M-theory in the Omega-background and 5-dimensional non-commutative gauge theory

Abstract

The $\Omega$-background is defined for supergravity, and a very general class of such backgrounds is constructed for 11-dimensional supergravity. 11-dimensional supergravity in a certain $\Omega$-background is shown to be equivalent to a 5-dimensional non-commutative gauge theory of Chern-Simons type. M2 and M5 branes are expressed as 1 and 2-dimensional extended objects in the 5-dimensional gauge theory. This 5-dimensional gauge theory is shown to admit a consistent quantization with two coupling constants, despite being formally non-renormalizable. A check of a twisted version of AdS/CFT is performed relating this 5-dimensional non-commutative gauge theory to the theory on N M5 branes, wrapping an $A_{k-1}$ singularity and placed in an $\Omega$-background. The operators on the M5 branes, in the $\Omega$-background, are described by a certain chiral algebra which in the large N limit becomes a $W_{k+\infty }$ algebra. This chiral algebra is recovered from the 5-dimensional gauge theory. This argument also provides a holographic explanation of the result of Maulik-Okounkov and Schiffmann-Vasserot that the $W_{k+\infty }$ algebra acts on the equivariant cohomology of the moduli of instantons on an $A_{k-1}$ singularity.

References in corpus (5)

• Supersymmetric gauge theory and the Yangian
• Ω-deformation and quantization
• The Coulomb Branch of 3d $\mathcal{N}=4$ Theories
• Quantization of open-closed BCOV theory, I
• Ω-deformation of B-twisted gauge theories and the 3d-3d correspondence

Cited by in corpus (13)

• Topological Holography: Towards a Unification of Landau and Beyond-Landau Physics
• Topological Chern-Simons/Matter Theories
• On Extensions of $\widehat{\mathfrak{gl}(m|n)}$ Kac-Moody algebras and Calabi-Yau Singularities
• Maximally twisted eleven-dimensional supergravity
• Twisted eleven-dimensional supergravity
• Playing with the index of M-theory
• Twisted holography of defect fusions
• Degenerate Classical Field Theories and Boundary Theories
• Evidence for an Algebra of ${\mathbf{G}}_2$ Instantons
• R-matrices and Miura operators in 5d Chern-Simons theory
• A domain wall in twisted M-theory
• Fermi-gas correlators of ADHM theory and triality symmetry
• Integrable models from 4d holomorphic BF theory