Research

In the following I will describe my research interests. If you think you might be interested in collaborating with me, do not hesitate to contact me at ivan_burbano@berkeley.edu. I welcome everyone to reach out, including undergraduate students!

The standard model of particle physics has been extremely successful at describing the elementary constituents of the universe. However, we know it is incomplete. An excellent retelling of the standard model, its achievements, and its limitations, can be found in this lecture by David Tong.

Quantum chromodynamics (QCD) is one of the sectors of this standard model. It describes the nucleus of atoms, its constituents, and the ways in which they interact. One of the fundamental difficulties in probing the standard model, and thus uncovering its limitations, is that analytic handling of this sector is beyond the scope of our current mathematical methods. This is evidence of undiscovered truths about the framework in which we describe the standard model, quantum field theory (QFT). We must then resort to advance computational methods which allow us to directly tackle the problem and extract its predictions.

Amongst these, lattice QCD has been the only systematically improvable method developed to directly probe QCD. In it we directly compute the path integral of a sibling of QCD, a statistical model known as Euclidean QCD. In order to do this we use Markov-chain Monte Carlo methods, which provides us with large ensembles of data. These are then analyzed using statistical bootstrapping methods to generate correlation functions. These have proven extremely useful in understanding the spectrum of QCD. A concrete example of this is the mass of the proton. Instead of being the simple sum of the masses of its constituent quarks, the mass of the proton is heavily dominated by the complex dynamics of the quark and gluon fields that it is made of.

More recently, big efforts have been done trying to understand real-time processes. Amongst these, scattering is particularly important, for it is directly probed in collider experiments. Accessing this information from Euclidean QCD is notoriously difficult, for the quantum real-time fluctuations are replaced by thermal ones in equilibrium. I work in two methods that solve this problem

Some of the links below correspond to published articles that are not open-access. Preprint versions of some of them (including mine) can however be downloaded from the arXiv.

Traditional Lattice QCD

On the side of traditional QCD, one of my advisors, Raúl Briceño, and his collaborators, have developed mechanisms to constraint scattering observables from the spectrum of finite-volume QCD, which coincides with that of Euclidean QCD. This effort started with Lüscher's method for two to two particle scattering. Since, the methods have been extended to incorporate more complicated scattering processes. These incorporate three particles and external currents, the latter of which is important to incorporate the effects of the other sectors of the standard model. These are however increasingly more complicated. My work in this field has focused on providing proofs of principle that these formalisms can be efficiently implemented by exploring them in the context of simpler QFTs. I have particularly focused on the two dimensional O(3) nonlinear sigma model. It shares many of the interesting features of QCD, including the confinement of fundamental massless particles (analogous to gluons) which condense into massive particles (analogous to the exotic glueballs whose existence continues to be a mystery) through quantum dynamical mass generation. It has furthermore played a key role in understanding quantum integrability and the AdS/CFT correspondence.

We are currently studying the example of two particle scattering in the presence of an external conserved current following the theoretical landscape formulated here. This will be in preparation to implement this on full lattice QCD.

Quantum Computers

Quantum computers are a recent technological advance that has great promise in providing significant speed-ups for several computational problems. In particular, as predicted by Richard Feynman, these are likely to be the most powerful tool we will have to directly explore quantum systems. I am particularly interested in developing the tools required to directly simulate QCD real-time dynamics using these.

Alongside my advisor Christian Bauer, we have developed a new formulation of Yang-Mills theory, the gluonic sector of QCD, which has several features that makes it a prime candidate for investigation using quantum computers. This formulation is completely gauge invariant, so that potential errors in near-term quantum computers cannot drive the state of the theory into unphysical regions. It is also described in terms of largely unconstrained discrete quantum numbers, so that it has a simple description in terms of qubits. Finally, it provides the simplest description to date of the magnetic sector of the theory in terms of such discrete quantum numbers. Due to asymptotic freedom, this sector is the dominant one near the continuum limit, in which we expect to be able to recover the predictions of the field theory of QCD.
We are also working on a formulation of QCD which is suitable for studies in which the number of quark colors is large. Even though in reality there are only three colors, continuum studies of this limit have already yielded important improvements to our qualitative understanding of QCD. With our formulation we expect we will be able to use quantum computers to turn this into a quantitative understanding of QCD, by generating a systematically improvable expansion. My collaborators have already given a first step in this direction.
Alongside Raúl Briceño, we are building up on previous work that shows that scattering information can be recovered from the real-time finite volume correlators that can be obtained in lattice QCD. We will show that this formalism can be extended directly to arbitrary kinematic regions and for arbitrarily complex processes. This is in stark contrast to the methodology developed for traditional computers, for the overhead due to the complexity of the scattering processes studied will be much smaller.

