Masahito Yamazaki

4d index to 3d index and 2d topological quantum field theory

We compute the 4d superconformal index for N = 1, 2 gauge theories on S × L(p, 1), where L(p, 1) is a lens space. We find that the 4d N = 1, 2 index on S × L(p, 1) reduces to a 3d N = 2, 4 index on S × S in the large p limit, and to a 3d partition function on a squashed L(p, 1) when the size of the temporal S shrinks to zero. As an application of our index, we study 4d N = 2 superconformal field theories arising from the 6d N = (2, 0) A1 theory on a punctured Riemann surface Σ, and conjecture the existence of a 2d Topological Quantum Field Theory on Σ whose correlation function coincides with the 4d N = 2 index on S × L(p, 1).

{\text{SL}}\left( {2,\mathbb{R}} \right) Chern-Simons, Liouville, and gauge theory on duality walls

We propose an equivalence of the partition functions of two different 3d gauge theories. On one side of the correspondence we consider the partition function of 3d

3d partition function as overlap of wavefunctions

{text{SL}}left( {2,mathbb{R}} right)

3d Chern-Simons theory from M5-branes

Chern-Simons theory on a 3-manifold, obtained as a punctured Riemann surface times an interval. On the other side we have a partition function of a 3d

Recursion relations for conformal blocks

mathcal{N} = 2

Semiclassical Analysis of the 3d/3d Relation

superconformal field theory on S3, which is realized as a duality domain wall in a 4d gauge theory on S4. We sketch the proof of this conjecture using connections with quantum Liouville theory and quantum Teichmüller theory, and study in detail the example of the once-punctured torus. Motivated by these results we advocate a direct Chern-Simons interpretation of the ingredients of (a generalization of) the Alday-Gaiotto-Tachikawa relation. We also comment on M5-brane realizations as well as on possible generalizations of our proposals.

Wilson Loops in 5d {\mathcal{N} = 1} SCFTs and AdS/CFT

We compute the partition function on S3 of 3d

Emergent 3-manifolds from four dimensional superconformal indices.

mathcal{N} = 4