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Technique in theoretical physics
In theoretical physics, compactification means changing a theory with respect to one of its space-time dimensions. Instead of having a theory with this
Compactification_(physics)
Topics referred to by the same term
Compactification (mathematics), making a topological space compact Compactification (physics), the "curling up" of extra dimensions in string theory Compaction
Compactification
Theory of subatomic structure
of models of particle physics going beyond the Standard Model. Typically, such models are based on the idea of compactification. Starting with the ten-
String_theory
Branch of physics
Theoretical physics is a branch of physics that uses mathematical models and abstractions of physical objects and systems to explain and predict natural
Theoretical_physics
Low energy theories not compatible with string theory
Irene (2022). "Lectures on the Swampland Program in String Compactifications". Physics Reports. 989: 1–50. arXiv:2102.01111. Bibcode:2022PhR...989.
Swampland_(physics)
Framework of superstring theory
realistic models of particle physics based on string and M-theory. Typically, such models are based on the idea of compactification. Starting with the ten-
M-theory
Parametrizes complex structures on a surface
continuous action on this compactification. Gardiner & Masur (1991) considered a compactification similar to the Thurston compactification, but using extremal
Teichmüller_space
Prize awarded by the International Centre for Theoretical Physics
the ICTP is given each year by the International Centre for Theoretical Physics (ICTP) in honour of physicist Paul Dirac. The award, announced each year
Dirac_Medal_(ICTP)
Unified field theory
spacetime. History of science portal Physics portal Classical theories of gravitation Compactification (physics) Complex spacetime Non-relativistic gravitational
Kaluza–Klein_theory
Division of elementary particles
generations, but the particular number depends on the details of the compactification of the D-brane intersections. Additionally, E8 grand unified theories
Generation_(particle_physics)
Theories trying to extend known physics
Physics beyond the Standard Model (BSM) refers to the theoretical developments needed to explain the deficiencies of the Standard Model, such as the inability
Physics beyond the Standard Model
Physics_beyond_the_Standard_Model
Collider Compact Muon Solenoid Compact dimension Compact star Compactification (physics) Compaction simulation Comparison of software for molecular mechanics
Index_of_physics_articles_(C)
Theory of strings with supersymmetry
occurring as a result of a Kaluza–Klein compactification of 11D M-theory that contains membranes. Because compactification of a geometric theory produces extra
Superstring_theory
Boundary region of asymptotically flat spacetimes in general relativity
{\displaystyle ds^{2}=-dt^{2}+dr^{2}+r^{2}d\Omega ^{2}} . Conformal compactification induces a transformation which preserves angles, but changes the local
Null_infinity
Supergravity in eleven dimensions
Kaluza–Klein compactification made it hard to acquire chiral fermions needed to build the Standard Model. Additionally, these compactifications generally
Eleven-dimensional supergravity
Eleven-dimensional_supergravity
In physics and geometry: conjectured relation between pairs of Calabi–Yau manifolds
In most realistic models of physics based on string theory, this is accomplished by a process called compactification, in which the extra dimensions
Mirror symmetry (string theory)
Mirror_symmetry_(string_theory)
Concept of mathematics in convex analysis
mathematics, specifically in convex analysis, the convex compactification is a compactification which is simultaneously a convex subset in a locally convex
Convex_compactification
Riemannian manifold with SU(n) holonomy
supercharges in a compactification of type IIA supergravity or 2 5 − n {\displaystyle 2^{5-n}} supercharges in a compactification of type I. When fluxes
Calabi–Yau_manifold
Hypothetical physical entity
In physics, a string is a physical entity postulated in string theory and related subjects. Unlike elementary particles, which are zero-dimensional or
String_(physics)
Mathematical object
with these properties. The 3-sphere is homeomorphic to the one-point compactification of R3. In general, any topological space that is homeomorphic to the
3-sphere
American theoretical physicist and professor (born 1970)
cosmology, condensed matter physics, and elementary particle theory. He has made central contributions to the study of compactifications of string theory from
Shamit_Kachru
British theoretical physicist
superconformal algebras in two dimensions or exact results on string compactification". Physics Letters B. 172 (1–2): 316–322. Bibcode:1986PhLB..172..316B. doi:10
Adrian_Kent
Duality between theories of gravity on anti-de Sitter space and conformal field theories
typically obtained from string and M-theory by a process known as compactification. This produces a theory in which spacetime has effectively a lower
AdS/CFT_correspondence
Space of vacuum states
g. the radius and complex structure) which govern the shape of the compactification manifold, et cetera. These parameters are represented, in the quantum
Moduli_(physics)
