Supersymmetric Yang-Mills Theory On A Four-Manifold

Edward Witten

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Supersymmetric Yang-Mills Theory On A Four-Manifold

Edward Witten

High Energy Physics - Theory · Submitted 31 Mar 1994

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim By exploiting standard facts about $N=1$ and $N=2$ supersymmetric Yang-Mills theory, the Donaldson invariants of four-manifolds that admit a Kahler metric can be computed.

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By exploiting standard facts about $N=1$ and $N=2$ supersymmetric Yang-Mills theory, the Donaldson invariants of four-manifolds that admit a Kahler metric can be computed. The results are in agreement with available mathematical computations, and provide a powerful check on the standard claims about supersymmetric Yang-Mills theory.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	By exploiting standard facts about $N=1$ and $N=2$ supersymmetric Yang-Mills theory, the Donaldson invariants of four-manifolds that admit a Kahler metric can be computed.	contribution 0.67	0.74	0.83	asserted 0.99
s1	The results are in agreement with available mathematical computations, and provide a powerful check on the standard claims about supersymmetric Yang-Mills theory.	interpretation 0.90	0.67	0.21	asserted 0.93

What kind of paper the classifier reports this is: theoretical result 0.96 · evidence from proof or derivation 0.88.

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The paper

Original abstract

By exploiting standard facts about $N=1$ and $N=2$ supersymmetric Yang-Mills theory, the Donaldson invariants of four-manifolds that admit a Kahler metric can be computed. The results are in agreement with available mathematical computations, and provide a powerful check on the standard claims about supersymmetric Yang-Mills theory.

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References

Forward citations

Cited by 14 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Seiberg-Witten Prepotential From Instanton Counting
hep-th 2002-06 conditional novelty 9.0 of 10

Equivariant localization on the instanton moduli space yields a closed combinatorial formula for the Seiberg-Witten prepotential, matching known instanton expansions up to five instantons.
Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
hep-th 1994-07 accept novelty 9.0 of 10

The exact low-energy effective action of N=2 SU(2) super Yang-Mills is determined by an elliptic curve, and the strong-coupling singularities are massless monopoles whose condensation confines electric charge.
Seiberg-Witten Theory and Random Partitions
hep-th 2003-06 accept novelty 8.0 of 10

The low-energy Seiberg-Witten prepotential of N=2 gauge theories is derived from the exact instanton partition function by a saddle-point analysis of random partitions.
Generalized Families of QFTs
hep-th 2026-02 unverdicted novelty 7.0 of 10

Generalized family anomalies for broken higher-group and non-invertible symmetries constrain RG flows and IR phases of QFT families, with explicit application to deformed 4d QCD.
The Geometry of Supersymmetric Partition Functions
hep-th 2013-09 conditional novelty 7.0 of 10

Supersymmetric partition functions on compact curved manifolds are independent of the metric and depend holomorphically on complex structure and holomorphic bundle moduli, in both four and three dimensions.

Show 9 more citing papers

Exploring Curved Superspace
hep-th 2012-05 accept novelty 7.0 of 10

A four-dimensional N=1 theory with a U(1) R-symmetry admits a single rigid supercharge on a Riemannian manifold if and only if that manifold is Hermitian.
GUTs and Exceptional Branes in F-theory - I
hep-th 2008-02 accept novelty 7.0 of 10

F-theory on a local elliptic fourfold is described by a partially twisted eight-dimensional Yang-Mills theory on the seven-brane surface, with chiral matter on curve defects whose intersections generate Yukawa couplings.
D-particle bound states and generalized instantons
hep-th 1998-04 conditional novelty 7.0 of 10

The principal contribution to the Witten index of the D0-brane quantum mechanics is 1/N^2 for D=4,6 and the divisor sum over 1/d^2 for D=10, computed by localization and residue evaluation.
Generalised $\Omega$-backgrounds in twisted $N=4$ super Yang-Mills
hep-th 2026-10 conditional novelty 6.0 of 10

The paper constructs Omega-deformed rigid supergravity backgrounds for the Donaldson-Witten, Vafa-Witten and Geometric Langlands twists of N=4 super Yang-Mills on general Euclidean manifolds.
Candidate Phases for SU(2) Adjoint QCD$_4$ with Two Flavors from $\mathcal{N}=2$ Supersymmetric Yang-Mills Theory
hep-th 2018-06 accept novelty 6.0 of 10

Deforming N=2 SU(2) Yang-Mills by a symmetry-preserving scalar mass generates anomaly-consistent candidate phases for two-flavor adjoint QCD, including a confining CP1 phase with a topological-insulator confining string.
From Rigid Supersymmetry to Twisted Holomorphic Theories
hep-th 2014-07 accept novelty 6.0 of 10

The partition function of N=1 theories on a complex manifold is metric-independent and holomorphic in complex structure and bundle moduli, and its dependence on R-symmetry mixing is fixed by a shift of those moduli.
Towards the String Dual of N=1 SQCD-like Theories
hep-th 2006-02 conditional novelty 6.0 of 10

Smeared flavor D5-branes are added to the Maldacena-Nunez background, producing a family of type IIB solutions whose BPS equations depend on Nf/Nc and which the authors argue describe N=1 SQCD with a quartic superpotential.
BPS/CFT correspondence IV: sigma models and defects in gauge theory
hep-th 2017-11 conditional novelty 5.0 of 10

Half-BPS surface defects in four-dimensional N=2 quiver gauge theories are realized as two-dimensional gauged linear sigma models on flag varieties, with explicit partition functions given for orbifold, quiver, and fo...
Unquenched flavor in the gauge/gravity correspondence
hep-th 2010-02 conditional novelty 4.0 of 10

Smeared flavor D-branes can be backreacted onto type II supergravity backgrounds, yielding tractable duals of gauge theories with dynamical fundamentals, at the price of a small flavor-loop expansion parameter.

How the literature uses it

30 arXiv papers cite this in 51 sentences

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Compares with it 1 paper

The numbers that we are considering look similar to Donaldson invariants [ref] .

On enumerative problems for maps and quasimaps: freckles and scars · Formulation of the problem · 0.94

Cites it as background 16 papers

On the other hand, it is known since the seminal paper [ref] that twisted $N=2$ supersymmetric gauge theories can be formulated on any Riemannian four-manifold and their observables realise many interesting topological invariants such as Donaldson invariants [ref] and knot invariants [ref] .

Exact results for ${\cal N}=2$ supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants · Introduction · 0.98
The cohomology in this constrained functional space defines the so called Witten observables [ref] ;

Let's Twist Again: N=2 Super Yang Mills Theory Coupled To Matter · Twisted algebra · 0.80
Correlations functions of topologically twisted quantum field theories provide many insights into non-perturbative aspects of quantum field theory as well as the geometry of four-manifolds [ref] .

Topological twists of massive SQCD, Part I · Introduction · 0.95

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