Quantum Field Theory and String Theory
The mathematical framework behind particle physics and its extensions, including string theory and holography (descriptions of gravity by theories without gravity on a boundary).
arXiv: hep-th, hep-lat
16 topics
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At a phase transition, matter looks the same at every magnification, and its physics is a conformal field theory. The bootstrap computes such theories from consistency alone, and some gauge theories become scale invariant at long distances only when they contain enough matter.
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Confinement in QCD-like gauge theories
7 problemsQuarks are never seen alone: the force between them does not fade with distance, as if they were tied by a string made of gluon field. Nobody has derived from the equations of the theory why this happens.
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Gravity scattering can be computed by squaring gluon scattering (the particles of the strong force), once the gluon formulas are written in a special form. Whether this squaring works at every loop order and for exact, non-perturbative solutions is unknown.
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Generalized and non-invertible symmetries
4 problemsSymmetries used to act only on particles at points and always had an undo operation. Newer symmetries act on lines and surfaces, and some have no undo, yet they still constrain what a theory can do.
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Basic rules such as causality and conservation of probability force certain numbers in low-energy theories to be positive. Once gravity is included, the long-range pull of the graviton (the particle carrying gravity) spoils the standard argument, and it is unclear which bounds survive.
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Lattice definition of chiral gauge theories
4 problemsThe weak force treats left-handed and right-handed particles differently. Nobody knows how to place such a theory on a grid of spacetime points for computer simulation without destroying that difference or its symmetry.
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The S-matrix bootstrap finds which scattering outcomes are allowed using only basic principles such as conservation of probability and causality. In four dimensions, massless particles like photons, gravitons and zero-mass pions make the method hard to set up.
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Holography in de Sitter and flat spacetimes
5 problemsIn spaces with negative vacuum energy, gravity inside is exactly equivalent to an ordinary quantum theory living on the boundary. Our universe is instead close to flat or slowly expanding, and the corresponding equivalent theory is unknown.
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Some quantum field theories are known to exist only indirectly, from string theory, and have no formula listing their fields and interactions. The six-dimensional (2,0) theory is the main example: its properties can be computed, but it cannot be written down.
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For one idealized gauge theory with infinitely many colors, scattering amplitudes equal the volume-like form of a geometric shape called the amplituhedron, with no Feynman diagrams needed. Whether similar shapes exist for finite numbers of colors, for realistic theories, for gravity and for cosmology is open.
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Calculations in quantum field theory produce series in powers of the coupling that never converge, because the terms eventually grow like factorials. Resurgence studies how the missing nonperturbative effects are encoded in this growth.
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When a quantum field theory is viewed at coarser and coarser resolution, its effective number of degrees of freedom appears always to drop. Theorems proving this exist in two, three and four dimensions, but not in five or six, and not for every kind of defect.
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In holography, the geometry of space inside appears to be built from how strongly parts of the boundary system are entangled, meaning quantum-mechanically linked. The rules of this construction are only partly known.
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String theory is defined mostly as a series of approximations around a fixed spacetime, and M-theory, its eleven-dimensional limit, has no general definition. Exact definitions exist only in special cases, such as spaces with negative vacuum energy.
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De Sitter vacua and the string landscape
3 problemsString theory allows a huge number of ways to curl up its extra dimensions, each giving a different low-energy universe. Whether any of them is a long-lived universe with small positive vacuum energy, as ours appears to be, and whether their number is finite, is disputed.
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Some apparently consistent theories of particles and gravity may never arise from any theory of quantum gravity; the set of such theories is called the swampland. Conjectured rules say which theories are excluded, for example that gravity must always be the weakest force.