Tetrahedron instantons

Abstract

We introduce and study tetrahedron instantons, which can be realized in string theory by D$1$-branes probing a configuration of intersecting D$7$-branes in flat spacetime with a proper constant $B$-field. Physically they capture instantons on ${\mathbb{C}}^3$ in the presence of the most general intersecting real codimension-two supersymmetric defects. Moreover, we construct the tetrahedron instantons as particular solutions of general instanton equations in noncommutative field theory. We analyze the moduli space of tetrahedron instantons and discuss the geometric interpretations. We compute the instanton partition function both via the equivariant localization on the moduli space of tetrahedron instantons and via the elliptic genus of the worldvolume theory on the D$1$-branes probing the intersecting D$7$-branes, obtaining the same result. The instanton partition function of the tetrahedron instantons lies between the higher-rank Donaldson-Thomas invariants on ${\mathbb{C}}^3$ and the partition function of the magnificent four model, which is conjectured to be the mother of all instanton partition functions. Finally, we show that the instanton partition function admits a free field representation, suggesting the existence of a novel kind of symmetry which acts on the cohomology of the moduli spaces of tetrahedron instantons.

arXiv comment62 pages; v2: additional references and minor corrections; v3: numerous minor improvements

References in corpus (79)

• String Theory and Noncommutative Geometry
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Noncommutative Field Theory
• Phases of $N=2$ Theories In Two Dimensions
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Noncommutative Geometry and Matrix Theory: Compactification on Tori
• Instantons in QCD
• Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes
• D-branes, Quivers, and ALE Instantons
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Instantons on noncommutative R^4, and (2,0) superconformal six dimensional theory
• Vortices, Instantons and Branes
• Loop and surface operators in N=2 gauge theory and Liouville modular geometry
• The intrinsic normal cone
• Integrating Over Higgs Branches
• D-particle bound states and generalized instantons
• Elliptic genera of 2d N=2 gauge theories
• Topological Amplitudes in String Theory
• Quantization of Integrable Systems and Four Dimensional Gauge Theories
• Gauge Fields and D-branes
• Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups
• Quantum Foam and Topological Strings
• Instanton counting on blowup. I. 4-dimensional pure gauge theory
• Issues in Topological Gauge Theory
• Darboux coordinates, Yang-Yang functional, and gauge theory
• 2d Index and Surface operators
• Solitons in Noncommutative Gauge Theory
• ABCD of instantons
• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters
• Surface Operators in N=2 4d Gauge Theories
• D-particles, Matrix Integrals and KP hierachy
• Sigma Models And The ADHM Construction Of Instantons
• Affine SL(2) conformal blocks from 4d gauge theories
• Walls, Lines, and Spectral Dualities in 3d Gauge Theories
• Special Quantum Field Theories In Eight And Other Dimensions
• BPS Bound States Of D0-D6 And D0-D8 Systems In A B-Field
• Exact Noncommutative Solitons
• Instanton counting with a surface operator and the chain-saw quiver
• Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions
• Negative Branes, Supergroups and the Signature of Spacetime
• BPS/CFT correspondence II: Instantons at crossroads, Moduli and Compactness Theorem
• Higher Dimensional Analogues of Donaldson-Witten Theory
• Extended Seiberg-Witten Theory and Integrable Hierarchy
• BPS/CFT Correspondence III: Gauge Origami partition function and qq-characters
• Ghost D-branes
• Chern-Simons and Twisted Supersymmetry in Higher Dimensions
• BPS/CFT correspondence IV: sigma models and defects in gauge theory
• Branes, Instantons, And Taub-NUT Spaces
• Affine sl(N) conformal blocks from N=2 SU(N) gauge theories
• Cohomological gauge theory, quiver matrix models and Donaldson-Thomas theory
• Spiked Instantons from Intersecting D-branes
• Brane/anti-Brane Systems and U(N|M) Supergroup
• Opers, surface defects, and Yang-Yang functional
• Magnificent Four with Colors
• Zero-dimensional Donaldson-Thomas invariants of Calabi-Yau 4-folds
• Moduli Spaces of Instantons on the Taub-NUT Space
• Construction of Hilbert and Quot Schemes
• Non-Commutative Instantons and the Seiberg-Witten Map
• A holomorphic anomaly in the elliptic genus
• Intersecting Surface Defects and Instanton Partition Functions
• Quiver Matrix Model and Topological Partition Function in Six Dimensions
• Riemann-Hilbert correspondence and blown up surface defects
• Localization and real Jacobi forms
• Splitting of surface defect partition functions and integrable systems
• Instantons, Quivers and Noncommutative Donaldson-Thomas Theory
• Quantum Spin Systems and Supersymmetric Gauge Theories, I
• Higher rank K-theoretic Donaldson-Thomas theory of points
• Surface defects in gauge theory and KZ equation
• M-theory on Calabi-Yau Five-Folds
• ADHM in 8d, coloured solid partitions and Donaldson-Thomas invariants on orbifolds
• Effective gravitational couplings of four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories
• Tautological stable pair invariants of Calabi-Yau 4-folds
• Super instanton counting and localization
• Elliptic non-Abelian Donaldson-Thomas invariants of ${\mathbb{C}}^3$
• Seiberg-Witten geometry of four-dimensional N=2 SO-USp quiver gauge theories, I
• Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties
• Counting zero-dimensional subschemes in higher dimensions
• Partition function of $\mathcal{N}=2$ supersymmetric gauge theory and two-dimensional Yang-Mills theory
• Dynamics of Two-Dimensional $\mathcal{N}=(2,2)$ Supersymmetric Theories with Semichiral Superfields I

Cited by in corpus (8)

• Gauge origami and quiver W-algebras
• Tetrahedron instantons in Donaldson-Thomas theory
• Noncommutative Instantons in Diverse Dimensions
• Double Quiver Gauge Theory and BPS/CFT Correspondence
• Evidence for an Algebra of ${\mathbf{G}}_2$ Instantons
• Gauge origami and quiver W-algebras III: Donaldson--Thomas $qq$-characters
• Gauge origami and quiver W-algebras IV: Pandharipande--Thomas $qq$-characters
• The 4-fold Pandharipande--Thomas vertex and Jeffrey--Kirwan residue