Magnificent Four with Colors

Abstract

We study the rank N magnificent four theory, which is the supersymmetric localization of U(N) super-Yang-Mills theory with matter (a super-group U(N|N) gauge theory) on a Calabi-Yau fourfold. Our theory contains the higher rank Donaldson-Thomas theory of threefolds. We conjecture an explicit formula for the partition function Z, and report on the performed checks. The partition function Z has a free field representation. Surprisingly, it depends on the Coulomb and mass parameters in a simple way. We also clarify the definition of the instanton measure.

arXiv commentv4: fixed two typos

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Cited by in corpus (36)

• $K$-theoretic DT/PT correspondence for toric Calabi-Yau 4-folds
• Toroidal and Elliptic Quiver BPS Algebras and Beyond
• Curve counting and DT/PT correspondence for Calabi-Yau 4-folds
• Counting sheaves on Calabi-Yau 4-folds, I
• Higher rank K-theoretic Donaldson-Thomas theory of points
• On the motive of the nested Quot scheme of points on a curve
• Quantum toroidal algebras and solvable structures in gauge/string theory
• ADHM in 8d, coloured solid partitions and Donaldson-Thomas invariants on orbifolds
• Canonical vertex formalism in DT theory of toric Calabi-Yau 4-folds
• On the D(-1)/D7-brane systems
• Quantum Integrable Systems from Supergroup Gauge Theories
• Tetrahedron instantons
• Super-Schur Polynomials for Affine Super Yangian $\mathsf{Y}({\widehat{\mathfrak{gl}}}_{1|1})$
• The Origin of Calabi-Yau Crystals in BPS States Counting
• Gauge origami and quiver W-algebras
• Noncommutative Instantons in Diverse Dimensions
• Tetrahedron instantons in Donaldson-Thomas theory
• BPS States Meet Generalized Cohomology
• On Supersymmetric Interface Defects, Brane Parallel Transport, Order-Disorder Transition and Homological Mirror Symmetry
• On the M2-Brane Index on Noncommutative Crepant Resolutions
• Charging solid partitions
• Double nested Hilbert schemes and the local stable pairs theory of curves
• Orthosymplectic Superinstanton Counting and Brane Dynamics
• Hyperquot schemes on curves: virtual class and motivic invariants
• Gauge origami and quiver W-algebras III: Donaldson--Thomas $qq$-characters
• Seven-dimensional super Yang-Mills at negative coupling
• Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
• A Donaldson-Thomas crepant resolution conjecture on Calabi-Yau 4-folds
• Tunnels Under Geometries (or Instantons Know Their Algebras)
• Gauge origami and quiver W-algebras IV: Pandharipande--Thomas $qq$-characters
• An Overview of Crystals and Double Quiver Yangians
• Generalized Calogero-Moser system and supergroup gauge origami
• The 4-fold Pandharipande--Thomas vertex and Jeffrey--Kirwan residue
• Wall-crossing for zero-dimensional sheaves and Hilbert schemes of points on Calabi-Yau 4-folds
• The chiral ring of gauge theories in eight dimensions
• Equivariant Segre and Verlinde invariants for Quot schemes