Weakly nonlinear SPDEs converge to KPZ on the whole line
A stochastic heat kernel argument extends KPZ universality to non-equilibrium initial data in infinite volume
· “KPZ equation from a class of nonlinear SPDEs in infinite volume”
math-ph
Mathematical Physics
Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
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Closed-string integrals become bilinears of open ones
The genus-g analogue of the KLT double-copy relations, with numerical checks at genus two.
Twistors make 3d CFT correlators simple
Lecture notes derive Penrose and super-Penrose transforms for conserved, scalar, and generic operators.
· “Lectures on the Spinor and Twistor Formalism in 3D Conformal Field Theory”
All positive braid knots gain the conjectured sl_3 invariant
The new R-matrix covers every irreducible representation of sl_3, not just the symmetric ones.
At Painlevé poles, Lax operators become NS gauge-theory ODEs
The modified Mathieu and doubly confluent Heun equations emerge from Painlevé III3 and III1, yielding the dual gauge period.
· “From Painlev\'e equations to {cal N}=2 susy gauge theories: prolegomena”
Stokes jumps turn a divergent 1/c series into the full correlator
For 2d CFT degenerate operators, forbidden singularities dissolve and minimal models emerge from resummation.
· “On the 1/c expansion in 2d CFTs with degenerate operators”
Brane currents yield curvature and torsion for gauged extended geometry
A Cartan-style construction unifies a global duality group and a local gauge group into one curvature hierarchy.
· “Gauged Extended Field Theory and Generalised Cartan Geometry”
Inside a black hole, entropy grows with time but trails the horizon
A review extends the growing interior volume to charged, rotating, higher-dimensional and f(R) black holes.
Borel singularities expose every critical loss value
A one-time calculation can hand any optimizer the loss value at every stationary point.
Stokes jumps of one conformal block summon the other
Borel-Laplace and alien calculus show CFT blocks I1 and I2 encode each other's large-c trans-series and monodromy.
· “Resurgence for large c expansion in Coulomb gas formalism”
Fuzzy-sphere geometry yields skyrmion Hall invariant and fusion rules
Quantizing with a deformed-fuzzy-sphere Lie derivative turns matrix Chern-Simons droplets into effective gauge theories.
· “Microscopic field theories of the quantum skyrmion Hall effect”
Band matrix eigenvectors localize at sharp W² scale
Proof puts the localization length at order W² for one-dimensional random band matrices, matching the predicted transition.
Two nonisomorphic matroids still pass a quantum isomorphism test
An 18-element pair built from the magic-square system cannot be told apart by quantum strategies in the nonbasis game.
On-site DNLS solitons stay stable via an exponentially small eigenvalue
Competing next-nearest-neighbour coupling makes the decisive eigenvalue exponentially small; Borel-Padé fixes its prefactor and sign.
Random band matrices delocalize once W passes square-root(N)
Full delocalization, universal eigenvalue statistics and quantum ergodicity follow from new resolvent laws.
Form factor matches random-matrix curve in all three Dyson classes
Beyond a Thouless time, kicked many-body spectra reproduce COE, CUE, and CSE form factors to second order.
Every knot's HOMFLY polynomial has a positive expansion
The planar calculus once limited to bipartite knots extends to all knots through one universal algebraic formula.
Exact entanglement found for every GHZ-W mixture
A complete geometric solution for the square root of the threetangle covers the whole Bloch sphere.
· “The exact convex roof for GHZ-W mixtures for three qubits and beyond”
Two-soliton collisions betray the ZK equation
Inverse neural-net analysis exposes a temporary interaction; refitting the equation restores its conservation law.
Two explicit formulas now cover all Virasoro singular vectors
They solve the recursion and yield the coefficient of every Virasoro monomial.
Drop the sun's azimuth when computing air temperature
A polarization-aware radiative transfer scheme shows an azimuth-averaged beam gives the same temperature as the full collimated beam.
