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Ten-dimensional supergravity
In supersymmetry, type IIA supergravity is the unique supergravity in ten dimensions with two supercharges of opposite chirality. It was first constructed
Type_IIA_supergravity
Ten-dimensional supergravity
supersymmetry, type I supergravity is the theory of supergravity in ten dimensions with a single supercharge. It consists of a single supergravity multiplet
Type_I_supergravity
Ten-dimensional supergravity
In supersymmetry, type IIB supergravity is the unique supergravity in ten dimensions with two supercharges of the same chirality. It was first constructed
Type_IIB_supergravity
Modern theory of gravitation that combines supersymmetry and general relativity
In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a modern field theory that combines the principles of supersymmetry and
Supergravity
4D N = 1 supergravity 4D N = 1 supergravity Type I supergravity Type IIA supergravity Type IIB supergravity Eleven-dimensional supergravity Theories studied
List of quantum field theories
List_of_quantum_field_theories
General relativity in M-theory
Higher-dimensional supergravity is the supersymmetric generalization of general relativity in higher dimensions. Supergravity can be formulated in any
Higher-dimensional supergravity
Higher-dimensional_supergravity
Compact astronomical body
main-sequence stars, where thermal pressure balances gravity. Instead, a type of quantum-mechanical pressure balances gravity at these temperatures and
Black_hole
Aspect of theoretical physics
M-theory. Consequently the low energy type IIA supergravity theory can also be derived from the unique maximal supergravity theory in 11 dimensions (low energy
Type_II_string_theory
Theory of supergravity in four dimensions
{\mathcal {N}}=1} supergravity is the theory of supergravity in four dimensions with a single supercharge. It contains exactly one supergravity multiplet, consisting
4D_N_=_1_supergravity
Symmetry between bosons and fermions
is included automatically, and the result is said to be a theory of supergravity. Another theoretically appealing property of supersymmetry is that it
Supersymmetry
Extended physical object in string theory
the free dictionary. In string theory and related theories (such as supergravity), a brane is a physical object that generalizes the notion of a zero-dimensional
Brane
Supergravity in eleven dimensions
In supersymmetry, eleven-dimensional supergravity is the theory of supergravity in the highest number of dimensions allowed for a supersymmetric theory
Eleven-dimensional supergravity
Eleven-dimensional_supergravity
American theoretical physicist
finding the classical equations which unify supergravity and Yang–Mills gauge theories in type I supergravity. These equations play an important role in
George_Chapline_Jr.
Theory of strings with supersymmetry
the second superstring revolution, the five superstring theories (Type I, Type IIA, Type IIB, HO and HE) are regarded as different limits of a single theory
Superstring_theory
Minimal supergravity in four dimensions
4D N = 1 {\displaystyle {\mathcal {N}}=1} supergravity describes the simplest four-dimensional supergravity, with a single supercharge and a supermultiplet
Pure_4D_N_=_1_supergravity
Aspect of theoretical physics
SO(32) via Chan–Paton factors. At low energies, type I string theory is described by the type I supergravity in ten dimensions coupled to the SO(32) supersymmetric
Type_I_string_theory
Hypothetical faster-than-light particle
particle types are called luxons (which always move at the speed of light) and bradyons (which always move slower than light); both of these particle types are
Tachyon
Superconformal quantum field theory
superconformal Supergravity Pure 4D N = 1 supergravity 4D N = 1 supergravity N = 8 supergravity Higher dimensional 11D supergravity Type I supergravity Type IIA
ABJM superconformal field theory
ABJM_superconformal_field_theory
248-dimensional exceptional simple Lie group
