high that we cannot apply classical equations. We really have to apply quantum equations, and string theory tries to build this quantum mechanical description.

We think that general relativity or Einstein’s theory should be replaced by something quantum mechanical when you reach these points like the beginning of the Big Bang, for example, or the interior of the black holes you also have a similar example of matter collapsing in a very small region of space-time and there you cannot describe space-time classically. You have to do it using quantum mechanics. String theory is a theory under construction that has been developed to describe quantum mechanical space-time.

**Interviewer: What is the most fundamental matter in string theory and extra dimensions?**

**JUAN:** The idea in string theory is electrons, photons, and gravitons are different modes of oscillation per string. So it’s the same string that’s oscillating in different ways and that would describe the different particles. That’s the basic idea. So, in string theory all particles have basically the same common origin.

**Interviewer: How many dimensions exist in string theory and extra dimensions?**

**JUAN:** If you want to connect string theory to our four-dimensional world we would have to start with a ten-dimensional space-time, which is the space-time in which strings live most naturally, and one has to consider four large dimensions for that space-time and six small dimensions.

**Interviewer: What role do extra dimensions have in explaining quantum gravity?**

**JUAN:** There is one particular scenario where within these internal dimensions we could have branes of different kinds. Branes are like membranes and these could be extended along all our four dimensions but they could be localized at one point in internal dimensions.

In that case, all the particles that make us would only live in this brane but the graviton would move in all of the internal dimensions. If those internal dimensions are very big then that is a way to explain this hierarchy between the scales of particle physics and the scale of gravity or to explain the weakness of gravity.

**Interviewer: What was the original motivation for your current research?**

**JUAN:** I was studying and many other people were also studying the dynamics of black holes in string theory. By thinking about this I was led to the duality between the two sides of a particle theory and the geometry.

**Interviewer: Describe your duality model (Anti-de-Sitter Space/Conformal Field Theory or “AdS/CFT”).**

**JUAN:** It’s the equivalence between a particle theory that lives on the boundary of some space-time and a gravity theory that lives in the interior of that space-time. So the duality is a relationship between a particle theory that lives on the boundary and a gravity theory that lives in the interior.

The idea is that a theory without gravity on the boundary is equal to a theory with gravity in the interior. It relates a theory without gravity to a theory with gravity. If you think that theories without gravity are simpler, it relates a more complicated theory, namely the theory with gravity, to a simpler theory, which is a theory on the boundary without gravity.

**Interviewer: How do strings come into the picture?**

**JUAN:** How do strings come in this picture? Strings are related to quantum gravity and so we described quantum gravity using strings. So, strings live in the interior where the gravitation theory lives.

**Interviewer: Describe the particles that live on the boundary.**

**JUAN:** Now, the theory on the boundary has certain particles called gluons, which are similar to the gluons of chromodynamics and these particles can form chains. So we can stack one following the other and form sort of necklaces or chains of these gluons and these are the chains that exist in this four-dimensional space. These chains have some thickness because these gluons move around.

The idea is that these chains that are moving here in the boundary are completely equivalent to the strings that move in the interior. That’s why strings appear in the gravitational description.

**Interviewer: How many dimensions exist in AdS/CFT?**

**JUAN:** If we want to use the duality, then we find that particle physics in four dimensions is equivalent to a theory of gravity in five dimensions, so we introduce an extra dimension, which could be infinitely big.

In this duality we have different examples. There are examples where the boundary is four-dimensional and the interior is five-dimensional, so then the theory on the boundary would be very similar to the theories we are used to. In particular, it’s a theory, which is rather similar to the theory of strong interactions which is called quantum chromodynamics (QCD). So, the boundary could be just simply a four-dimensional flat space.

**Interviewer: How is the interior space-time different than the one we observe in nature?**

**JUAN:** The five-dimensional space is a space, which has an extra dimension and at each point in the extra dimension we have four-dimensional space similar to our own but there is a gravitational potential that pushes us to the interior of the space-time. So a particle that sits at one point in the extra dimension would be pushed towards the interior. You have a geometry with constant negative curvature. The fact that you have a gravitational potential is related to the fact that the space is curved.

Now, we don’t live in a negatively curved space like this. We live in a space that is closer to positively curved space and so it might have a boundary but the boundary would be in the future, not in some spatial direction. We don’t know how to generalize this duality for cases like expanding universes where the boundary is in the future rather than being in some in a space-like direction.

**Interviewer: Can you give an analogy for the AdS/CFT model?**

**JUAN:** You could have a space-time, which is, let’s say, the surface of a sphere or an apple or an orange and then the surface or the skin of the apple would be the boundary and the rest is the interior. Then, you can have a theory that lives only on the boundary, that’s the particle theory, and an equivalent description would be the gravitational theory living in the interior.

**Interviewer: Can you describe a hologram and why it is analogous for duality?**

**JUAN:** The idea is that all the physics that occurs in the interior is recorded on the boundary of some region. In holograms, a three-dimensional image is stored on a two-dimensional photographic plate so you have the information encoded in these two dimensions but when you look at it you see a three-dimensional image. The idea is that in quantum gravity something similar would happen where you encode all the physics in the interior by some theory that lives on the boundary.

**Interviewer: How does AdS/CFT help solve the dynamics of black holes?**

**JUAN:** The duality gives us a description for one class of space-time and then you can use it to analyze various processes inside this space-time. If you have, for example, a black hole in the space-time, in a negatively curved space-time, you know that the black hole will obey the laws of quantum mechanics.

I’m saying this because due to the results of Hawking people had the suspicion that perhaps black holes violate the laws of quantum mechanics and if that were the case that would be dramatic for string theory. So if we were to discover that quantum mechanics is wrong then string theory would be wrong, and that would be a way to disprove wtring theory.

