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Space of vacuum states
In quantum field theory, the term moduli (sing.: modulus; more properly moduli fields) is sometimes used to refer to scalar fields whose potential energy
Moduli_(physics)
Geometric space whose points represent algebro-geometric objects of some fixed kind
In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric
Moduli_space
Topics referred to by the same term
modus meaning measure or manner. It, or its plural moduli, may refer to the following: Moduli (physics), scalar fields for which the potential energy function
Modulus
Partial differential equations whose solutions are instantons
anti-self-dual finite-action solutions are called instantons. The Yang–Mills moduli space was used by Simon Donaldson to prove Donaldson's theorem. In their
Yang–Mills_equations
Geometric space
In algebraic geometry, a moduli space of curves is a space whose points correspond to isomorphism classes of algebraic curves. The term "modulus" was introduced
Moduli_of_algebraic_curves
Physical property when materials or objects return to original shape after deformation
state if the external force is no longer applied. There are various elastic moduli, such as Young's modulus, the shear modulus, and the bulk modulus, all of
Elasticity_(physics)
Physical property that measures stiffness of material
fully described by two elastic moduli, and one may choose any pair. Given a pair of elastic moduli, all other elastic moduli can be calculated according
Elastic_modulus
Moduli space in the Grothendieck category of schemes
In algebraic geometry, a moduli scheme is a moduli space that exists in the category of schemes developed by French mathematician Alexander Grothendieck
Moduli_scheme
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)
Theory of subatomic structure
self-dual harmonic forms on the multi-monopole moduli space, and SL(2,Z) invariance in string theory". Physics Letters B. 329 (2): 217–221. arXiv:hep-th/9402032
String_theory
Field theory involving topological effects in physics
theory of four-manifolds, and algebraic topology, and to the theory of moduli spaces in algebraic geometry. Donaldson, Jones, Witten, and Kontsevich have
Topological quantum field theory
Topological_quantum_field_theory
Low energy theories not compatible with string theory
In physics, the term swampland refers to effective low-energy physical theories which are not compatible with quantum gravity. This is in contrast with
Swampland_(physics)
Most basic type of physical force
is an ongoing line of experimental physics research. In supersymmetric theories, some particles, known as moduli, acquire their masses only through supersymmetry
Fundamental_interaction
American mathematician (born 1937)
point. The concept of stable vector bundle from moduli theory has been consequential in mathematical physics: "This is a mathematical notion of stability
David_Mumford
Russian and French mathematician (born 1964)
geometry, topology, and mathematical physics, including the proof of Witten's conjecture of intersection numbers in moduli spaces of stable curves, construction
Maxim_Kontsevich
Material property in strain-stress relationship
Lamé parameters (also called the Lamé coefficients, Lamé constants or Lamé moduli) are two material-dependent quantities denoted by λ and μ that arise in
Lamé_parameters
model Modulated ultrasound Modulation sphere Modulational instability Moduli (physics) Moens–Korteweg equation Moffat distribution Mohammad Aslam Khan Khalil
Index_of_physics_articles_(M)
Logarithmic distance scale
distance moduli uncorrected for interstellar absorption, the values of which would overestimate distances if used naively, and absorption-corrected moduli. The
Distance_modulus
Mechanical property that measures stiffness of a solid material
Elena; Ehre, David; et al. (November 9, 2015). "Unusually Large Young's Moduli of Amino Acid Molecular Crystals" (PDF). Angewandte Chemie. 54 (46) (International ed
Young's_modulus
4-manifold invariants
to work with than Donaldson invariants; for example, the Seiberg–Witten moduli space of solutions of the Seiberg–Witten equations up to gauge tends to
Seiberg–Witten_invariants
Professor of mathematics (born 1969)
the moduli space of curves. His father Vijay Raghunath Pandharipande was a renowned theoretical physicist who worked in the area of nuclear physics. He
Rahul_Pandharipande
Study of vector bundles, principal bundles, and fibre bundles
alternative descriptions of important structures in algebraic geometry such as moduli spaces of vector bundles and coherent sheaves. Gauge theory has its origins
Gauge_theory_(mathematics)
