Beliebiger Eintrag,
A 2d/1d Holographic Duality
(26.03.2017)
Zusammenfassung
We propose \$AdS\_2\$/CFT\$\_1\$ dualities between exactly solvable topological
quantum mechanics theories with vector or matrix large \$N\$ limits (on the
boundary) and weakly coupled gauge theories on a fixed \$AdS\_2\$ background (in
the bulk). The boundary theories can be embedded as 1d sectors of 3d \$N
= 4\$ superconformal field theories with holographic duals, from which they can
be obtained using supersymmetric localization. We study a few examples of such
1d theories: theories with vector large \$N\$ limits that are embedded into 3d
theories of many free massless hypermultiplets with \$AdS\_4\$ higher spin duals;
and a 1d theory with a matrix large \$N\$ limit embedded into the 3d ABJM theory
at Chern-Simons level \$k=1\$, which has an \$AdS\_4\$ supergravity dual. We propose
that the \$U(N)\$ singlet sectors of the 1d vector models are dual to 2d gauge
theories on \$AdS\_2\$ whose gauge algebras are finite dimensional and whose full
non-linear actions we completely determine in some cases. The 1d theory
embedded into ABJM theory has a \$Z\_2\$-invariant sector dual to a 2d
gauge theory on \$AdS\_2\$ whose gauge algebra is the infinite dimensional algebra
of area preserving diffeomorphisms of a two-sphere. We provide evidence that
the 2d gauge theories on \$AdS\_2\$ can be obtained from localizing the \$AdS\_4\$
duals of the 3d SCFTs mentioned above, and thus argue that our 2d/1d dualities
can be obtained via supersymmetric localization on both sides of their parent
\$AdS\_4\$/CFT\$\_3\$ dualities. We discuss the boundary terms required by
holographic renormalization in the 2d gauge theories on \$AdS\_2\$ and show how
they arise from supersymmetric localization.