Proven: zero-free disk 1/(eB_R) for repulsive many-body gases
The volume of a ball of interaction range R sets the radius of the zero-free disk.
· “Simple analyticity criteria for repulsive multi-body potentials”
Connection's transverse-traceless part adds no degrees of freedom
Only constants survive in the symmetric transverse part; geodesics match autoparallels only in special cases.
Non-local current turns free U(1) into a noncommutative gauge theory
The same bootstrap that yields Yang-Mills on flat space fixes U(N) as the only allowed noncommutative gauge group.
· “On a non-geometric approach to noncommutative gauge theories”
Five conditions reveal when a W-algebra is secretly affine
Explicit checkable tests yield new collapsing levels and isomorphisms like W_{-12}(E6,2A2) ≅ L_{-2}(G2).
Mean-field cluster laws proven for long-range percolation
New real-space RG yields n^{-1/2} cluster tails and superprocess limits in all high-effective-dimension regimes.
· “Critical long-range percolation I: High effective dimension”
Both Painlevé I approaches yield matching Lax pairs
Meromorphic isomonodromic and KP-minimal-model constructions are explicitly identified, giving new Hamiltonians.
Two extensions of the Z-hat invariant clash on Brieskorn spheres
Effective central charge exposes a violation of the expected Chern-Simons relation in some Brieskorn spheres.
Two edge-state curves traverse square-lattice band gaps
Each curve is seeded by a bound state of one matrix Schrödinger or Dirac operator, matching bulk-edge correspondence.
· “Edge states in square lattice media and their deformations”
Tacking is time-optimal in non-convex Zermelo navigation
Abstract promises global results and tacking paths; the submitted full text contains none of them.
ℓ+3 operators may generate every banana-integral annihilator
A proven rank match up to ℓ=8 suggests the operator set is complete at all loop orders.
· “D-ideal of generic mass banana integrals in dimensional regularization”
One decaying parameter predicts the fate of nine interacting universes
As the Hubble rate falls, full and averaged systems converge to the same late-time attractors in nine interacting Bianchi I models.
BV master equation becomes a Maurer–Cartan equation
Three explicit L∞ algebras realize the BV bracket on local functionals for any compatible Q.
Complex-contour path integral unifies instantons and resonant states
Decay rates from bounces and from resonant states become one and the same boundary value problem.
New Ricci-flat instantons break Riemannian black-hole uniqueness
Complete non-Hermitian Ricci-flat metrics exist on non-spin simply connected 4-manifolds for every n≥1.
Gapped fermion ground states connect by automorphism flows
The result extends quasi-adiabatic evolution to infinite lattices and makes Goldstone's theorem a corollary.
· “Automorphic equivalence within gapped phases of infinitely extended fermion systems”
Extended energy distances match Fourier metrics at every order
Whitening makes them scale-free with unbiased gradients, giving machine learning a unit-invariant loss family.
· “From Kinetic Theory to AI: a Rediscovery of High-Dimensional Divergences and Their Properties”
Inverse gradient descent turns uniform points into fresh data samples
Three deterministic steps replace score estimation and noise: push points apart, add a uniform point, run the inverse map.
Noise completes cosmic reheating where resonance alone stalls
Light-scalar noise could rescue inflation models whose weak couplings would otherwise never reheat the universe.
· “Fluctuations in Hill's equation parameters and application to cosmic reheating”
New index computes 2D symmetry anomalies from symmetry restriction
A nontrivial H^4(G,U(1)) class forbids any trivially gapped symmetric ground state.
· “Anomaly diagnosis via symmetry restriction in two-dimensional lattice systems”
Doubly logarithmic depth suffices for random unitaries
A two-layer circuit of hash-based phase gates and shuffles matches Haar randomness exponentially faster than prior ensembles.
A BV pushforward equates two formulations of Palatini–Cartan gravity
The standard action and the restricted boundary-compatible action yield the same expectation values on Σ × I.
Sharp constant decides when nonlocal wave equations are solvable
The number 8eδ² decides: below its inverse, strong solutions exist; above it, existence can fail.
