conformal field theory

Electrons in an ultra-clean gallium arsenide film behave like a crowd at a crossroads, where the tilt of the magnetic field sets the direction. At zero tilt, they form a compressible liquid of composite fermions, particles made of an electron and a pair of vortices.

Imagine an interferometer as a giant ear listening to the radio whisper of a distant galaxy. Three antennas spread across continents capture the signal, and the difference in their phases combines into a quantity that is immune to atmospheric jitter. This quantity is called the closure phase.

A handful of coins drops onto a table — heads and tails land wherever they please. The same goes for an instantaneous snapshot of a quantum chain: in some places a particle is present, in others it is not. But behind the disorder lurks a precise angle. In this work, a chain of particles closed into a ring was considered. It was divided into four arcs: two were measured, two were left untouched.

A stone thrown at a wall bounces off. In the quantum world, a particle can pass right through, as if the wall were woven from mist. This is quantum tunneling: it lights up stars, works in microchips, and even operates in the cells of our bodies. But most particles have spin — an intrinsic rotation, like a spinning top.

A quantum particle moves in a circle, passing through several stations. At each station, something happens to it — for example, its properties change slightly. After completing a full circle, the particle returns, but its state is no longer exactly what it was at the start.

Quantum field theory is the language physicists use to describe elementary particles and their interactions. The authors of the work decided to slightly "tweak" this language: they introduced deformations, that is, small changes to the rules of the game.

Two observers, Alice and Bob, sit at opposite ends of the same lab. Between them is a source that fires off two pulses in turn. Each pulse gives birth to a wave packet flying toward its own detector. So far, this looks like an ordinary experiment with quantum particles.

A pale green crystal was placed in a magnetic field and cooled below one kelvin — almost to absolute zero. Inside it hide chains of copper atoms that behave like tiny magnetic needles. Usually their orientation is chaotic, but the strong field and cold make the needles align in a unified impulse, like soldiers on a parade ground.

The Standard Model of particle physics is a catalog of all known building blocks of the universe: electrons, quarks, and others. But it is silent about dark matter and doesn't get along with gravity.

A black hole's horizon is not a wall but rather a one-way membrane. Anything that crosses it disappears forever. Stephen Hawking showed that this boundary should glow faintly, emitting particles. But catching such radiation from a real black hole is impossible: it's too far and too dim. Physicists have found a workaround: build a "toy" black hole out of magnetic atoms.

The boundary of a black hole is like the edge of a waterfall: cross it, and there's no way back. But unlike a waterfall, this boundary can be very fragile: a light nudge is enough to make it vanish. Physicists have found that the horizon's stability is set by an imaginary 'light flow' coming from the past. Invisible streams pierce spacetime.

In quantum physics, there are theories where everything follows clear proportions, like a musical rhythm that always returns to the beginning of the bar. But there are also 'irrational' theories where the rhythm breaks and predicting the next beat is nearly impossible. One such theory is the compactified boson: a particle lives on a circle, and its behavior depends on the radius of that circle.

Building a house on sand is a bad idea. In physics, it was long believed that a quantum theory of gravity could not be built on a fixed "sand"—a pre-existing spacetime.

Quantum computers of the future will likely communicate via light. An atom stores information, and a photon carries it across the network. But an atom doesn't hang still: it jitters and oscillates, and this motion can corrupt the signal. Previously, engineers could only calculate for a stationary atom.

Two-dimensional worlds never cease to amaze: here even crystal melting is not a symmetry breaking but a vortex drama discovered by Kosterlitz and Thouless. At the heart of this theater are topological сингулярности, whose energy and энтропия bargain for order. This language is common to сверхтекучести и сверхпроводимости.

In the early 20th century, Einstein showed that gravity is the curvature of space and time. A bit earlier, Maxwell had unified electricity and magnetism into a single theory.

A quantum calculation sometimes resembles an interpreter who gets distracted by every rustle in the hall, and a one-hour meeting turns into two. In physics, such a "rustle" is called the sign problem: it arises when probabilities in formulas become negative or complex, and ordinary computer simulations start to fail.

A black hole is like a spinning top: the faster it spins, the more noticeable its behavior. It has two boundaries — the outer and inner horizons, the edges beyond which even light cannot return. In the new work, physicists looked inside a rotating charged black hole and multiplied the areas of these two surfaces.

Time is a fickle thing. Inside a massive star, it flows calmly, like sand in an old clock on a mantelpiece. Outside, on the scale of the entire universe, it stretches along with space, as if the same clock were in an elevator that speeds up and slows down. For a long time, physicists puzzled over whether these two worlds could be glued together without visible seams.

