A 2d/1d Holographic Duality

Understand

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 ${\cal N} = 4$ 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.