Holography for 2d $\mathcal{N}=(0,4)$ quantum field theory

TL;DR

This paper explores the holographic duality between AdS$_3$ supergravity solutions and 2D $ ext{(0,4)}$ quiver quantum field theories, clarifying the structure and anomaly cancellation mechanisms of the dual theories.

Contribution

It categorizes gravity solutions, demonstrates anomaly cancellation via D-brane bound states, and proposes the inclusion of $ ext{(4,4)}$ hypermultiplets to complete the quiver field theory structure.

Findings

Identified gravity solutions corresponding to $ ext{(0,4)}$ theories.

Showed D-brane bound states provide correct flavor symmetry for anomaly cancellation.

Constructed dual BPS string operators and analyzed their properties.

Abstract

We study the correspondence between AdS$_3$ massive IIA supergravity vacua and two-dimensional $\mathcal{N}=(0,4)$ quiver quantum field theories. After categorizing all kinds of gravity solutions, we demystify the ones that seem to reflect anomalous gauge theories. In particular, we prove that there are bound states of D-branes on the boundary of the space which provide the dual quiver theory with exactly the correct amount of flavor symmetry in order to cancel its gauge anomalies. Then we propose that the structure of the field theory should be complemented with additional bifundamental matter, which we argue may only be $\mathcal{N}=(4,4)$ hypermultiplets. Finally, we construct a BPS string configuration and we use the old and new supersymmetric matter to build its dual ultraviolet operator. During this holographic synthesis, we uncover some interesting features of the quiver superpotential and associate the proposed operator with the same classical mass of its dual BPS string.