explained this dimensional reduction by a hidden supersymmetry." Compactification (physics) Kaluza–Klein theory String theory § Extra dimensions Supergravity
Dimensional_reduction
Branch of string theory
referred to as the string theory landscape may be dominated by F-theory compactifications on Calabi–Yau four-folds, with 10 272 , 000 {\displaystyle 10^{272
F-theory
American theoretical physicist
the theory of automorphic forms to conformal field theory, string compactification, black hole entropy counting, and the AdS/CFT correspondence; potential
Greg_Moore_(physicist)
Asymmetry of classical and quantum action
In quantum physics an anomaly or quantum anomaly is the failure of a symmetry of a theory's classical action to be a symmetry of any regularization of
Anomaly_(physics)
Partial differential equations whose solutions are instantons
In physics and mathematics, and especially differential geometry and gauge theory, the Yang–Mills equations are a system of partial differential equations
Yang–Mills_equations
Mathematical concept
the topological space of the real numbers, producing the two-point compactification of the real numbers. Adding algebraic properties to this gives us the
Infinity
French physicist (1942–2019)
E Cremmer, J Scherk: Spontaneous compactification of space in an Einstein-Yang-Mills-Higgs model - Nuclear Physics B, 1976 Cremmer, E.; Ferrara, S.;
Eugène_Cremmer
Concept in particle physics
at an energy scale that is directly related to the inverse size ("compactification scale") of the extra dimension, M KK ≈ R − 1 . {\displaystyle M_{\text{KK}}\approx
Universal_extra_dimensions
Italian mathematical physicist (born 1977)
theory with compactification on a surface to a conformal field theory on the surface (Liouville field theory). High Energy and Particle Physics Division
Davide_Gaiotto
Topics referred to by the same term
number 107 named after Niels Bohr Bohr bug, a type of software bug Bohr compactification, a mathematical concept due to Harald Bohr This disambiguation page
Bohr_(disambiguation)
Modern theory of gravitation that combines supersymmetry and general relativity
construct a chiral fermion from a compactification — the compactified manifold needed to have singularities, but physics near singularities did not begin
Supergravity
Venezuelan theoretical physicist (born 1959)
theory. Font has contributed to development of Calabi–Yau dimensional compactification and she and her collaborators introduced the concept of S-duality to
Anamaría_Font
Theory of rapid universe expansion
magnitude less than the scale of inflation. The discovery of flux compactifications opened the way for reconciling inflation and string theory. Brane
Cosmic_inflation
Concept in mathematics
construction closely related to state spaces or phase spaces in physics. In physics, these are used to describe the state of a whole system as a single
Configuration space (mathematics)
Configuration_space_(mathematics)
need to be compactified on a Calabi–Yau manifold. (In string theory, compactification is a generalization of Kaluza–Klein theory, which was first proposed
History_of_string_theory
Namikawa, Yukihiko (1980). "Main problem and main results". Toroidal Compactification of Siegel Spaces. Lecture Notes in Mathematics. Vol. 812. Springer
List of letters used in mathematics, science, and engineering
List_of_letters_used_in_mathematics,_science,_and_engineering
Algebraic variety that is a moduli space for principally polarized abelian varieties
particular, a compactification of A2(2) is birationally equivalent to the Segre cubic which is in fact rational. Similarly, a compactification of A2(3) is
Siegel_modular_variety
Compact astronomical body
affects the motion of other matter. This formed the basis for black hole physics. Only a few months after Einstein published the field equations describing
Black_hole
Extra-dimensional model of the universe
83.3370. Randall, Lisa; Sundrum, Raman (1999). "An Alternative to Compactification". Physical Review Letters. 83 (23): 4690–4693. arXiv:hep-th/9906064
Randall–Sundrum_model
Principle in theoretical physics
unexpected connection between the world of information theory and classical physics. This connection was first described shortly after the seminal 1948 papers
Holographic_principle
Comprehensive physical model
string theory, the resultant four-dimensional theory after spontaneous compactification on a six-dimensional Calabi–Yau manifold resembles a GUT based on the
Grand_Unified_Theory
Secondary characteristic classes of 3-manifolds
quadratic functional and Ray-Singer invariants". Letters in Mathematical Physics. 2 (3): 247–252. Bibcode:1978LMaPh...2..247S. doi:10.1007/BF00406412. S2CID 123231019
Chern–Simons_form
Black brane solution in eleven-dimensional supergravity
The M5-brane is the electric-magnetic dual of the M2-brane. Upon compactification, the M5-brane becomes either the D4-brane or the NS5-brane of type
M5-brane
Objects in eleven-dimensional supergravity
dimensional strings. J. Hughes, L Jun, J Polchinski, "Supermembranes", Physics Letters B (1988) Jansson, Ronnie (2003). The Membrane Vacuum State (PDF)
Supermembranes
Extended physical object in string theory
the behavior of elementary particles in the Standard Model of particle physics. This connection has led to important insights into gauge theory and quantum
Brane
