Abstract
We discuss instanton operators in five-dimensional gauge theories. These are defined as disorder operators which create a non-vanishing second Chern class on a foursphere surrounding their insertion point. As such they may be thought of as higherdimensional analogues of three-dimensional monopole (or ‘t Hooft) operators. We argue that they play an important role in the enhancement of the Lorentz symmetry for maximally supersymmetric Yang-Mills to SO(1, 5) at strong coupling.
Highlights
We introduce a new local operator In(x), which modifies the boundary conditions of the gauge field at infinity via the condition
In this note we have discussed a particular class of disorder operators in five-dimensional gauge theories, dubbed instanton operators
These are defined through a modification of the boundary conditions for the gauge field in the path integral, which imposes a nonvanishing second Chern class on any four-sphere that surrounds the insertion point in Euclidean space
Summary
We will define an instanton operator in analogy with monopole operators in three dimensions. The simplest solution to these equations is to set Ar = 0, Vi = 0 and ∂rAi = 0 so that Fij satisfies the Yang-Mills equations on the four-sphere: D[iFjk] = 0 and DjFji = 0 with Fij independent of r. The above ratio is always an integer and scales like N 3 for large N Another equivalent definition of instanton operators comes from generalising the approach of [7], that is by requiring that In(x) creates a charge-n instanton-soliton in 5D Yang-Mills theory. We have no need for these here and include an integration over all instanton configurations at the insertion point
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