Balanced Topological Field Theories

Abstract

We describe a class of topological field theories called ``balanced topological field theories.'' These theories are associated to moduli problems with vanishing virtual dimension and calculate the Euler character of various moduli spaces. We show that these theories are closely related to the geometry and equivariant cohomology of ``iterated superspaces'' that carry two differentials. We find the most general action for these theories, which turns out to define Morse theory on field space. We illustrate the constructions with numerous examples. Finally, we relate these theories to topological sigma-models twisted using an isometry of the target space.

40 pages, harvmac, references added, to appear in Commun. Math. Phys

References in corpus (6)

• Dirichlet-Branes and Ramond-Ramond Charges
• D-Branes and Topological Field Theories
• Algebras, BPS States, and Strings
• Counting Dyons in N=4 String Theory
• D-branes and Fat Black Holes
• Gas of D-Branes and Hagedorn Density of BPS States

Cited by in corpus (54)

• GUTs and Exceptional Branes in F-theory - I
• A Lattice Formulation of Super Yang-Mills Theories with Exact Supersymmetry
• Super Yang-Mills Theories on the Two-Dimensional Lattice with Exact Supersymmetry
• Schwinger-Keldysh formalism I: BRST symmetries and superspace
• Aspects of N_{T}\geq 2 Topological Gauge Theories and D-Branes
• Euclidean SYM Theories by Time Reduction and Special Holonomy Manifolds
• Twisted Supersymmetric Gauge Theories and Orbifold Lattices
• The Fluid Manifesto: Emergent symmetries, hydrodynamics, and black holes
• Various Super Yang-Mills Theories with Exact Supersymmetry on the Lattice
• Effective Action for Relativistic Hydrodynamics: Fluctuations, Dissipation, and Entropy Inflow
• Euclidean D-branes and higher-dimensional gauge theory
• Schwinger-Keldysh formalism II: Thermal equivariant cohomology
• Cohomological gauge theory, quiver matrix models and Donaldson-Thomas theory
• Vafa-Witten invariants for projective surfaces I: stable case
• Topological sigma models & dissipative hydrodynamics
• Vafa-Witten invariants for projective surfaces II: semistable case
• N=4 Twisted Superspace from Dirac-Kahler Twist and Off-shell SUSY Invariant Actions in Four Dimensions
• Holomorphic maps and the complete 1/N expansion of 2D SU(N) Yang-Mills
• Topological Open Membranes
• Les Houches Lectures on Fields, Strings and Duality
• 3-manifold topology and the Donaldson-Witten partition function
• Instantons, Quivers and Noncommutative Donaldson-Thomas Theory
• Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges
• Topological Vector Symmetry of BRSTQFT and Construction of Maximal Supersymmetry
• On the Multi-Instanton Measure for Super Yang--Mills Theories
• Mass Perturbations in Twisted N=4 Supersymmetric Gauge Theories
• An $\mathcal{N}=1$ 3d-3d Correspondence
• N_T=4 equivariant extension of the 3D topological model of Blau and Thompson
• Six-Dimensional TQFTs and Twisted Supersymmetry
• Renormalization and BRST symmetry in Donaldson-Witten theory
• Duality from Topological Symmetry
• Restoration of supersymmetry in two-dimensional SYM with sixteen supercharges on the lattice
• Duality in Topological Quantum Field Theories
• Supersymmetry and gauge theory on Calabi-Yau 3-folds
• Noncommutative Cohomological Field Theory and GMS soliton
• Higher dimensional analogue of the Blau-Thompson model and N_T=8, D=2 Hodge-type cohomological gauge theories
• On Forms with Non-Abelian Charges and Their Dualities
• Twisted N=4 Super Yang-Mills Theory in Omega-background
• Large N Expansion of q-Deformed Two-Dimensional Yang-Mills Theory and Hecke Algebras
• New Results on N=4 SuperYang-Mills Theory
• Euler number of Instanton Moduli space and Seiberg-Witten invariants
• The gauging of BV algebras
• A model for complex analytic equivariant elliptic cohomology from quantum field theory
• Basic and Equivariant Cohomology in Balanced Topological Field Theory
• Monads, Strings, and M Theory
• Chiral expansion and Macdonald deformation of two-dimensional Yang-Mills theory
• Metric Reduction and Generalized Holomorphic Structures
• Sigma Models for Bundles on Calabi-Yau: A Proposal for Matrix String Compactifications
• An anisotropic hybrid non-perturbative formulation for 4D N = 2 supersymmetric Yang-Mills theories
• Non-Geometric Magnetic Flux and Crossed Modules
• Cohomological Field Theories with Kähler Structure
• Lattice Formulation of $\mathcal{N}=2^{\ast }$ Yang-Mills
• Higgs Bundles and Four Manifolds
• $\mathcal{N}=2^{\ast }$ Yang-Mills on the Lattice