M. Cheng

J. Wang

X. Yang

We show that Weyl fermions and anomalous topological order in 4 dimensions can live on the edge of the same 5-dimensional superconductor.

(3+1)d boundary topological order of (4+1)d fermionic SPT state

Topological boundary

O. Gamayun

Y. Zhuravlev

A new approach to the large distance asymptotic of the finite-temperature deformation is discussed for a sine-kernel Fredholm determinant.  

On finite-temperature Fredholm determinants

Fredholm meets Toeplitz

Y. He

V. Jejjala

T. S. R. Silva

We use simulated annealing to efficiently construct all brane tilings that encode supersymmetric gauge theories and discover a new one.

Metaheuristic generation of Brane tilings

Metaheuristic tilings

A. Pinardin

A. Sarikyan

E. Yasinsky

We give a solution of the linearisation problem in the Cremona group of rank two over an algebraically closed field of characteristic zero. 

Linearization problem for finite subgroups of the plane Cremona group Linearization problem for finite subgroups of the plane Cremona group

Linearising actions 

We propose that dark matter consists of topological order, so gapped anyon excitations decay to generate the Standard Model's lepton asymmetry.

Topological leptogenesis

A New leptogenesis

P. Putrov

We demonstrate that the Standard Model's baryon minus lepton symmetry defect can become categorical by absorbing the gravitational anomaly.

Categorical symmetry of the standard model from gravitational anomaly

Categorical symmetry

A. V. Kosyak

P. Moree

We construct the unitary representation of an infinite-dimensional general linear group acting on a space and establish its irreducibility.

Irreducible actions of the group GL(∞) on L²-spaces on 3 infinite rows

Irreducible group action

J. Bao

E. Choi

R. Seong

S. Yau

We compute Futaki invariants for gauge theories from D3-branes that probe toric Calabi-Yau singularities arising from reflexive polytopes. 

Futaki invariants and reflexive polygons

Futaki for reflexives

A. Stepanenko

M. Di Liberto

Modelling the behaviour of two interacting bosonic particles in a chiral, dimerized optical lattice shows the pair form a vortex bound state.

Vortex bound states in dimerized π-flux optical lattices: characterization, state preparation and current measurement

Vortex bound states

T. Fink

An analysis of UKRI grant funding gives a strategy for maximising unrestricted funds, thereby helping research centres cover their costs.

Paying for science: a theory of UKRI grant funding

Paying for science

E. Sobko

Continuous quivers enable exact Wilson loop calculation, reveal an emergent dimension, and raise tantalising questions on dual strings.

Continuous Quivers

Continuous quivers

A. Losev

M. Shifman

Inconsistencies between two approaches to deriving beta functions in two-dimensional sigma models are resolved by adding heavy superpartners.

First-order formalism for β functions in bosonic sigma models from supersymmetry breaking

Peculiar betas tamed

A. Esterov

A uniform approach to a class of varieties is described that includes important types of objects from geometry, optimisation and physics.

Schön complete intersections

The tools used to study polynomial equations with indeterminate coefficients are extended to some important cases with interrelated ones.

Engineered complete intersections: slightly degenerate Bernstein-Kouchnirenko-Khovanskii

Slight degenerations

M. Brandenbourger

J. Veenstra

F. Gorp

H. Terwisscha-Dekker

J. Caux

C. Coulais

Producing the first examples of breathing solitons in one-dimensional non-reciprocal media allows their propagation dynamics to be analysed.

Non-reciprocal breathing solitons

Non-reciprocal breather

Reviewing progress in the field of AI-assisted discovery for maths and theoretical physics reveals a triumvirate of different approaches.

AI-driven research in pure mathematics and theoretical physics

On AI-driven discovery

P. Berglund

G. Butbaia

E. Heyes

E. Hirst

Machine learning generates desirable triangulations of geometric objects that are required for Calabi-Yau compactification in string theory.

Generating triangulations and fibrations with reinforcement learning

Triangulating polytopes

Z. Yao

S. Yao

Using Inception, a convolutional neural network, we predict certain divisibility invariants of Calabi-Yau manifolds with up to 90% accuracy.

Distinguishing Calabi-Yau topology using machine learning

Convolution in topology

C. Mishra

E. Sharnoff

Neural networks classify simple finite groups by generators, unlike earlier methods using Cayley tables, leading to a proven explicit criterion.

Learning to be Simple

A. Renner

F. Sheldon

A. Zlotnik

L. Tao

A. Sornborger

The training algorithm for digital neural networks is adapted and implemented entirely on an experimental chip inspired by brain physiology.

The backpropagation algorithm implemented on spiking neuromorphic hardware

Spiky backpropagation

We link the statistical properties of one-dimensional systems of free fermions initialised in states of either half- or alternating-occupancy.

Full-counting statistics for the alternating and domain-wall states

Counting free fermions

A general approach to proving the irreducibility of representations of infinite-dimensional groups within the frame of Ismagilov's conjecture.