· “The Cauchy Problem for Symmetric Hyperbolic Systems with Nonlocal Potentials”
Gaussian-preserving open dynamics reduces to finite matrices
A new Lie algebra isomorphism solves the quadratic Redfield equation exactly for non-Gaussian states.
· “Gaussian Open Quantum Dynamics and Isomorphism to Superconformal Symmetry”
4D Palatini-Cartan gravity becomes a zero-Hamiltonian constraint theory
Eliminating the auxiliary field leaves exactly the torsion-free, Hamiltonian, and momentum constraints.
CMB data near Earth can be inverted to rebuild the early universe
A tomography proof shows the shell of initial gravitational perturbations is stably recoverable from ISW observations.
· “Reconstruction of the observable universe from the integrated Sachs-Wolfe effect”
Mean walk lifetime flips at trap-spacing constant c=1
It fixes how much dissipation a one-dimensional sandpile can absorb before losing criticality.
· “Random walks in a field of soft traps and criticality for the dissipative Abelian Sandpile Model”
Stable kernel spectra track cPIKAN convergence gains
Chebyshev-based neural PDE solvers keep their learning kernel structured, and that structure tracks their error drops.
For cyclic circuits, K algebra copies cost no new parameters
For cyclic circuits, one observable splits the reachable algebra into K copies for log K extra qubits.
MLE recovers Curie-Weiss group couplings
Consistency, asymptotic normality, and exponential error bounds — and it feeds optimal voting weights.
· “Reconstruction of the Probability Measure and the Coupling Parameters in a Curie-Weiss Model”
Multiple SLE partition functions become Calogero-Moser eigenstates
Pairwise-distance conjugation turns multiple SLE null vector equations into the Calogero-Moser Hamiltonian.
· “Multiple chordal SLE(kappa) and quantum Calogero-Moser system”
Six-loop φ³ beta and mass anomalous dimension computed
First published values in 6−ε dimensions, extending known five-loop results.
One distribution captures charge noise in a stochastic cellular automaton
Exact full counting statistics interpolate from single-file Mainardi-Wright at pure reflection to Gaussian at pure transmission.
Stochastic quantization builds 2-D Moyal λφ⁴ for every λ ≥ 0
Global solutions and an invariant measure make the non-commutative quantum field theory rigorous for all couplings.
· “Stochastic quantization of λ φ₂⁴- theory in 2-d Moyal space”
Pauli backpropagation handles amplitude-damping noise efficiently
Same backpropagation trick that works for depolarizing noise now covers realistic amplitude damping.
Kalb-Ramond black hole passes solar tests only if parameters are tiny
Four solar-system tests force the new terms between 10^-9 and 10^-4.
· “Black hole with global monopole charge in self-interacting Kalb-Ramond field”
Exact droplet boundary found for overlapping charges on a sphere
A rational conformal map fixed by one quartic root gives the equilibrium measure and leading energy in the pre-critical phase.
· “Properties of the one-component Coulomb gas on a sphere with two macroscopic external charges”
One threshold sets where quasiperiodic driving heats a system
A matrix-cocycle calculation gives the exact heating phase boundary and Lyapunov exponent for driven critical systems.
· “Phase Transitions in Quasi-Periodically Driven Quantum Critical Systems: Analytical Results”
Curved space shrinks and reddens the blackbody spectrum
A circle-based model of blackbody radiation predicts dimmer, narrower, redshifted spectra as curvature grows.
Wide 1D random band matrices delocalize and match GUE
Above band width $N^{1/2+\varepsilon}$, bulk eigenvectors spread out and the local eigenvalue statistics are GUE.
Degenerate limits yield integrable vectorial Adler-Yamilov map
A reduction chain from 3×3 Lax matrices recovers the Adler-Yamilov map and new integrable birational YB maps.