particularly simple formula for certain integrals on the Deligne–Mumford compactification M ¯ g , n {\displaystyle {\overline {\mathcal {M}}}_{g,n}} of the moduli
Lambda_g_conjecture
Set of mathematical concepts in quantum gravity
needed for computation. By utilizing compactifications, string theory describes geometric states, where a compactification is a spacetime that looks four-dimensional
Quantum_geometry
Reformulation of supergravity
Bernard Julia found that E7(7) symmetries are present upon toroidal compactification of 11-dimensional supergravity to 4 dimensions. In 1985, Bernard de
Exceptional_field_theory
Professor of mathematics (born 1969)
his PhD from Harvard University in 1994 with a thesis entitled `A Compactification over the Moduli Space of Stable Curves of the Universal Moduli Space
Rahul_Pandharipande
Solitons in Euclidean spacetime
pseudoparticle) is a notion appearing in theoretical and mathematical physics. An instanton is a classical solution to equations of motion with a finite
Instanton
Hypothetical faster-than-light particle
particles cannot exist because they are inconsistent with the known laws of physics. If such particles did exist they perhaps could be used to send signals
Tachyon
Quantum mechanical model based on mathematical matrices
In theoretical physics, the matrix theory is a quantum mechanical model proposed in 1997 by Tom Banks, Willy Fischler, Stephen Shenker, and Leonard Susskind;
Matrix_theory_(physics)
Romanian-American physicist (1936–2018)
was a professor of theoretical physics at the University of Chicago. He made important contributions to particle physics and string theory. He was also
Peter_Freund
Soviet mathematician (1896–1982)
contributions to set theory and topology. In topology, the Alexandroff compactification and the Alexandrov topology are named after him. Alexandrov attended
Pavel_Alexandrov
American physicist
1103/physrevd.36.1800. PMID 9958364. Ginsparg, P. (1987). "On toroidal compactification of heterotic superstrings". Physical Review D. 35 (2): 648–654. Bibcode:1987PhRvD
Paul_Ginsparg
Symmetry between bosons and fermions
Supersymmetry is a theoretical framework in physics that suggests the existence of a symmetry between particles with integer spin (bosons) and particles
Supersymmetry
Collection of possible string theory vacua
comprising a collective "landscape" of choices of parameters governing compactifications. The term "landscape" comes from the notion of a fitness landscape
String_theory_landscape
Process in particle physics
Tachyon condensation is a process in particle physics in which a system can lower its potential energy by spontaneously producing particles. The end result
Tachyon_condensation
Seven-dimensional Riemannian manifold
are therefore sometimes known as "Joyce manifolds", especially in the physics literature. In 2015, a new construction of compact G 2 {\displaystyle G_{2}}
G2_manifold
Concept in mathematical group theory
a complete description, so the alternative complex planes require compactification for complete description of conformal mapping. Nevertheless, the conformal
Conformal_group
Soviet mathematician (1906–1993)
Mathematics and Mathematical Physics. 6 (4): 28–33. doi:10.1016/0041-5553(66)90003-6. Regularization Stone–Čech compactification Tikhonov cube Tikhonov distribution
Andrey Tikhonov (mathematician)
Andrey_Tikhonov_(mathematician)
Candidate "Theory of Everything"
they can't be observed day-to-day. The technical term for this is compactification. These dimensions are usually made to take the shape of mathematical
Introduction_to_M-theory
Italian theoretical physicist
four-dimensional effective Lagrangians for lower energies from the compactification of magnetised D-brane models, and the high-energy scattering of closed
Paolo_Di_Vecchia
British physicist and mathematician
Witten, Andrew Strominger, and Gary Horowitz in which they introduced compactification to string theory using Calabi–Yau manifolds. Candelas is also notable
Philip_Candelas
Theorem of physical impossibility
theorem. Goddard–Thorn theorem Maldacena–Nunez no-go theorem: any compactification of type IIB string theory on an internal compact space with no brane
No-go_theorem
Energy driving the accelerated expansion of the universe
a positive Lambda term was Paál, G.; et al. (1992). "Inflation and compactification from galaxy redshifts?". Astrophysics and Space Science. 191 (1): 107–124
Dark_energy
Study of vector bundles, principal bundles, and fibre bundles
gave an alternate algebraic description of the moduli space and its compactification, because the moduli space of semistable holomorphic vector bundles
Gauge_theory_(mathematics)
Aspect of theoretical physics
In theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings theories. Type II string theory
Type_II_string_theory
Mathematical model of the time dependence of a point in space
useful to study the continuous extension Φ* of Φ to the one-point compactification X* of X. Even after losing the differential structure of the original
Dynamical_system
Theory in particle physics
4 {\displaystyle n<4} , the results presented here imply that the compactification topology is more complicated than a torus, i.e., all large extra dimensions
Large_extra_dimensions
Theories of higher-dimensional general relativity
(2025-03-27). "Compactification on Calabi-Yau threefolds: consistent truncation to pure supergravity". Journal of High Energy Physics. 2025 (3): 200.
