@article{570fe0a03614418b9dcd64bb7b592b8f,

title = "Topological gravity",

abstract = "A version of conformal gravity is formulated with a local fermionic symmetry that is reminiscent of BRST invariance. It may have mathematical applications (gravitational counterpart of Donaldson theory) or physical ones (unbroken phase of general relativity).",

author = "Edward Witten",

note = "Funding Information: In ref. \[1 \], Donaldson initiated a program of using Yang-Mills fields to study the geometry and topology of four-manifolds. Some of the ingredients, notably the self-dual Yang-Mills equations, were familiar to physicists, but other crucial ideas did not have any obvious relation to physics. Floer's work \[2 \] on instantons and three-manifolds has provided a crucial link between Donaldson theory and physics. For on the one hand \[3 \], Floer theory can be interpreted in terms of a certain non-relativistic quantum field theory, and on the other hand Floer theory enters when one tries to define Donaldson invariants of a four-dimensional manifold with boundary. The latter connection between Floer and Donaldson theory led Atiyah to suggest that there should be a relativistic quantum field theory underlying Donaldson theory. This indeed turns out to be the case; the relevant theory, formulated in ref. \[4\] (where more background can be found), is a sort of twisted version of supersymmetric Yang-Mills theory. In ordinary, supersymmetric Yang-Mills theory, the supercharges are space-time spinors, conserved only on a fiat four-manifold M. In the twisted, topological version, there is a single global supercharge Q, obeying Q2=0, and conserved on an arbitrary M. Q relates bosons and fermions all of integer spin. The Q cohomology classes J On leave from Department of Physics, Princeton University, Princeton, NJ 08544, USA. 2 Research supported in part by NSF Grants Nos. PHY 80-19754, 86-16129, 86-20266.",

year = "1988",

month = jun,

day = "2",

doi = "10.1016/0370-2693(88)90704-6",

language = "English (US)",

volume = "206",

pages = "601--606",

journal = "Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics",

issn = "0370-2693",

publisher = "Elsevier",

number = "4",

}