groups that can be coupled to the N = 1 supergravity in ten dimensions. E8 is the U-duality group of supergravity on an eight-torus (in its split form)
E8_(mathematics)
Principle in theoretical physics
of type IIA string theory. The matrix theory they proposed was first suggested as a description of two branes in eleven-dimensional supergravity by Bernard
Holographic_principle
Base space for supersymmetric theories
directions which are spanned by Θ i {\displaystyle \Theta _{i}} and Θ i ∗ {\displaystyle \Theta _{i}^{*}} , where i {\displaystyle i} runs from 1 to N {\displaystyle
Superspace
Hypothetical elementary particle that mediates gravity
interacting strings. Dual graviton – Hypothetical particle found in supergravity Gravitino – Hypothetical superpartner to the graviton Gravitoelectromagnetism –
Graviton
Theories in particle physics and cosmology
"Towards a naturally small cosmological constant from branes in 6-D supergravity". Nucl. Phys. B. 680 (1–3): 389–414. arXiv:hep-th/0304256. Bibcode:2004NuPhB
Brane_cosmology
Secondary characteristic classes of 3-manifolds
K-theory Supersymmetry Supergravity Eleven-dimensional supergravity Type I supergravity Type IIA supergravity Type IIB supergravity Superspace Lie superalgebra
Chern–Simons_form
Solitons in Euclidean spacetime
that absolutely minimize the energy functional within their topological type. The first such solutions were discovered in the case of four-dimensional
Instanton
British mathematical physicist
Collider. His other work includes the construction of type I supergravity, a 10-dimensional supergravity theory with Yang–Mills fields, which is also a low-energy
Nicholas_Manton
Process in particle physics
K-theory Supersymmetry Supergravity Eleven-dimensional supergravity Type I supergravity Type IIA supergravity Type IIB supergravity Superspace Lie superalgebra
Tachyon_condensation
Algebraic structure used in theoretical physics
{\widetilde {S}}(2n)} and H ( n ) {\displaystyle H(n)} . For the Cartan type of simple Lie superalgebras, the odd part is no longer completely reducible
Lie_superalgebra
Superconformal Yang–Mills theory
N = 8 supergravity theory. The Lagrangian for the theory is L = tr { − 1 2 g 2 F μ ν F μ ν + θ I 8 π 2 F μ ν F ¯ μ ν − i λ ¯ a σ ¯ μ D μ λ a − D μ X i D
N = 4 supersymmetric Yang–Mills theory
N_=_4_supersymmetric_Yang–Mills_theory
superconformal algebra Bagger, Jonathan; Wess, Julius (1992), Supersymmetry and supergravity, Princeton Series in Physics (2nd ed.), Princeton University Press, ISBN 0-691-02530-4
Supersymmetry_algebra
26-dimensional string theory
) ⋯ V i p ( k p μ ) ⟩ = ∑ h = 0 ∞ ∫ D g m n D X μ N exp ( − I [ g , X ] ) V i 1 ( k 1 μ ) ⋯ V i p ( k p μ ) {\displaystyle \left\langle V_{i_{1}}(k_{1}^{\mu
Bosonic_string_theory
Asymmetry of classical and quantum action
the symmetry. Vector gauge anomalies are always chiral anomalies. Another type of gauge anomaly is the gravitational anomaly. Quantum anomalies were discovered
Anomaly_(physics)
Algebraic structure used in theoretical physics
{\displaystyle \mu :G\times G\rightarrow G} , an inversion morphism i : G → G {\displaystyle i:G\rightarrow G} and a unit morphism e : 1 → G {\displaystyle e:1\rightarrow
Supergroup_(physics)
Simple Lie group; the automorphism group of the octonions
groups of type G2 in fields of even characteristic. Ree, Rimhak (1960), "A family of simple groups associated with the simple Lie algebra of type (G2)",
G2_(mathematics)
133-dimensional exceptional simple Lie group
and the group of field automorphisms (i.e., cyclic of order f if q = pf where p is prime). N = 8 supergravity in four dimensions, which is a dimensional
E7_(mathematics)
78-dimensional exceptional simple Lie group
ad(q)) and the group of field automorphisms (i.e., cyclic of order f if q=pf where p is prime). N = 8 supergravity in five dimensions, which is a dimensional
E6_(mathematics)
Duality between theories of gravity on anti-de Sitter space and conformal field theories
Juan (1998). "The large N limit of superconformal field theories and supergravity". Advances in Theoretical and Mathematical Physics. 2 (4): 231–252.
