Seiberg–Witten curve
E860092
Riemann surface
algebraic curve
auxiliary curve in quantum field theory
complex curve
tool in supersymmetric gauge theory
The Seiberg–Witten curve is an auxiliary complex algebraic curve encoding the low-energy effective dynamics of certain supersymmetric gauge theories, particularly their moduli spaces and BPS spectra.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
Riemann surface
ⓘ
algebraic curve ⓘ auxiliary curve in quantum field theory ⓘ complex curve ⓘ tool in supersymmetric gauge theory ⓘ |
| appearsIn |
Seiberg–Witten solution of N=2 SU(2) gauge theory
ⓘ
Seiberg–Witten theory NERFINISHED ⓘ |
| context |
N=2 supersymmetry
ⓘ
four-dimensional quantum field theory ⓘ |
| definedOver | complex numbers ⓘ |
| determines |
period matrix of the effective theory
ⓘ
prepotential of the low-energy effective action ⓘ |
| encodes |
BPS spectrum
ⓘ
Coulomb branch moduli space ⓘ central charges of BPS states ⓘ effective gauge couplings ⓘ low-energy effective dynamics ⓘ special Kähler geometry of the Coulomb branch ⓘ |
| generalizationOf | elliptic curve in SU(2) N=2 theory ⓘ |
| hasPart | meromorphic Seiberg–Witten differential ⓘ |
| hasProperty |
degenerates at singular points of moduli space
ⓘ
depends on Coulomb branch parameters ⓘ genus equals rank of gauge group in many examples ⓘ |
| introducedBy |
Edward Witten
NERFINISHED
ⓘ
Nathan Seiberg NERFINISHED ⓘ |
| introducedIn | mid-1990s ⓘ |
| mathematicalArea |
algebraic geometry
ⓘ
complex geometry ⓘ |
| namedAfter |
Edward Witten
NERFINISHED
ⓘ
Nathan Seiberg NERFINISHED ⓘ |
| physicalArea |
high-energy theoretical physics
ⓘ
string theory ⓘ |
| relatedTo |
Hitchin system
NERFINISHED
ⓘ
M-theory fivebrane constructions ⓘ electric–magnetic duality ⓘ geometric engineering of gauge theories ⓘ integrable systems ⓘ moduli space of vacua ⓘ monodromy of the Coulomb branch ⓘ spectral curves of integrable systems ⓘ |
| togetherWith | Seiberg–Witten differential NERFINISHED ⓘ |
| usedFor |
computing BPS masses
ⓘ
computing effective couplings ⓘ describing confinement and monopole condensation ⓘ studying singularities of moduli space ⓘ |
| usedIn |
N=2 supersymmetric gauge theory
ⓘ
low-energy effective field theory ⓘ supersymmetric gauge theory ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.