Concept in theoretical physics
Reffert; Schulgin; Stieberger (2007). "Moduli Stabilization in Type IIB Orientifolds, Lust et al". Nuclear Physics B. 766 (1): 68–149. arXiv:hep-th/0506090
Orientifold
American theoretical physicist (born 1963)
Theory". Nuclear Physics. B416 (1994) 414–480. B.R. Greene and M.R. Plesser, "Duality in Calabi-Yau Moduli Space". Nuclear Physics. B338 (1990) 15. "The
Brian_Greene
Theory in supersymmetric gauge theory
freedom), of which the kinetic part coincides with the Kähler potential of the moduli space of vacua. Before taking the low-energy effective action, the theory
Seiberg–Witten_theory
Parametrizes complex structures on a surface
homeomorphisms from S {\displaystyle S} to itself. It can be viewed as a moduli space for marked hyperbolic structure on the surface, and this endows it
Teichmüller_space
American theoretical physicist
supersymmetric quantum field theories, and other areas of mathematical physics. Witten's work has also significantly impacted pure mathematics. In 1990
Edward_Witten
Resistance of a material to uniform pressure
pressure increase to the resulting relative decrease of the volume. Other moduli describe the material's response (strain) to other kinds of stress: the
Bulk_modulus
Ratio of shear stress to shear strain
material's response to shear stress (like cutting it with dull scissors). These moduli are not independent, and for isotropic materials they are connected via
Shear_modulus
Mathematics award
"For major advances in the minimal model program and applications to the moduli of algebraic varieties." Karim Adiprasito – "For the development, with Eric
Breakthrough Prize in Mathematics
Breakthrough_Prize_in_Mathematics
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)
Energy driving the accelerated expansion of the universe
having energy densities that vary in time and space) such as quintessence or moduli. A cosmological constant would remain constant across time and space, while
Dark_energy
Algebraic variety that is a moduli space for principally polarized abelian varieties
In mathematics, a Siegel modular variety or Siegel moduli space is an algebraic variety that parametrizes certain types of abelian varieties of a fixed
Siegel_modular_variety
Type of smooth complex surface of kodaira dimension 0
self-intersection −2.) The moduli space of quasi-polarized K3 surfaces of genus g is still irreducible of dimension 19 (containing the previous moduli space as an open
K3_surface
In material science and solid mechanics, orthotropic materials have material properties at a particular point which differ along three orthogonal axes
Orthotropic_material
Chemical data page
properties are most often characterized by a set of numerical parameters called moduli. The elastic properties can be well-characterized by the Young's modulus
Elastic properties of the elements (data page)
Elastic_properties_of_the_elements_(data_page)
282 GPa which is one of the highest bulk moduli known for any solid, and is exceeded only by the bulk moduli of diamond and c-BN. The hardness of c-BC2N
Heterodiamond
British-Lebanese mathematician (1929–2019)
have arisen out of physics in the past have been the lifeblood of mathematics. — Michael Atiyah Atiyah's work on instanton moduli spaces was used in Donaldson's
Michael_Atiyah
Partial differential equation with nonlinear terms
the tangent space of a point of the moduli space of all solutions. Ideally one would like to describe the (moduli) space of all solutions explicitly,
Nonlinear partial differential equation
Nonlinear_partial_differential_equation
Method of constructing instanton solutions
the fundamental and antifundamental representations, The metric on the moduli space of instantons is that inherited from the flat metric on B, I and J
ADHM_construction
Yang–Mills theory in two dimensions with a well-defined measure
"Topological sectors and measures on moduli space in quantum Yang-Mills on a Riemann surface". Journal of Mathematical Physics. 37 (3): 1161–1170. arXiv:hep-th/9504103
Two-dimensional Yang–Mills theory
Two-dimensional_Yang–Mills_theory
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
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
Branch of mathematics
the theory of four-manifolds in algebraic topology, and the theory of moduli spaces in algebraic geometry. Donaldson, Jones, Witten, and Kontsevich have
Topology
Concept in string theory
in the moduli spaces of stable maps, which can be thought of as spaces parametrizing curves in X {\displaystyle X} . However, as these moduli spaces can
Gromov–Witten_invariant
Mathematical concept
