Trisecting non-Lagrangian theories

TL;DR

This paper introduces a novel approach to defining invariants of smooth 4-manifolds by leveraging topological twists of non-Lagrangian 4d supersymmetric theories, reducing the problem to computations in topological A-models with complex targets.

Contribution

It presents a new framework for 4-manifold invariants using topological twists of non-Lagrangian theories, expanding the toolkit beyond traditional Lagrangian-based methods.

Findings

Invariants computed via topological A-models with unusual targets.

Reduction of 4-manifold problems to standard topological string computations.

Application to a variety of complex geometries and models.

Abstract

We propose a way to define and compute invariants of general smooth 4-manifolds based on topological twists of non-Lagrangian 4d N=2 and N=3 theories in which the problem is reduced to a fairly standard computation in topological A-model, albeit with rather unusual targets, such as compact and non-compact Gepner models, asymmetric orbifolds, N=(2,2) linear dilaton theories, "self-mirror" geometries, varieties with complex multiplication, etc.