A. V. Kosyak

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 representations

O. Gamayun

M. A. Mir

O. Lychkovskiy

Z. Ristivojevic

Quantum many-body systems share patterns of dynamics that are exactly described by tridiagonal matrices based on continuous Hahn polynomials.

Exactly solvable models for universal operator growth

On universal dynamics

F. Carta

A. Gauntlett

F. Griffin

Y. He

We show reinforcement learning can be used to check whether a certain class of quantum field theory has a finite spectrum of stable particles.

BPS spectroscopy with reinforcement learning

Reinforcing spectra

S. Lal

S. Majumder

E. Sobko

We introduce an AI-based framework for finding solutions to the Yang-Baxter equation and discover hundreds of new integrable Hamiltonians.

Deep learning based discovery of integrable systems

Learning integrability

J. Wang

Sterile neutrinos are replaced by topological order as dark matter candidates to counterbalance the Standard Model’s gravitational anomalies.

Topological quantum dark matter via global anomaly cancellation

Topological dark matter

A. Bulatov

Y. Kuratov

M. Burtsev

The abilities and power of a type of transformer model with memory are greatly improved by learning several key tasks at once during training.

Mastering long-context multi-task reasoning with transformers and recurrent memory

Multitasking memory

K. Anokhin

P. Bateson

Based on computer simulations, we argue developmental plasticity accelerates evolution and drives organisms towards ever-greater complexity.

Facilitation of evolution by plasticity scales with phenotypic complexity

Adaptability speeds evo

Y. Li

Y. You

Charge conjugation C, space reflection R, and time-reversal T operators are regularised in a quantum many-body Hilbert space on a discrete lattice.

Quantum many-body lattice C-R-T symmetry: fractionalisation, anomaly, and symmetric mass generation

Regularising CRT

Z. Wan

S. Yau

Varying the spacetime dimensions fermions occupy shows charge-conjugation C, space-reflection R and time-reversal T symmetries are 8-fold periodic.

C-R-T fractionalisation in the first quantised Hamiltonian theory

An 8-fold way for CRT

Charge-conjugation, space-parity and time-reversal symmetries are shown to form noncommutative groups, including the order-16 Pauli group.

C-R-T Fractionalisation, Fermions, and Mod 8 Periodicity

C, P and T in fractions

F. Barrows

F. Sheldon

F. Caravelli

We derive dynamical equations for networks with memristors and the Lyapunov functions of purely memristive circuits to study their stability.

Network analysis of memristive device circuits: dynamics, stability and correlations

Circuits with memory

I. Shkredov

A polynomial criterion is obtained for a set to have a small doubling, expressed in terms of the common additive energy of its subsets. 

On common energies and sumsets

Common energies

A. Stepanenko

K. S. Chernova

M. A. Gorlach

We use the quantum brachistochrone method to design an optimal control strategy for the fastest quantum state transfer in long qubit chains.

Time-optimal transfer of the quantum state in long qubit arrays

Optimal transfer

M. Cheng

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

We achieve maximal-fidelity state transfer in the fastest possible time for a 3-qubit chain by applying the quantum variational method.

Optimizing state transfer in a three-qubit array via quantum brachistochrone method

Three-qubit shortcut

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

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

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

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

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

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

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

Continuous quiver gauge theories

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

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

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

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