In mathematics, the spectral gap is the difference between the moduli of the two largest eigenvalues of a matrix or operator; alternately, it is sometimes
Spectral_gap
Concept in polymer physics
materials from known properties at a reference temperature. The elastic moduli of typical amorphous polymers increase with loading rate but decrease when
Time–temperature superposition
Time–temperature_superposition
Framework of superstring theory
self-dual harmonic forms on the multi-monopole moduli space, and SL(2,Z) invariance in string theory". Physics Letters B. 329 (2): 217–221. arXiv:hep-th/9402032
M-theory
Mathematical conjecture
study hypothetical moduli spaces of Kahler structures on a manifold. In the A-model the corresponding moduli space are the moduli of pseudoholomorphic
Mirror_symmetry_conjecture
In physics and geometry: conjectured relation between pairs of Calabi–Yau manifolds
Greene, Brian; Plesser, Ronen (1990). "Duality in Calabi–Yau moduli space". Nuclear Physics B. 338 (1): 15–37. Bibcode:1990NuPhB.338...15G. doi:10
Mirror symmetry (string theory)
Mirror_symmetry_(string_theory)
Force needed to pull a spring grows linearly with distance
In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly
Hooke's_law
Material with Vickers hardness exceeding 40 gigapascals
more standardized representation of a material's hardness. Bulk moduli, shear moduli, and elasticity are the key factors in the superhard classification
Superhard_material
Algebraic surface defined by a cubic polynomial
theory (GIT) gives a moduli space of smooth cubic surfaces, with one point for each isomorphism class of smooth cubic surfaces. This moduli space has dimension
Cubic_surface
Indian physicist (born 1956)
monopole bound states, selfdual harmonic forms on the multi – monopole moduli space, and SL(2,Z) invariance in string theory". Phys. Lett. B329 (2–3):
Ashoke_Sen
the study of families of curves, where it provides an invariant in the moduli theory of algebraic curves. Furthermore, it has applications to the theory
Hodge_bundle
Hypothetical physical concept
David R. (1994). "Calabi-Yau moduli space, mirror manifolds and spacetime topology change in string theory". Nuclear Physics B. 416 (2): 414. arXiv:hep-th/9309097
Theory_of_everything
Discrete dynamical system on polygons in the projective plane and on their moduli space
This is a projectively equivariant procedure, hence it descends to the moduli space of polygons and defines another dynamical system (which is also referred
Pentagram_map
Indian mathematician (born 1937)
is an Indian mathematician who works in the area of algebraic geometry, moduli spaces and Lie groups. He is one of India's leading mathematicians and recognised
S._Ramanan
British mathematician
studies moduli problems in algebraic geometry, and ‘mirror symmetry’—a phenomenon in pure mathematics predicted by string theory in theoretical physics. Thomas
Richard Thomas (mathematician)
Richard_Thomas_(mathematician)
Science of materials that compose the interior of planets
Mineral physics is the science of materials that compose the interior of planets, particularly the Earth. It overlaps with petrophysics, which focuses
Mineral_physics
Conjectures connecting number theory and geometry
algebraic curve to objects of the derived category of l-adic sheaves on the moduli stack of vector bundles over the curve. In 2024, a 9-person collaborative
Langlands_program
Spanish mathematician
research interests lie in the study of moduli spaces and geometric structures, including moduli spaces of vortices, moduli spaces of Higgs bundles and their
Oscar_Garcia_Prada
Chinese mathematician
University. He focuses primarily on moduli problems in algebraic geometry and their applications to mathematical physics, geometry and topology. Li graduated
Jun_Li_(mathematician)
SI derived unit of angle
prodibit 57.2957795130 &c. Cujus Reciprocus eft 0.0174532925 &c. Hujus moduli subsidio (quem in chartula quadam Auctoris manu descriptum inveni) commodissime
Radian
System of partial differential equations used in Higgs field theory
the Higgs bundle moduli space, and to the moduli space of holomorphic connections. Using the metric structure on the Higgs bundle moduli space afforded
Hitchin's_equations
Branch of mathematics
Theory and Moduli in Algebraic Geometry Mazur, Barry (2004), "Perturbations, Deformations, and Variations (and "Near-Misses" in Geometry, Physics, and Number
Deformation_(mathematics)
Israeli American theoretical physicist
Prize for Mathematical Physics in 1998. In July 2012, he was an inaugural awardee of the Breakthrough Prize in Fundamental Physics, the creation of physicist
Nathan_Seiberg
Conjecture in algebraic geometry