· “Reductions and degenerate limits of Yang-Baxter maps with 3times 3 Lax matrices”
Stability of Soler solitons reduces to radial spectra
A spherical-harmonic split turns 3D Dirac stability checks into one-dimensional radial problems.
· “On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D”
Complete spinor data tabulated for real and complex Clifford algebras
Idempotents, spinor bases, matrix reps, and norms for every real and complex algebra, extending a 1998 computation.
· “Clifford geometric algebra: Real and complex spinor data tables”
No solenoid needed: punctured plane generates Aharonov-Bohm field
If right, the AB effect follows from topology of the punctured plane, not a coil outside the electron's reach.
One formula captures pole-to-branch-cut transition at T=0
An explicit analytic series for the charged scalar correlator, with QNM dispersions and superconducting Tc.
· “Exact low-temperature Green's functions in AdS/CFT: From Heun to confluent Heun”
ROM misfit cuts clean layered-inversion error 14-fold
A normalized reduced-operator objective wins on layer and time-origin perturbations and stays competitive on noise.
· “Reduced-order modeling for electromagnetic inverse problems: a layered medium benchmark”
SYK spectrum matches Gaussian law down to tiny scales
A weak local law yields Gaussian eigenvalue counts and delocalized bulk eigenvectors.
· “Weak local law and delocalization for the Sachdev-Ye-Kitaev model”
Chemotaxis alone can drive patterns from stable
Strong directed movement can destabilize a non-reactive equilibrium even when diffusion alone predicts no patterns.
· “Pattern formation: reactivity is not necessary for chemotaxis--driven instabilities”
Noise record: polynomial for metrology
A small type summary preserves the whole noise model in O(log n) memory; universal state recovery still needs every trajectory.
· “Task-Dependent Syndrome Memory in Quantum Sensing and State Recovery”
One edge-deletion rule now counts maps of every genus
A bijective skin-and-core splitting gives every term of topological recursion a direct combinatorial meaning; no analytic assumptions needed
One Poisson bracket governs Hamiltonian systems with q time directions
q-cosymplectic manifolds make multi-time dynamics integrable and reducible, with fast-slow clocks as a test case.
For beta = 4, 16, 36,
Exact formulas extend the beta=4 Pfaffian machinery to every even-square beta.
· “Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer”
Zero-stress solutions survive every analytic TTbar-like flow
The theorem in any dimension: instantons and their on-shell action are fixed by vanishing energy-momentum.
· “Soliton Surfaces and the Geometry of Integrable Deformations of the mathbb{CP}^(N-1) Model”
Ground-state entanglement hits volume law on every interval
A periodic Feynman–Kitaev clock turns shift-register Floquet states into zero-energy eigenstates with maximal block entropy.
Top level-lines get a proven L^{1/3} Ferrari-Spohn law
The boundary of a random crystal plateau shows cube-root fluctuations with an Airy-function limit law.
Nonlinear resonator crystals have a valid tight-binding limit
A capacitance operator links continuous and discrete solitons with O(δ) error, opening the way to gap and defect solitons.
Arbitrarily large viscous shocks are L2-contracting
The a-contraction method with a shock-strength weight gives stability for u_t + (u^p)_x = u_xx when 2 ≤ p ≤ 4.
· “L²-contraction and asymptotic stability of large shock for scalar viscous conservation laws”
N-particle mechanics mirrors a nonlinear field's states
Truncating at N modes gives Jacobi-elliptic stationary solutions plus a checkable error for time evolution.
· “Solving the nonlinear Klein-Gordon equation: semianalytical Galerkin method”
A strong local coupling slows quantum spread to a logarithmic lightcone
For spin chains with or without disorder, one large local coupling shrinks the Lieb-Robinson amplitude to 1/Δ.
· “Logarithmic lightcones in the multiparticle Anderson model with sparse interactions”
Unruh state built for linearized gravity on rotating black holes
Pairing the two Teukolsky scalars works for every rotation below extremality—a step toward evaporation models.
· “The Teukolsky scalar as a gateway for quantizing gravity on rotating black holes”