Complementary Projection Defects and Decompositions

TL;DR

This paper explores how projection defects in topological quantum field theories lead to a natural decomposition of the unprojected theory into two parts, demonstrated within Landau-Ginzburg orbifold models.

Contribution

It reveals that projection defects have complementary counterparts, enabling the unprojected theory to decompose into two distinct theories, a novel insight in the context of triangulated defect categories.

Findings

Projection defects always have complementary counterparts.

Unprojected theories decompose into two theories associated with these defects.

Demonstrated in Landau-Ginzburg orbifold theories.

Abstract

As put forward in [arXiv:1907.12339] topological quantum field theories can be projected using so-called projection defects. The projected theory and its correlation functions can be completely realized within the unprojected one. An interesting example is the case of topological quantum field theories associated to IR fixed points of renormalization group flows, which by this method can be realized inside the theories associated to the UV. In this note we show that projection defects in triangulated defect categories (such as defects in 2d topologically twisted N=(2,2) theories) always come with complementary projection defects, and that the unprojected theory decomposes into the theories associated to the two projection defects. We demonstrate this in the context of Landau-Ginzburg orbifold theories.