conjecture is a conjecture about intersection numbers of stable classes on the moduli space of curves, introduced by Edward Witten in the paper Witten (1991)
Witten_conjecture
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
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
Equivalence in 3D quantum field theory
eight supercharges). It is a version of mirror symmetry that relates the moduli spaces of these theories. The principle was first proposed by Kenneth Intriligator
3D_mirror_symmetry
Ratio used in material engineering
storage and shear loss moduli, G ′ {\displaystyle G'} and G ″ {\displaystyle G''} . Complex variables can be used to express the moduli E ∗ {\displaystyle
Dynamic_modulus
Research and education institute in Chennai, India
programmes in physics, mathematics and computer science. CMI is noted for its research in algebraic geometry, in particular in the area of moduli of bundles
Chennai Mathematical Institute
Chennai_Mathematical_Institute
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
compactification M ¯ g , n {\displaystyle {\overline {\mathcal {M}}}_{g,n}} of the moduli space of curves with marked points. It was first found as a consequence
Lambda_g_conjecture
On when a definite intersection form of a smooth 4-manifold is diagonalizable
for his Fields Medal in 1986. Donaldson's proof utilizes the Yang–Mills moduli space M P {\displaystyle {\mathcal {M}}_{P}} of solutions to the anti-self-duality
Donaldson's_theorem
Study of complex manifolds and several complex variables
algebraic varieties through the minimal model program and the construction of moduli spaces sets the field apart from differential geometry, where the classification
Complex_geometry
subject with connections to quantum gravity, particle and condensed matter physics, cosmology, and pure mathematics. String theory represents an outgrowth
History_of_string_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
Branch of string theory
K3 manifold is dual to heterotic string theory on a two-torus. Also, the moduli spaces of those theories should be isomorphic. The large number of semirealistic
F-theory
Type of Riemannian manifold
physics (Rome, 1999). Rome: Univ. Studi Roma "La Sapienza". pp. 195–230. doi:10.1142/9789812810038_0010. Maciocia, A. (1991). "Metrics on the moduli spaces
Hyperkähler_manifold
Method of studying partial differential equations
these materials are material properties such as shear modulus, elastic moduli, etc. Frequently, inhomogeneous materials (such as composite materials)
Asymptotic_homogenization
Temperature and pressure point where phase boundaries disappear
"hidden" and reveals itself in the onset of inhomogeneities in elastic moduli, marked changes in the appearance and local properties of non-affine droplets
Critical point (thermodynamics)
Critical_point_(thermodynamics)
Geometric structure used in certain particle interactions
to the principle of unitarity, the sum of the probabilities (the squared moduli of the probability amplitudes) for every possible outcome is 1. The on-shell
Amplituhedron
One-dimensional complex manifold
be seen as a fixed homeomorphism to the torus). To obtain the analytic moduli space (forgetting the marking) one takes the quotient of Teichmüller space
Riemann_surface
American mathematician
Pardon, John (2016). "An algebraic approach to virtual fundamental cycles on moduli spaces of pseudo-holomorphic curves". Geometry & Topology. 20 (2): 779–1034
John_Pardon
Duality between theories of gravity on anti-de Sitter space and conformal field theories
In theoretical physics, the anti-de Sitter/conformal field theory correspondence (frequently abbreviated as AdS/CFT) is a conjectured relationship between
AdS/CFT_correspondence
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)
Theory in particle physics
Giryavets; S. Kachru; W. Taylor (2005). "Type IIA moduli stabilization". Journal of High Energy Physics. 0507 (7): 066. arXiv:hep-th/0505160. Bibcode:2005JHEP
Large_extra_dimensions
Riemannian manifold with SU(n) holonomy
04879. doi:10.1112/blms/bdp106. S2CID 1070427. Reid, Miles (1987). "The Moduli space of 3-folds with K = 0 may nevertheless be irreducible". Mathematische
Calabi–Yau_manifold
Symbol representing a mathematical object
{Nk_{\text{B}}T}{V}}.} Considering constants and variables can lead to the concept of moduli spaces. For illustration, consider the equation for a parabola, y = a x
Variable_(mathematics)
Formalism in string theory
Witten's open string theory gives a single cover of moduli space". Communications in Mathematical Physics. 142 (1). Springer Science and Business Media LLC:
String_field_theory
American physicist (born 1961)