A kitchen sponge soaked in syrup: in some spots there's more syrup, and your finger sticks right away; in others, it barely touches. That's roughly how a catalyst surface works. Molecules don't react everywhere but at especially sticky points — active sites.

Quantum laws reign supreme in the microworld, but macroscopic objects usually behave classically: the thermal motion of atoms drowns out quantum effects.

Unlike the Standard Model, where fundamental particles are point-like objects with no internal structure, string theory describes them as tiny vibrating threads — one-dimensional extended objects.

A guitar string decides for itself how tightly to stretch when a musician plays a chord in different octaves. That's roughly the picture physicists paint when they try to unite gravity, the weakest but most pervasive force, with the quirky laws of the microcosm.

Throw a stone into a pond, and ripples spread across the water. Throw two stones nearby, and the ripples intersect, creating a pattern of reinforced and canceled waves. That's interference.

A mathematical doughnut, a torus, sits on the boundary of a three-dimensional world where gravity acts. You can crumple and stretch it, and physicists decided to see how it behaves. Inside this world, space can be flat like a table, expanding like a soap bubble, or curved like a saddle. The doughnut boundary refused to stay smooth.

If you check where an electron is every second, its quantum properties change. It's like a child playing hide-and-seek but constantly being called by name: they freeze and stop running. In the particle world, such a "caller" is a measurement. It prevents particles from freely forming a shared quantum state, or entanglement.

In one model, spacetime is a smooth lake, and quantum particles are fish swimming in it. Their motion inevitably creates ripples. The math insists that the water trembles — otherwise the theory collapses. This trembling is strictly ordered and comes in two types.

A stone thrown into a pond leaves ripples spreading across the water. In quantum physics, the role of such ripples is played by equations that relate the properties of particles. Recently, mathematicians proposed a set of such equations for a world without gravity but with a large number of 'degrees of freedom'—roughly like the complex ripples on water.

The atomic nucleus is not a billiard ball but rather a hazy cloud that constantly changes its contours. Protons and neutrons inside are in continuous motion, and the nucleus can take on many different shapes: elongated, flattened, or pear-like. To describe this quivering diversity, physicists usually picked a few most probable shapes and mixed them, like an artist mixing paints on a palette.

A stone falls into a pond, and ripples spread across the water. But if the stone is very small and the water is not quite ordinary, the ripples pass right through it, as if it weren't there.

A rubber band stretched in different directions behaves differently from a whole sheet of paper. If you pull on an edge, the deformation does not spread evenly but seems to linger in certain spots.

A baker follows a recipe for a cake, but instead of a fluffy sponge, they get a hard crust. They start running through possible causes: maybe the flour was damp, or the oven heats unevenly, or the eggs were too cold.

A tailor cuts a suit, but the seams pucker and the buttons won't align. In quantum field theory, similar glitches are called anomalies: they appear when a symmetry of the equations breaks down in the transition to a quantum description. Usually, they are fixed by sewing in extra patches, the so-called Bardeen–Wess–Zumino counterterms.

A stone drops into a pond. Ripples spread, fade, and soon the surface is smooth again. But what if the pond has no shores, no bottom, and no characteristic ripple size? That is the world, a scale-free world, where quantum systems live when surrounded by an environment that picks out no particular length or energy.

A quantum computer is like an orchestra where every musician must come in at exactly the right moment. Previously, to play a complex piece, you had to constantly move the instruments around — slow and noisy. The new scheme, called "parity architecture," keeps everyone in place, and the conductor simply changes the notes.

A beam of light travels through the void, and its own 'ticking'—an invisible clock embedded in the very fabric of spacetime. Physicists have taken this beam and allowed it to measure itself: the gravitational field on the beam is quantized, and the role of the clock is played by the so-called dressing time — the time that the field 'puts on' like a coat.

A hot chain of atoms lined up in a row behaves like a tiny black hole. Such a chain is a series of particles, each resembling a tiny magnet. At normal temperatures, the little magnets flip randomly, but when cooled, they align in a uniform order. Physicists have discovered that when heated, this simple system reproduces the strange properties of black holes.

Electrons in a conductor behave like a crowd on an escalator: each one moves on its own, but together they create a flow. If you make them circle around a ring, their angular momentum (a measure of rotation) can couple to a magnetic field, like gears in a clock.

On the surface of a tiny sphere, electrons line up in patterns that look like ripples on water. Physicists have long noticed that this simple picture describes the behavior of quantum systems with surprising accuracy. But why it works has remained a mystery. The authors of a new study have unraveled the mathematical mechanism behind this model.

A compass needle points north, but what if space itself has a hidden axis? Physicists have used Earth's magnetic field to test whether the universe's structure is truly the same in all directions.