AdS/CFT_correspondence
1016/0550-3213(71)90351-8. Gliozzi, F.; Scherk, J.; Olive, D. I. (1977). "Supersymmetry, Supergravity Theories and the Dual Spinor Model". Nucl. Phys. B. 122
History_of_string_theory
that a supersymmetric gauge theory with the E8 gauge group propagates on a type of domain wall. This domain wall, a Hořava–Witten domain wall, behaves as
Hořava–Witten_theory
2D conformal field theory used in string theory
forms the Poincaré symmetry of the target manifold. The invariance under (i) follows since the action S {\displaystyle {\mathcal {S}}} depends only on
Polyakov_action
Seven-dimensional Riemannian manifold
N=1 supersymmetry. The resulting low energy effective supergravity contains a single supergravity supermultiplet, a number of chiral supermultiplets equal
G2_manifold
Riemannian manifold with SU(n) holonomy
in a compactification of type IIA supergravity or 2 5 − n {\displaystyle 2^{5-n}} supercharges in a compactification of type I. When fluxes are included
Calabi–Yau_manifold
Concept in theoretical physics
orientations are equivalent. Type I string theory is the simplest example of such a theory and can be obtained by orientifolding type IIB string theory. In mathematical
Orientifold
Type of supersymmetric quantum field theory
is W ( Φ ) = a i Φ i + 1 2 m i j Φ i Φ j + 1 3 λ i j k Φ i Φ j Φ k {\displaystyle W(\Phi )=a_{i}\Phi ^{i}+{\frac {1}{2}}m_{ij}\Phi ^{i}\Phi ^{j}+{\frac
Wess–Zumino_model
Conjectured duality combining S-duality and T-duality
K-theory Supersymmetry Supergravity Eleven-dimensional supergravity Type I supergravity Type IIA supergravity Type IIB supergravity Superspace Lie superalgebra
U-duality
Hypothetical physical entity
closed strings. The oldest superstring theory containing open strings was type I string theory. However, the developments in string theory in the 1990s have
String_(physics)
Quantum mechanical model based on mathematical matrices
energy limit of this matrix model is described by eleven-dimensional supergravity. These calculations led them to propose that the BFSS matrix model is
Matrix_theory_(physics)
Candidate "Theory of Everything"
Bibcode:2004fcst.book.....G. ISBN 978-0-375-41288-2. Miemic, A.; Schnakenburg, I. (2006). "Basics of M-theory". Fortschritte der Physik. 54 (1): 5–72. arXiv:hep-th/0509137
Introduction_to_M-theory
Equivalence of two physical theories
observation that type IIA and E8×E8 heterotic string theories are closely related to a gravitational theory called eleven-dimensional supergravity. His announcement
S-duality
Unobservable spacetime curves needed to describe Dirac monopoles
K-theory Supersymmetry Supergravity Eleven-dimensional supergravity Type I supergravity Type IIA supergravity Type IIB supergravity Superspace Lie superalgebra
Dirac_string
Type of smooth complex surface of kodaira dimension 0
315–326, MR 2310254 Pjateckiĭ-Šapiro, I. I.; Šafarevič, I. R. (1971), "Torelli's theorem for algebraic surfaces of type K3", Mathematics of the USSR-Izvestiya
K3_surface
Breakdown of conformal symmetry at the quantum level
conformal anomaly, scale anomaly, trace anomaly or Weyl anomaly is an anomaly, i.e. a quantum phenomenon that breaks the conformal symmetry of the classical
Conformal_anomaly
Lie algebra, usually infinite-dimensional
of indefinite type, most work has focused on those hyperbolic type, for which the matrix S is indefinite, but for each proper subset of I, the corresponding
Kac–Moody_algebra
Differential geometry of supermanifolds
theories involving odd fields, e.g., SUSY field theory, BRST theory, or supergravity. Supergeometry is formulated in terms of Z 2 {\displaystyle \mathbb {Z}
Supergeometry
Class of quantum field theory models
finite-action solutions, one may identify the points at infinity as a single point, i.e. that space-time can be identified with a Riemann sphere. Since the n̂-field
Non-linear_sigma_model
Theory of subatomic structure
superstring revolution. In the 1970s, many physicists became interested in supergravity theories, which combine general relativity with supersymmetry. Whereas
String_theory
Simplest supersymmetric extension to the Standard Model
mSUGRA stands for minimal supergravity. The construction of a realistic model of interactions within N = 1 supergravity framework where supersymmetry
Minimal Supersymmetric Standard Model
Minimal_Supersymmetric_Standard_Model
Unified field theory
Oskar Klein. It is not supported by experiments, but is a precursor to supergravity and modern string theory (in eleven-dimensional spacetime). In his 1921
Kaluza–Klein_theory
Quantum mechanics with supersymmetry
