Topological M-theory as unification of form theories of gravity
By R. Dijkgraaf, Sergei Gukov, Andrew Neitzke, C. Vafa. 2004
146 citations recorded by the source corpus.
We introduce a notion of topological M-theory and argue that it provides a unification of form theories of gravity in various dimensions. Its classical solutions involve G_2 holonomy metrics on 7-manifolds, obtained from a topological action for a 3-form gauge field introduced by Hitchin. We show that by reductions of this 7-dimensional theory, one can classically obtain 6-dimensional topological A and B models, the self-dual sector of loop quantum gravity in four dimensions, and Chern–Simons gravity in 3 dimensions. We also find that the 7-dimensional M-theory perspective sheds some light on the fact that the topological string partition function is a wavefunction, as well as on S-duality between the A and B models. The degrees of freedom of the A and B models appear as conjugate variables in the 7-dimensional theory. Finally, from the topological M-theory perspective, we find hints of an intriguing holographic link between non-supersymmetric Yang–Mills in four dimensions and A model topological strings on twistor space.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/85aa43a993f794ae07d399d587f101d0f4124a6d
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Citations in the corpus
- The String Landscape, the Swampland, and the Missing Corner (2017, background): “However, it has been conjectured that all these other theories can be attained as a special limit of string theory[66].”
- Instanton counting, Macdonald function and the moduli space of D-branes (2005, background): “In A-model picture the geometric transition implies the equivalence of the Gromov-Witten invariants of local P1 (the resolved conifold side) and the Chern-Simons invariants of S3 (the deformed conifold side), while in B-model picture it leads to the Dijkgraaf-Vafa proposal of matrix model computatio”
- Hitchin functionals in N = 2 supergravity (2005, background): “It has recently been argued [53, 54, 55] that these are equivalent to theories based on the Hitchin functionals H(χ) and H(χ−) where χ = Re(c e−B−iJ) and χ− = nρ.”
- Membranes at Quantum Criticality (2008, background): “In particular, the Lifshitz scalar is believed to be in the same universality class as the quantum dimer problem, which is particularly intriguing because of the close connection [8, 13] between dimer models, topological string theory and noncritical M-theory.”
- Hartle–Hawking Wave-Function for Flux Compactifications: the Entropic Principle (2005, methodology): “To write down such an equation, we start with a holomorphic section XI0 (z) (I = 0, 1, ..., h 2,1) over the moduli space of complex structure.”
- Dirichlet Branes and Mirror Symmetry (2009, background): “In addition, in [120], the authors relate the Hitchin functionals in six and seven dimensions to topological string theory and topological M-theory.”
- Loop quantum gravity: an outside view (2005, background): “25 Finding a connection between classical two-form gravity in four dimensions and topological string theory [157] can hardly be considered evidence for the connection between LQG and string theory.”
- The effective action of type II Calabi‐Yau orientifolds (2004, methodology): “More precisely, we compare (24)In terms of the Hitchin functionals [30] recently discussed in [58, 59] the reduction of the G2 Kähler potential (5.”
- Topological Strings and (Almost) Modular Forms (2006, background): “The symmetry 1 This fact was also recently explored in [18,14,31,39].”