Topological sigma models

@article{Witten1988TopologicalSM,
  title={Topological sigma models},
  author={Edward Witten},
  journal={Communications in Mathematical Physics},
  year={1988},
  volume={118},
  pages={411-449}
}
  • E. Witten
  • Published 1 February 1988
  • Physics
  • Communications in Mathematical Physics
A variant of the usual supersymmetric nonlinear sigma model is described, governing maps from a Riemann surfaceΣ to an arbitrary almost complex manifoldM. It possesses a fermionic BRST-like symmetry, conserved for arbitraryΣ, and obeyingQ2=0. In a suitable version, the quantum ground states are the 1+1 dimensional Floer groups. The correlation functions of the BRST-invariant operators are invariants (depending only on the homotopy type of the almost complex structure ofM) similar to those that… Expand

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References

SHOWING 1-10 OF 21 REFERENCES
Topological quantum field theory
A twisted version of four dimensional supersymmetric gauge theory is formulated. The model, which refines a nonrelativistic treatment by Atiyah, appears to underlie many recent developments inExpand
INTRODUCTION TO STRING AND SUPERSTRING THEORY. 2.
Conformal field theory is reviewed, then conformal invariance is used to rederive the basic results on the embedding dimensionality for bosonic and fermionic strings. The spectrum of the bosonic andExpand
Heterotic string theory (I). The free heterotic string
A new theory of closed orientable superstrings is constructed as a chiral combination of the closed D = 26 bosonic and D = 10 fermionic strings. The resulting ten-dimensional theory is N = 1Expand
CLOSED STRING FIELD THEORY
Abstract A gauge invariant cubic action describing bosonic closed string field theory is constructed. The gauge symmetries include local spacetime diffeomorphisms. The conventional closed stringExpand
Heterotic string theory (II). The interacting heterotic string
Abstract The theory of interacting heterotic strings is presented. Vertex operators are derived in both the bosonic and fermionic formulations of the theory and are shown to be consistent with gaugeExpand
Conformal invariance, supersymmetry and string theory
Covariant quantization of string theories is developed in the context of conformal field theory and the BRST quantization procedure. The BRST method is used to covariantly quantize superstrings, andExpand
Pseudo holomorphic curves in symplectic manifolds
Definitions. A parametrized (pseudo holomorphic) J-curve in an almost complex manifold (IS, J) is a holomorphic map of a Riemann surface into Is, say f : (S, J3 ~(V, J). The image C=f(S)C V is calledExpand
A polynomial invariant for knots via von Neumann algebras
Thus, the trivial link with n components is represented by the pair (l ,n), and the unknot is represented by (si$2 * * • s n i , n) for any n, where si, $2, • • • > sn_i are the usual generators forExpand
High-energy symmetries of string theory.
  • Gross
  • Physics, Medicine
  • Physical review letters
  • 1988
By means of a recent analysis of the high-energy limit of string scattering, linear relations between string scattering amplitudes are derived. These are shown to hold order by order in perturbationExpand
Morse theory for fixed points of symplectic diffeomorphisms
On demontre le cas particulier suivant de la conjecture de Arnold sur les points fixes d'une deformation exacte φ d'une variete symplectique compacte close P: si π 2 (P)=0 et tous les points fixes deExpand
...
1
2
3
...