; Louis, Jan (27 May 1991). "Moduli dependence of string loop corrections to gauge coupling constants". Nuclear Physics B. 355 (3): 649–688. Bibcode:1991NuPhB
Lance_J._Dixon
Type of 2D conformal field theory
In theoretical physics and mathematics, a Wess–Zumino–Witten (WZW) model, also called a Wess–Zumino–Novikov–Witten model, is a type of two-dimensional
Wess–Zumino–Witten_model
American mathematician
(1): 1–49, CiteSeerX 10.1.1.568.9148, doi:10.2307/120991, JSTOR 120991 Moduli spaces of commutative ring spectra (PDF) Goerss – Topological Modular Forms
Michael_J._Hopkins
American mathematician
recursion for chord diagrams, RNA complexes, and cells in moduli spaces". Nuclear Physics B. 866 (3): 414–443. arXiv:1205.0658. doi:10.1016/j.nuclphysb
Robert_Penner
British mathematician
an interpretation as a moduli space of semistable Higgs bundles over a compact Riemann surface or algebraic curve. This moduli space has emerged as a
Nigel_Hitchin
Solitons in Euclidean spacetime
Simon Donaldson, for which he was later awarded the Fields Medal, used the moduli space of instantons over a given four-dimensional differentiable manifold
Instanton
Everything in space and time
filling space homogeneously, and scalar fields such as quintessence or moduli, dynamic quantities whose energy density can vary in time and space while
Universe
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
MODULI PHYSICS
MODULI PHYSICS
Boy/Male
Hindu
Precious, Valuable
Girl/Female
Bengali, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
A Small Rain Cloud
Girl/Female
Indian
Name of Godeess Durga
Girl/Female
Indian, Sanskrit
A Bud
Boy/Male
Hindu, Indian, Telugu
Lord Shiva; Wearing
Girl/Female
Indian
Valley of Flowers
Girl/Female
Hindu, Indian
Good Music
Boy/Male
Indian, Sanskrit
Logician
Boy/Male
Christian, Hindu, Indian
Special Smile; Sweet Little Attitude
Girl/Female
Hindu
Delightful
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Telugu
Valuable; Original
Boy/Male
Hindu
Name of Lord Shiva
Boy/Male
Hindu
Girl/Female
Hindu
Melodious, A musical Raag
Girl/Female
Hindu
Happy, Cheerful
Girl/Female
Hindu, Indian, Marathi
Sacred Thread; Mother
Boy/Male
Indian, Malayalam
Cartoon Character
Girl/Female
Hindu
Boy/Male
Arabic, Assamese, Indian, Muslim
Main; New
Female
English
Variant spelling of Middle English Mauld, MOULD means "mighty in battle."
MODULI PHYSICS
MODULI PHYSICS
Boy/Male
Celtic
Dark stranger.
Boy/Male
Tamil
God knowledge
Biblical
it is the Lord that opens
Boy/Male
Australian, Celtic
Son of Flann
Male
African
second-born of twin brothers.
Girl/Female
Hindu
Ardhanareeshwar, Goddess of justice, Name of a Goddess
Boy/Male
Tamil
Pashunath | பஷà¯à®¨à®¾à®¤
Lord Shiva
Boy/Male
English
From the west brook.
Girl/Female
Spanish
Lifted up.
Girl/Female
Australian, British, Chinese, Christian, English, French, Greek, Hebrew
Gift of God; Gift; A Diminutive of Dorothy; Well Loved
MODULI PHYSICS
MODULI PHYSICS
MODULI PHYSICS
MODULI PHYSICS
MODULI PHYSICS
v. i.
To make a copy or a pattern; to design or imitate forms; as, to model in wax.
n.
A model or measure.
a.
Of or pertaining to mode, modulation, module, or modius; as, modular arrangement; modular accent; modular measure.
n.
The size of some one part, as the diameter of semi-diameter of the base of a shaft, taken as a unit of measure by which the proportions of the other parts of the composition are regulated. Generally, for columns, the semi-diameter is taken, and divided into a certain number of parts, called minutes (see Minute), though often the diameter is taken, and any dimension is said to be so many modules and minutes in height, breadth, or projection.
v. t.
To form into a particular shape; to shape; to model; to fashion.
pl.
of Modus
p. pr. & vb. n.
of Moult
n.
Something intended to serve, or that may serve, as a pattern of something to be made; a material representation or embodiment of an ideal; sometimes, a drawing; a plan; as, the clay model of a sculpture; the inventor's model of a machine.
v. t.
To plan or form after a pattern; to form in model; to form a model or pattern for; to shape; to mold; to fashion; as, to model a house or a government; to model an edifice according to the plan delineated.
n.
Anything which serves, or may serve, as an example for imitation; as, a government formed on the model of the American constitution; a model of eloquence, virtue, or behavior.
n.
A fixed compensation or equivalent given instead of payment of tithes in kind, expressed in full by the phrase modus decimandi.
imp. & p. p.
of Moult
pl.
of Modulus
pl.
of Morula
n.
A fixed part of a module. See Module.
n.
To model; also, to modulate.
a.
Suitable to be taken as a model or pattern; as, a model house; a model husband.