Self-Dual Yang-Mills in AdS${}_4$

Abstract

Quantum Yang-Mills theory in Euclidean AdS${}_4$ with Neumann boundary conditions is studied as a function of the complex couplings $\frac{1}{g_{\pm }^2}\equiv \frac{1}{g^2}\mp \frac{i\theta }{8{\pi }^2}$. We define a "self-dual limit" by $g_{-}\to 0$ with $g_{+}\mathrm{fixed}$. We argue that the limiting theory is well-defined perturbatively and equivalent to the BF formulation of self-dual Yang-Mills theory with a particular boundary condition relating $B$ and $F$ at the boundary $\partial$AdS${}_4$. $g_{+}$ is the loop-counting parameter of the self-dual theory. This is in stark contrast to flat space, where $\theta$ has no effect on perturbative dynamics. In the self-dual limit, it is shown that all tree-level zero-plus and single-plus boundary correlators vanish. A closed form expression is given for any number of gluons for the double-plus tree correlators. Finally, we show that in the flat space limit of AdS${}_4$, the total energy poles in the tree boundary correlators correctly reduce to the single-minus gluon amplitudes.

30 pages + 6 appendices, 6 figures