Author:
Dimofte Tudor,Paquette Natalie M.
Abstract
Abstract
We propose that a simple, Lagrangian 2d
$$ \mathcal{N} $$
N
= (0, 2) duality interface between the 3d
$$ \mathcal{N} $$
N
= 2 XYZ model and 3d
$$ \mathcal{N} $$
N
= 2 SQED can be associated to the simplest triangulated 4-manifold: the 4-simplex. We then begin to flesh out a dictionary between more general triangulated 4-manifolds with boundary and 2d
$$ \mathcal{N} $$
N
= (0, 2) interfaces. In particular, we identify IR dualities of interfaces associated to local changes of 4d triangulation, governed by the (3), (2, 4), and (2, 4) Pachner moves. We check these dualities using supersymmetric half-indices. We also describe how to produce stand-alone 2d theories (as opposed to interfaces) capturing the geometry of 4-simplices and Pachner moves by making additional field-theoretic choices, and find in this context that the Pachner moves recover abelian
$$ \mathcal{N} $$
N
= (0, 2) trialities of Gadde-Gukov-Putrov. Our work provides new, explicit tools to explore the interplay between 2d dualities and 4-manifold geometry that has been developed in recent years.
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
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