Higher-dimensional Einstein gravity
Higher-dimensional_Einstein_gravity
American physicist
theory-based approaches inspired by particle physics. In 1985 he co-discovered Calabi–Yau manifold compactifications, showing that a superstring theory could
Andrew_Strominger
American theoretical physicist (born 1963)
Currently, Greene is studying non-simply connected and non-orientable compactifications and has showed that in some of these contexts, signals can have an
Brian_Greene
proposed subatomic or composite entities arising in theoretical particle physics and cosmology that have not been experimentally confirmed. They are typically
List of hypothetical particles
List_of_hypothetical_particles
Center-of-Momentum System, a coordinate system where the total momentum is 0. compactification A method for reducing the apparent dimension of spacetime by wrapping
Glossary_of_string_theory
Fresnel rhomb Fresnel zone Fresnel–Arago laws Fretting Freund–Rubin compactification Friction Friction loss Friedel Sellschop Friedmann equations
Index_of_physics_articles_(F)
American Internet personality and musician (born 1975)
Michigan, and the Queen Mary University of London. Specialized in particle physics, his work included research on string theory, supersymmetry, and quantum
Brian_Wecht
Application of K-theory in string theory
Hisham (2006), "Flux Compactifications on Projective Spaces and The S-Duality Puzzle", Advances in Theoretical and Mathematical Physics, 10 (3): 345–394,
K-theory_(physics)
Hypothetical particle
dimensions varies. It appears as a radion in Kaluza–Klein theory's compactifications of extra dimensions. In Brans–Dicke theory of gravity, Newton's constant
Dilaton
Hypothetical elementary particle that mediates gravity
forces appear to be accurately described by the Standard Model of particle physics. In the classical limit, a successful theory of gravitons would reduce
Graviton
Lorentzian manifold where curvature vanishes at large distances
{\displaystyle M} is asymptotically simple if it admits a conformal compactification M ~ {\displaystyle {\widetilde {M}}} such that every null geodesic
Asymptotically_flat_spacetime
Form of dimensional reduction
Freund–Rubin compactification is a form of dimensional reduction in which a field theory in d-dimensional spacetime, containing gravity and some field
Freund–Rubin_compactification
Theories in particle physics and cosmology
Brane cosmology refers to several theories in particle physics and cosmology related to string theory, superstring theory and M-theory. The central idea
Brane_cosmology
Diagrams describing the matter content
In theoretical physics, a quiver diagram is a graph representing the matter content of a gauge theory that describes D-branes on orbifolds. Quiver diagrams
Quiver_diagram
Class of quantum field theory models
formulation. This means they can only arise as effective field theories. New physics is needed at around the distance scale where the two point connected correlation
Non-linear_sigma_model
Indian physicist
American theoretical physicist and the Cathy and Marc Lasry Professor of Physics and Astronomy at the University of Pennsylvania. He has conducted research
Vijay_Balasubramanian
Quantum field theory
Unsolved problem in physics Yang–Mills theory and the mass gap. Quantum particles described by the theory have mass but the classical waves of the field
Yang–Mills_theory
83.3370. Randall, Lisa; Sundrum, Raman (1999). "An Alternative to Compactification". Physical Review Letters. 83 (23): 4690–3. arXiv:hep-th/9906064. Bibcode:1999PhRvL
1999_in_science
Gauge field loop operator
of matter multiplets left after compactification. These properties make Wilson lines important in compactifications of superstring theories. In a topological
Wilson_loop
Value representing energy density of space
(2015a), p. 27. Paál, G.; Horváth, I.; Lukács, B. (1992). "Inflation and compactification from Galaxy redshifts?". Astrophysics and Space Science. 191 (1): 107–124
Cosmological_constant
American theoretical physicist
potential for the radion that possesses a stable minimum, yielding a compactification scale that solves the hierarchy problem without fine-tuning of parameters