**Interviewer: What is a black hole?**

**JUAN:** A black hole is an object that forms when you put too much matter in a small region of space so that the gravitational forces become so big that essentially nothing can escape. Not even light can escape and that’s why it’s called black.

In the end you get this horizon and the black hole ends up being a region of space-time where it looks like there’s a hole in space. You go through this hole and then you can never come back out, and it was very surprising when these solutions were first found. It’s one of the strangest predictions of general relativity, of the theory that space-time can be dynamical. Space-time can bend; it can bend so much that it produces a hole in the middle of space.

**Interviewer: Why did Hawking’s research lead to a violation of quantum mechanics?**

**JUAN:** Hawking had noticed that if you consider quantum mechanical theory near a black hole you will start emitting particles quantum mechanically. This emission looked like the emission you got from a thermal object at high temperature.

Now, why would this hole in space have a certain temperature? It’s not clear. If you have just simply flat, empty space well it has no temperature. In this case you have this hole and depending on the size of the hole you have different temperatures. Ordinarily in any system in nature where you have finite temperature it means that the object is made out of little particles that are moving around.

So the question was what is moving inside a black hole? Something should be moving so you get this temperature, so this was the first problem.

**Interviewer: What was the second problem that Hawking proposed?**

**JUAN:** The second problem was the problem of information loss. Due to this Hawking realized that if this emission was exactly thermal, so perfectly thermal, then it would carry no information about what object made the black hole in the first place.

Since a black hole would form and emit this radiation and completely disappear because it’s losing mass to this radiation and, in the end, you would be left with nothing, you would have a situation where you would form the black hole in many different ways. They always evaporate in the same way and, therefore, the evolution would have different initial states that would lead to the same final state. This is not allowed in quantum mechanics.

In quantum mechanics if you have different initial states you should get different final states. The final states may look similar at first approximation but indeed they should be different. So, this was known as the information problem or the information loss problem or information loss paradox for black holes and so we’re trying to understand how to solve it.

**Interviewer: What is Hawking radiation?**

**JUAN:** A black hole has a horizon and the horizon is such that if you fall inside than you can never come back out, right? So this would lead you to think that black holes are perfect absorbers, so they’re completely black and they absorb everything.

However, when you consider quantum particles in a vacuum these quantum particles are constantly being created and annihilated. In flat space they are created and annihilated and nothing happens; you don’t have any net creation of particles but when you have a black hole horizon then out of this pair one could be emitted to infinity and one could fall into the black hole. So, this is essentially the origin of Hawking radiation.

**Interviewer: What effect does Hawking radiation have on a black hole?**

**JUAN:** In practice what it means is that if you have a black hole it would emit radiation at some temperature, which is related to the size. As you make the black hole smaller the temperature gets hotter and the radiation emitted by the black hole becomes hotter.

So, in practice it also means that a black hole can sometimes look white. If you have a very small black hole let’s say roughly of the size of a microbe it would look white. So, black holes are not really black. Hawking radiation implies that black holes are not really black. So, they look black and as you make them smaller that start glowing a little more into red and then as you make them smaller it becomes white.

**Interviewer: How does AdS/CFT explain Hawking radiation?**

**JUAN:** It says that Hawking radiation is an approximation to the exact answer. The exact answer is given by this gas of particles on the boundary and it allows you to compute things precisely in a way that information is not lost. If you use the duality it gives a more accurate description than Hawking radiation.

**Interviewer: Where is the black hole in Ads/CFT?**

**JUAN:** The black hole is inside. The boundary is always the same space; the boundary doesn’t change but the black hole horizon exists at some point in the extra dimension. Near the boundary the geometry is always the same but as you move inside you can either have a black hole or not have a black hole.

**Interviewer: What do you learn about the description of the particles on the boundary of a black hole that you didn’t know before?**

**JUAN:** The main lesson was the fact that this description is unitary. It obeys the laws of quantum mechanics. The main new thing is that, using these particles, you understand the entropy; you also understand the evolution of the whole system is according to the laws of quantum mechanics because the boundary particles obey the laws of quantum mechanics. That is what was not known before.

Now we understand that the temperature or thermal properties are due to the motion of the particles on the boundary and that explains the thermal properties of black holes from a microscopic point of view, the same way that we understand the temperature of the gas in this room in terms of the motion of air molecules.

**Interviewer: Is there any evidence for AdS/CFT in nature?**

**JUAN:** No. There is no evidence and the duality is a statement of equivalence between two classes of theories.

In a very precise way it is not applicable to anything that we know so far because the theories for which we know the duality are very specific and idealized configurations in string theory. However, there are many examples, which are fairly close to theories we have in nature.

**Interviewer: Are there applications for AdS/CFT?**

**JUAN:** It has been used to analyze or to get some intuition about theories in nature. So, for that it has been used and it’s useful as a theoretical tool for analyzing possible behaviors in nature.

The nature of the duality is such that when the gravity description is relatively simple the particles on the boundary are very strongly interacting, so they interact a lot with each other.

Now, theories of particles where the particles are strongly interacting are generally very difficult to understand and there are very, very few cases where you can understand anything about them. Now, we encounter in nature many situations where lots of particles are strongly interacting.

You can use this duality to be able to solve or to understand how in these certain cases of strongly interacting particles behave. Then, theorists use these examples as a jumping board for starting to understand the real, natural systems.

**Interviewer: Is AdS/CFT useful for solving systems with strongly acting particles as well as space-times?**

**JUAN:** You can also use it the other way. The duality is a kind of bridge, which you can cross in two directions. You can go from one theory to the other and vice versa. If your interest is really to understand particles that are strongly interacting then you can use the black holes for that purpose. If you don’t know what the thermal properties of these particles are you can use the black holes to deduce them. So, you use them in the opposite direction.