The generalized characteristic polynomial, corresponding resolvent and their application

Group representation irreducibility

O. Lychkovskiy

Modelling the final state of a mobile impurity particle immersed in a one-dimensional quantum fluid after the abrupt application of a force.

One-dimensional Fermi polaron after a kick: two-sided singularity of the momentum distribution, Bragg reflection and other exact results

A kicked polaron

L. Cangemi

M. Chiodaroli

H. Johansson

A. Ochirov

P. Pichini

E. Skvortsov

Classical Kerr amplitudes for a rotating black hole derived using insights from recent advances in massive higher-spin quantum field theory.

Compton amplitude for rotating black hole from QFT

Brightening black holes

Two approaches that provide local formulae for Compton amplitudes of higher-spin massive objects in the quantum regime and classical limit.

From higher-spin gauge interactions to Compton amplitudes for root-Kerr

Spinning Root-Kerr

V. Kazakov

K. Zarembo

The first exact solution for the vacuum state of an asymptotically free QFT in a general external field found for the Principal Chiral Model.

Large-N principal chiral model in arbitrary external fields

PCM in arbitrary fields

E. Statnik

A. Voorhaar

Geometric properties, including delta invariants, are computed for singular points defined by polynomials with indeterminate coefficients.

Sparse curve singularities, singular loci of resultants, and Vandermonde matrices

Sparse singularities

L. Lang

The Galois group of a typical rational function is described and similar problems solved using the topology of braids and tropical geometry.

Permuting the roots of univariate polynomials whose coefficients depend on parameters

Permuting the roots

S. Chen

P. Dechant

D. Riabchenko

Coxeter transformations for root diagrams of simply-laced Lie groups are exhaustively computed then machine learned to very high accuracy.

Machine Learning Clifford invariants of ADE Coxeter elements

Clifford invariants by ML

X. Guo

A. Sarvi

C. Meinersen

A new non-linear mechanical metamaterial can sustain topological solitons, robust solitary waves that could have exciting applications.

Non-reciprocal topological solitons in active metamaterials

Strange kinks

M. Burtsev

M. Reeves

A. Job

Large language models like ChatGPT can generate human-like text but businesses that overestimate their abilities risk misusing the technology.

The working limitations of large language models

The limits of LLMs

I. Shkredov

Expanding the known multiplicative properties of large difference sets yields a new, quantitative proof on the structure of product sets.

On some multiplicative properties of large difference sets

Multiplicativity of sets

We study the geometry of finite dimensional space as the dimension grows to infinity with an accent on the height of the parallelotope.

The height of an infinite parallelotope is infinite

Infinite parallelotope

V. F. Lev

A cyclic group with small difference set has a nonzero element for which the second largest number of representations is twice the average.

The popularity gap

Additive combinatorics sheds light on the distribution of the set of squares in the prime field, revealing a new upper bound for the number of gaps.

On the distribution of quadratic residues

Quadratic residues

M. Panfil

F. Taha Sant'Ana

Explicit computation of injection and ejection impurity’s Green’s function reveals a generalisation of the Kubo-Martin-Schwinger relation. 

Kubo-Martin-Schwinger relation for an interacting mobile impurity

Mobile impurity

Investigating cluster algebras through the lens of modern data science reveals an elegant symmetry in the quiver exchange graph embedding.

Cluster algebras: network science and machine learning

AI for cluster algebras

Three new closed-form expressions give the number of recursive divisors and ordered factorisations, which were until now hard to compute.

Number of ordered factorizations and recursive divisors

Counting recursive divisors

A. Ashmore

B. A. Ovrut

By approximating the basis of eigenfunctions, we computationally determine the harmonic modes of bundle-valued Laplacians on Calabi-Yau manifolds.


Numerical spectra of the Laplacian for line bundles on Calabi-Yau hypersurfaces

Bundled Laplacians

The criteria of irreducibility of representations of the inductive limit of certain general linear groups acting on three infinite rows.

Irreducibility of the Koopman representations for the group GL0(2∞,R), acting on three infinite rows

Infinite dimensional irreducibility

The recursive divisor function has a simple Dirichlet series that relates it to the divisor function and other standard arithmetic functions.

Properties of the recursive divisor function and the number of ordered factorisations

Recursive divisor properties

R. Aoude

How gravitational waves are absorbed by a black hole is understood, for the first time, through effective on-shell scattering amplitudes.

Gravitational partial-wave absorption from scattering amplitudes

Absorption with amplitudes

The beta function for a class of sigma models is not found to be geometric, but rather has an elegant form in the context of algebraic data.

Peculiarities of beta functions in sigma models

Peculiar betas

D. Zharikova

D. Kornev

F. Ignatov

A new open-source platform is specifically tailored for developing complex dialogue systems, like generative conversational AI assistants.

Quantum generalisation of feedforward neural networks