Walter_D._Goldberger
American theoretical physicist (born 1955)
paper with Philip Candelas, Andrew Strominger and Edward Witten on the compactification of superstrings in Calabi-Yau spaces. In the early 1990s, Horowitz
Gary_Horowitz
Grassmannian of 2-planes in 4-dimensional complex space. This is a compactification of complex Minkowski space. Y is the flag manifold whose elements correspond
Penrose_transform
Topologically stable solution of a partial differential equation
thought of as having the topology of a sphere, obtained by one-point compactification: adding a point at infinity. This is reasonable, as one is generally
Topological_defect
Italian mathematician and academic
completed her Ph.D. at Harvard University in 1993. Her dissertation, On a Compactification of the Universal Picard Variety over the Moduli Space of Stable Curves
Lucia_Caporaso
Five-dimensional Einstein field equations
{\displaystyle \square \phi =0.} Through the process of Kaluza–Klein compactification, the additional extra dimension is rolled up in a circle. Hence spacetime
Kaluza–Klein–Einstein field equations
Kaluza–Klein–Einstein_field_equations
COMPACTIFICATION PHYSICS
COMPACTIFICATION PHYSICS
COMPACTIFICATION PHYSICS
COMPACTIFICATION PHYSICS
Girl/Female
Australian, Finnish
Ewe
Boy/Male
Arabic
Observant; Spectator
Boy/Male
Tamil
Aryan Raj | ஆரà¯à®¯à®¨ ராஜÂ
Illustrious, Noble, Spiritual
Boy/Male
British, English
Happy
Boy/Male
Indian, Sanskrit
Ruler of the World
Boy/Male
Hindu, Indian
Peace
Girl/Female
Biblical
Lights, fires.
Girl/Female
Australian, British, English, Finnish
Mercy; God is My Light
Male
Portuguese
Portuguese form of Latin Henricus, HENRIQUE means "home-ruler."
Boy/Male
American, Anglo, British, English
Spear Fighter
COMPACTIFICATION PHYSICS
COMPACTIFICATION PHYSICS
COMPACTIFICATION PHYSICS
COMPACTIFICATION PHYSICS
COMPACTIFICATION PHYSICS
a.
Pertaining to the physics of astronomical science.
n.
That branch of physics which treats of heat and electricity.
n.
Logic illustrated by physics.
n.
That department of physics which treats of the atmosphere.
n.
That branch of physics which relates to the determination of the humidity of bodies, particularly of the atmosphere, with the theory and use of the instruments constructed for this purpose.
v. i.
Subdivision of business or official duty; especially, one of the principal divisions of executive government; as, the treasury department; the war department; also, in a university, one of the divisions of instruction; as, the medical department; the department of physics.
a.
Above or beyond physics; not explainable by physical laws.
n.
That branch of physics which treats of the laws of motion, or of moving bodies.
n.
One versed in physics.
a.
Involving the principles of both physics and chemistry; dependent on, or produced by, the joint action of physical and chemical agencies.
n.
In philosophy and physics: A rule of being, operation, or change, so certain and constant that it is conceived of as imposed by the will of God or by some controlling authority; as, the law of gravitation; the laws of motion; the law heredity; the laws of thought; the laws of cause and effect; law of self-preservation.
n.
Physics.
a.
Of or pertaining to physics, or natural philosophy; treating of, or relating to, the causes and connections of natural phenomena; as, physical science; physical laws.
adv.
In a physical manner; according to the laws of nature or physics; by physical force; not morally.
n.
Theology or divinity illustrated or enforced by physics or natural philosophy.
n.
That branch of physics which treats of the mechanics of liquids, or of their laws of equilibrium and of motion.
n.
The science of nature, or of natural objects; that branch of science which treats of the laws and properties of matter, and the forces acting upon it; especially, that department of natural science which treats of the causes (as gravitation, heat, light, magnetism, electricity, etc.) that modify the general properties of bodies; natural philosophy.
n.
A certain function relating to a system of forces and their points of application, -- first used by Clausius in the investigation of problems in molecular physics.