Previous Work

I used to be a mathematical physicist and a physical mathematician. Throughout history, the necessity of describing increasingly abstract and complex phenomena has prompted the development of new mathematics. However, field theory has also shown to be a new way of doing new mathematics (see for example the article by Mina Aganagic). By this I mean that the techniques developed to explore the physics of fields have provided deep insights into mathematical phenomena. These insights are at times so deep that they provide complete proofs of evasive theorems. The fundamental reason for the power of physics in mathematics remains mysterious. However the lectures of David Tong do point out some aspects of it:

This seems unfair, like physicists have some kind of secret weapon that mathematicians are unable to wield. And we do. In fact, we have two. The first is the path integral. The second, a wilful disregard for rigour.

I believe the lack of rigor can be mended. However, I think that the path integral is absolutely fundamental to the development of new mathematics.

I am interested in understanding in a mathematically rigorous fashion the quantum and statistical behavior of fields. I believe that, much like it has happened with past theories, understanding the rigorous mathematics of field theory will force us to develop deeper physical insights on what fields are.

- One of the ways in which I am approaching this objective is by trying to understand the relationship between two complementary approaches to the perturbative aspects of quantum field theory. One of them is the approach extending algebraic quantum field theory (see for example the book by Kasia Rejzner or the one by Michael Dütsch). The other is the approach based on factorization algebras and effective field theory (see for example the book by Kevin Costello or the books by Costello and Owen Gwilliam ). One of the points in common of both approaches is the BV formalism, which is used to treat in a cohomological way the presence of gauge redundancies. During my master's thesis I did a review of this formalism.
- I have also examined the non-perturbative aspects of QFT. For example, with my collaborator Francisco Calderón we have examined the nature of the overall normalization of path integrals in this paper. We have in particular proposed a method of normalizing path integrals. It is based on an extension of an observation due to Stephen Hawking where certain path integrals self-normalize. We can then cut and paste these integrals to find the normalization of others that do not.
- I am interested in the more classic approaches to axiomatic QFT as well. In particular, I am interested in the use of the methods of operator algebras to understand the locality in physics that fields implement (see for example the book by Rudolf Haag for the quantum aspects and the book by Ola Bratteli and Derek Robinson for the statistical, or the reviews written by Edward Witten or by Cristopher Fewster and Kasia Rejzner). During my bachelor's thesis I reviewed the aspect of this formalism which connects the thermal equilibrium and the dynamical evolution. With Aiyalam Balachandran, Andrés F. Reyes Lega and Souad Maria Tabban Sabbagh we explored the space of extensions of a state in the Hilbert space of its canonical (GNS) purification in a finite dimensional toy model to QFT. We interpreted this space by identifying an emergent gauge symmetry in the description which could be traversed using entropy increasing quantum operations. The results can be found in this paper (see for example this paper by Xi Dong, Daniel Harlow and Donald Marolf, for physical implementations of this gauge symmetry in the exploration of fixed-area states in quantum gravity).
I am also interested in the use of extended operators, also known as defects, to probe QFTs.
- The chiral Wess-Zumino-Witten (WZW) model $(E_8)_1$ is an important two-dimensional QFT with conformal symmetry. It has discrete symmetries which can be gauged, producing related theories known as orbifolds. Duality defects are defects supported on lines which separate the original theory on one side to its orbifold on the other. With Justin Kulp and Jonas Neuser we classified the duality defects of this theory in this paper .
- An important technique used to study the flow of information in relativistic theories, has been to couple QFTs to simple quantum mechanical probes, particle detectors. With Tales Rick Perche and Bruno de Souza Leão Torres we reinterpreted these detectors as line defects by integrating them out withing the path integral formalism. In particular, we found a simple generalization of the Unruh-DeWitt model to gauge theories where the detector couples via the derivative of an associated Wilson line. The paper can be found here.

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