( p − i W ) b + ( p + i W † ) b † ] {\displaystyle Q_{1}={\frac {1}{2}}\left[(p-iW)b+(p+iW^{\dagger })b^{\dagger }\right]} Q 2 = i 2 [ ( p − i W ) b −
Supersymmetric quantum mechanics
Supersymmetric_quantum_mechanics
Lower energy limit in string theory
theories and are related to the concept of S-duality. Black Holes: In supergravity and string theory, extremal black holes can be BPS states. Their mass
Bogomol'nyi–Prasad–Sommerfield bound
Bogomol'nyi–Prasad–Sommerfield_bound
Set of equations that describe superstring theory in a non-perturbative framework
equations that describe superstring theory in a non-perturbative framework. Type IIA string theory can be shown to be equivalent to a maximally supersymmetric
Matrix_string_theory
In physics and geometry: conjectured relation between pairs of Calabi–Yau manifolds
manifold. Instead, two different versions of string theory called type IIA string theory and type IIB can be compactified on completely different Calabi–Yau
Mirror symmetry (string theory)
Mirror_symmetry_(string_theory)
Mathematical concept
line concept for a point particle in special and general relativity. The type of string, the geometry of the spacetime in which it propagates, and the
Worldsheet
No-go theorem pertaining the triviality of space-time and internal symmetries
a subgroup, Below any mass, there are only a finite number of particle types, Any two-particle state undergoes some reaction at almost all energies,
Coleman–Mandula_theorem
Hypothetical particle
Hayashi, M.; Watanabe, T.; Aizawa, I.; Aketo, K. (2003). "Dilatonic inflation and SUSY breaking in string-inspired supergravity". Modern Physics Letters A. 18
Dilaton
Theorem in theoretical physics
symmetries since these are not symmetries at the level of the S-matrix. Supergravity S-matrix Haag, R.; Łopuszański, J.T.; Sohnius, M. (1975). "All possible
Haag–Łopuszański–Sohnius theorem
Haag–Łopuszański–Sohnius_theorem
Representation of the supersymmetry algebra
= C + i θ χ − i θ ¯ χ ¯ + i 2 θ 2 ( M + i N ) − i 2 θ 2 ¯ ( M − i N ) − θ σ μ θ ¯ A μ + i θ 2 θ ¯ ( λ ¯ + i 2 σ ¯ μ ∂ μ χ ) − i θ ¯ 2 θ ( λ + i 2 σ μ
Supermultiplet
Manifold with Riemannian, complex and symplectic structure
symmetric spaces of compact type, such as Grassmannians. The natural Kähler metric on a Hermitian symmetric space of compact type has nonnegative sectional
Kähler_manifold
Strong-weak duality in supersymmetric theories of theoretical physics
{SO} (8)} , E 7 {\displaystyle E_{7}} and E 11 {\displaystyle E_{11}} supergravity. A massive spin-2 dual gravity, to lowest order, in D = 4 and N − D is
Montonen–Olive_duality
Equivalence of two physical theories
fact that type IIA and E8×E8 heterotic string theories are closely related to a gravitational theory called eleven-dimensional supergravity. His announcement
T-duality
Type of Riemannian manifold
4-form Ω {\displaystyle \Omega } . Bonan's later results include a Lefschetz-type result: wedging with this powers of this 4-form induces isomorphisms Ω n
Hyperkähler_manifold
Algebra used in 2D conformal field theories and string theory
have ∑ i ∈ Z ( m i ) ( u q + i ( v ) ) m + n − i ( w ) = ∑ i ∈ Z ( − 1 ) i ( q i ) ( u m + q − i ( v n + i ( w ) ) − ( − 1 ) q v n + q − i ( u m + i ( w
Vertex_operator_algebra
Generalized manifold
"Groups acting simply transitively on the vertices of a building of type Ã2, I". Geometriae Dedicata. 47 (2): 143–166. doi:10.1007/BF01266617. Cooper
Orbifold
Generalization of electrodynamics
are D-branes are examples for all values of p. In eleven-dimensional supergravity or M-theory, we have a 3-form electrodynamics. Just as we have non-abelian
P-form_electrodynamics
four-dimensional, but either none or two of its dimensions are time-like, i.e. it has either 4+0 or 2+2 dimensions. The spectrum consists of only one
N_=_2_superstring
Formalism in string theory
Relationship between string theory and quantum field theory String cosmology Supergravity The Elegant Universe Zeta function regularization Sen, Ashoke (1999-12-29)
String_field_theory
Theory in supersymmetric gauge theory
background of four dimensional N = 2 {\displaystyle {\mathcal {N}}=2} supergravity. It can be engineered, formally by lifting the super Yang–Mills theory
Seiberg–Witten_theory
Physics concept of subatomic structure
only two anomaly-free gauge groups that can be coupled to the N = 1 supergravity in 10 dimensions. (Although not realized for quite some time, U(1)496
Heterotic_string_theory
Superstring quantization approach
the IIB string gives rise to type I string theory. Starting instead from a ( 1 , 0 ) {\displaystyle (1,0)} supergravity action gives rise to heterotic string
RNS_formalism
Predicted field theory in physics
