Research

Research Identity

My background is in mathematical physics: quantum field theory in curved backgrounds, the AdS/CFT correspondence, and the renormalization of interacting theories. I study how bulk field theories in Anti-de Sitter space encode the data of a conformal field theory on the boundary, and how interactions deform that dictionary.

My master’s thesis and a follow-up article work this out for the Sine-Gordon model in two-dimensional Euclidean Anti-de Sitter space ($\text{EAdS}_2$), where the vertex operators are the main observables.

I also keep a second, active interest in geometric and differentiable machine learning: energy-based modeling of geometric graphs and differentiable physics. It runs on the same variational and geometric structures as field theory, so the two sides feed each other.

Featured Work

Core Research Direction

Quantum Field Theory in Euclidean AdS₂

The AdS/CFT correspondence conjectures a duality between a field theory in $(d+1)$-dimensional Anti-de Sitter space and a $d$-dimensional conformal field theory on its boundary. I work in the two-dimensional Euclidean case, in the Poincaré patch with metric

$$ds^2 = \frac{L^2}{z^2}\left(dz^2 + dp^2\right), \qquad R = -\frac{2}{L^2},$$

where $z>0$ is the holographic radial direction and $p$ is the boundary coordinate. A free scalar of mass $m$ is dual to a boundary operator whose scaling dimension is fixed by the Breitenlohner-Freedman analysis,

$$\Delta = \tfrac{1}{2} + \sqrt{\tfrac{1}{4} + m^2 L^2}.$$

The observables I care about are normal-ordered vertex operators $V_\beta = {:}e^{i\beta\phi}{:}$, drawn from the Sine-Gordon interaction. Building the free massive bulk propagator and its boundary limit gives a bulk-to-boundary dictionary that maps these vertex operators to dual scalar primaries on the boundary CFT.

Interacting Theory & Renormalization

Adding a Sine-Gordon bulk interaction and expanding the connected generating functional perturbatively produces UV and IR structure that has to be regularized. I use a heat-kernel decomposition of the propagators to define a Gaussian measure and keep the divergences under control. Renormalizing the two- and three-point functions of the vertex operators gives an anomalous dimension of the dual operator,

$$\Delta \;\longrightarrow\; \Delta_1 = \Delta + \lambda\,\Delta^{(1)} + \mathcal{O}(\lambda^2),$$

which I extract by explicit holographic renormalization, scheme dependence included.

The Logarithmic-CFT Question

The thesis noticed that the logarithmic terms and the apparent multiplets $\widetilde{\mathcal{O}} = \{\hat{\mathcal{O}}, {:}\mathcal{O}^2{:}\}$ look like a logarithmic CFT on the boundary. The follow-up article sharpens that. Once you treat the connected correlators and the renormalization group carefully, the boundary theory turns out to show ordinary anomalous scaling, not a genuine logarithmic CFT. Working out exactly when curved-space interactions do and do not generate logarithmic multiplets is one of the main threads I am still pulling on.

Trajectory

Research Topics

Secondary Direction: Geometric & Differentiable ML

Next to the field-theory work, I build energy-based models of geometric graphs and differentiable physics. Graphs embedded in 3D space, like neuronal morphologies or botanical trees, are neither purely geometric nor purely combinatorial, and modeling them means coupling discrete topology to continuous geometry. So far that has meant a from-scratch graph ML framework for spatial tree generation, mesh-based differentiable simulators, and computational work on mesh embeddings into curved spaces (the basis for the Bridges 2026 submission above). The structures here are the same ones that organize field theory, which is what keeps the two directions connected for me.

Research Philosophy

I am motivated by questions of the form:

• How does bulk geometry shape the boundary data of a quantum field theory?
• What survives renormalization, and what structure does the renormalization group reveal?
• When do interactions in curved space generate genuinely new operator structure?
• How can geometric and variational principles be made computational?

These questions run through everything I do, from field theory to simulation, and they shape how I approach applied R&D and machine-learning engineering.