Alex Radcliffe

Alex Radcliffe

I am a PhD student in mathematical physics at King's College London, with research interests in conformal field theory and pure mathematics. One major focus of my research has been connections between conformal field theory and number theoretic objects such as automorphic forms and L-functions, and another has been the study of exotic setups we can build in CFT's using extended objects.

Curriculum Vitae (PDF)

My Papers

Monodromy Pinning Defects in the Critical $\mathrm{O}(2N)$ Model

Authors: Petr Kravchuk, Alex Radcliffe

We investigate a novel class of defects in the critical $\mathrm{O}(2N)$ model that preserve conformal symmetry along the defect, but not the symmetry under rotations transverse to the defect. Instead, they only preserve a combination of transverse rotations and a global symmetry. These defects are constructed as IR fixed points of RG flows originating at monodromy defects, triggered by a relevant operator with non-zero transverse spin. Using large-$N$ and $4-\varepsilon$ expansions, we compute leading-order scaling dimensions of defect operators and the one-point functions of the bulk fields. In various limits this theory coincides with the monodromy defect or the pinning field defect, and we compare our results to existing results for these defects.

[arXiv, pdf, InspireHEP]

Weyl bound for trilinear periods via conformal bootstrap

Authors: Anshul Adve, James Bonifacio, Petr Kravchuk, Dalimil Mazac, Sridip Pal, Alex Radcliffe, Gordon Rogelberg

Let $f_1,f_2$ be holomorphic modular forms of the same weight for a cocompact lattice $\Gamma < \mathrm{PSL}_2(\mathbf{R})$. We estimate the rate of decay of the coefficients in the expansion of $f_1\overline{f_2}$ in a Laplace eigenbasis. By specializing our main theorem to the case where $\Gamma$ is arithmetic, we obtain new instances of the Weyl bound for triple product $L$-functions in the spectral aspect. Our method builds on the conformal bootstrap in physics.

[arXiv, pdf, InspireHEP]

Effective theory for fusion of conformal defects

Authors: Petr Kravchuk, Alex Radcliffe, Ritam Sinha

We construct an effective field theory for fusion of conformal defects of any codimension in $d\geq 3$ conformal field theories. We fully solve the constraints of Weyl invariance for defects of arbitrary shape on general curved bulk manifolds and discuss the simplifications that arise for spherical defects on the conformal sphere. As applications, we study the structure of cusp anomalous dimensions in the anti-parallel lines limit and derive high-energy spin-dependent asymptotics for the one-point functions of bulk operators. We point out the potential importance of defects that break transverse rotations and initiate a classification of their Weyl anomalies.

[arXiv, pdf, InspireHEP]

Non-saturation of Bootstrap Bounds by Hyperbolic Orbifolds

Author: Alex Radcliffe

In recent years the conformal bootstrap has produced surprisingly tight bounds on many non-perturbative CFTs. It is an open question whether such bounds are indeed saturated by these CFTs. A toy version of this question appears in a recent application of the conformal bootstrap to hyperbolic orbifolds, where one finds bounds on Laplace eigenvalues that are exceptionally close to saturation by explicit orbifolds. In some instances, the bounds agree with the actual values to 11 significant digits. In this work we show, under reasonable assumptions about the convergence of numerics, that these bounds are not in fact saturated. In doing so, we find formulas for the OPE coefficients of hyperbolic orbifolds, using links between them and the Rankin-Cohen brackets of modular forms.

[arXiv, pdf, InspireHEP]

Videos of My Talks

Spinning Defects in the $\mathrm{O}(2N)$ Model

Venue: Bootstrap 2025, Instituto Principia, São Paulo, Brazil

An introduction to conformal defects, defects with cusps and defect fusion

Venue: Imperial College London, UK

Non-academic stuff

I was fortunate enough to appear on BBC2's quiz show, University Challenge in 2022-2023, where I managed to win the series with my team on behalf of Durham University.

This is the first episode, but the rest of my TV appearances are in a playlist here (including an interview on BBC Breakfast).