superconformal Supergravity Pure 4D N = 1 supergravity 4D N = 1 supergravity N = 8 supergravity Higher dimensional 11D supergravity Type I supergravity Type IIA
6D (2,0) superconformal field theory
6D_(2,0)_superconformal_field_theory
Branch of string theory
By doing so, one obtains type IIB superstring theory in 10 dimensions. The SL(2,Z) S-duality symmetry of the resulting type IIB string theory is manifest
F-theory
Collection of possible string theory vacua
P p r i o r ( x ) × P s e l e c t i o n ( x ) , {\displaystyle P(x)=P_{\mathrm {prior} }(x)\times P_{\mathrm {selection} }(x),} where P p r i o r {\displaystyle
String_theory_landscape
Application of K-theory in string theory
in type II supergravity theories also enjoy these large gauge transformations, but due to the presence of Chern-Simons terms in the supergravity actions
K-theory_(physics)
Type of Lie algebra of interest in physics
In mathematics, loop algebras are certain types of Lie algebras, of particular interest in theoretical physics. For a Lie algebra g {\displaystyle {\mathfrak
Loop_algebra
Geometric space whose points represent algebro-geometric objects of some fixed kind
:{\mathcal {L}}\to {\mathcal {L}}'} such that ϕ ( s i ) = s i ′ {\displaystyle \phi (s_{i})=s_{i}'} . This means the associated moduli functor P Z n :
Moduli_space
Mathematical theory
D-branes, Ramond-Ramond field strengths and in some cases even spinors in type II string theory. For more information on twisted K-theory in string theory
Twisted_K-theory
Algebra combining both supersymmetry and conformal symmetry
{Q}}^{i}} [ T j i , S k ] = δ j k S i {\displaystyle [T_{j}^{i},S^{k}]=\delta _{j}^{k}S^{i}} [ T j i , S ¯ k ] = − δ k i S ¯ j {\displaystyle [T_{j}^{i},{\overline
Superconformal_algebra
Peruvian theoretical physicist (b. 1954)
K-theory Supersymmetry Supergravity Eleven-dimensional supergravity Type I supergravity Type IIA supergravity Type IIB supergravity Superspace Lie superalgebra
Barton_Zwiebach
Framework of superstring theory
approximated by one of the three supergravities in ten dimensions, known as type I, type IIA, and type IIB supergravity. Similarly, M-theory is approximated
M-theory
Object in six-dimensional spacetime
fraction of supersymmetry and wiggle in space are well-described by supergravity solutions of Lunin and Mathur. David Tong (2002). "NS5-Branes, T-Duality
NS5-brane
Eight-dimensional Riemannian manifold
K-theory Supersymmetry Supergravity Eleven-dimensional supergravity Type I supergravity Type IIA supergravity Type IIB supergravity Superspace Lie superalgebra
Spin(7)-manifold
Diagrams describing the matter content
K-theory Supersymmetry Supergravity Eleven-dimensional supergravity Type I supergravity Type IIA supergravity Type IIB supergravity Superspace Lie superalgebra
Quiver_diagram
Invariant action in bosonic string theory
the action for a free point particle is proportional to its proper time – i.e., the "length" of its world-line – a relativistic string's action is proportional
Nambu–Goto_action
Extension to the MSSM solving the mu-problem
Srednicki, M.; Wyler, D. (1983). "Weak interaction breakdown induced by supergravity". Physics Letters B. 120 (4–6): 346. Bibcode:1983PhLB..120..346N. doi:10
Next-to-Minimal Supersymmetric Standard Model
Next-to-Minimal_Supersymmetric_Standard_Model
Brane in eleven-dimensional supergravity
eleven-dimensional supergravity which possesses a three-dimensional world volume. The M2-brane solution can be found by requiring ( P o i n c a r e ) 3 ×
M2-brane
Supersymmetric generalization of Yang–Mills
the form of Wess–Zumino model type superfields Φ {\displaystyle \Phi } . Under a gauge transformation, Φ ↦ exp ( − 2 i q Ω ) Φ {\displaystyle \Phi \mapsto
N = 1 supersymmetric Yang–Mills theory
N_=_1_supersymmetric_Yang–Mills_theory
52-dimensional exceptional simple Lie group
The F4 lattice is a four-dimensional body-centered cubic lattice (i.e. the union of two hypercubic lattices, each lying in the center of the other)
F4_(mathematics)
Superstring quantization approach
K-theory Supersymmetry Supergravity Eleven-dimensional supergravity Type I supergravity Type IIA supergravity Type IIB supergravity Superspace Lie superalgebra
GS_formalism
Extended objects found in string theory
1995, Polchinski identified D-branes with black p-brane solutions of supergravity, a discovery that triggered the second superstring revolution and led
D-brane
Theory in physics
dimensions. Of much recent interest are matrix models of the two-dimensional Type 0 string theories. These "matrix models" are understood as describing the
Non-critical_string_theory
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