Generalized lattices, conformal manifolds, and symmetries

TL;DR

This paper explores supersymmetric conformal quantum field theories with lattice-labeled degrees of freedom, focusing on their conformal manifolds, symmetries, and exactly marginal deformations, including topological lattice holonomies.

Contribution

It introduces a framework connecting lattice data with conformal manifolds and symmetries, including novel interpretations of current non-conservation and topological deformations.

Findings

Symmetries broken by interactions can be interpreted as conserved along lattice directions.

Certain exactly marginal deformations are labeled by topological lattice holonomies.

Concrete examples illustrate the relevance to SCFT compactifications.

Abstract

We consider supersymmetric conformal quantum field theories (SCFTs) with degrees of freedom labeled by lattice data. We will assume that in terms of the corresponding lattice the interactions are nearest neighbor and exactly marginal. For example, one can construct such theories by coupling many copies of a single SCFT with exactly marginal deformations. In particular, we discuss the interplay between conformal manifolds of such theories and their global, on-site and lattice, symmetries. We show that one can interpret certain current non-conservation equations for symmetries broken by the interactions as conservation equations including the lattice directions. Moreover, we discuss a class of exactly marginal deformations which are labeled by lattice holonomies that are topological on the lattice. We discuss concrete examples of such constructions and comment on their relevance to compactifications of SCFTs.