2d (0,2) quiver gauge theories and D-branes

Abstract

We initiate a systematic study of 2d (0, 2) quiver gauge theories on the worldvolume of D1-branes probing singular toric Calabi-Yau 4-folds. We present an algorithm for efficiently calculating the classical mesonic moduli spaces of these theories, which correspond to the probed geometries. We also introduce a systematic procedure for constructing the gauge theories for arbitrary toric singularities by means of partial resolution, which translates to higgsing in the field theory. Finally, we introduce Brane Brick Models, a novel class of brane configurations that consist of D4-branes suspended from an NS5-brane wrapping a holomorphic surface, tessellating a 3-torus. Brane Brick Models are the 2d analogues of Brane Tilings and allow a direct connection between geometry and gauge theory.

3d printing of 2d $$ \mathcal{N}=\left(0,2\right) $$ gauge theories

“…These developments motivated a program aimed at realizing 2d (0, 2) theories in terms of branes and, in turn, exploiting such branes configuration to study the field theory dynamics. The engineering of 2d (0, 2) theories on the worldvolume of D1-branes probing singular toric Calabi-Yau (CY) 4-folds was developed in [1], following the seminal work in [2]. Brane brick models, a new class of brane configurations in Type IIA string theory that are connected to D1-branes probing toric CY 4-folds by T-duality, were introduced and developed in [3][4][5].…”

“…In addition, several results obtained with brane brick models were recovered in [25], exploiting the topological B-model to map the CY 4 geometry to the gauge theory on D1-branes. 1 The probed CY 4 emerges as the moduli space of the gauge theory on the D1-branes. The computation of the moduli space remains one of the most practical approaches for establishing this connection.…”

“…A standard class of starting points for partial resolution is given by orbifolds of C 4 . Multiple examples of this method can be found in [1]. An alternative approach is the fast inverse algorithm for brane brick models [3].…”

“…These are geometries for which the normalized volume of the toric diagram cannot be obtained by a triangulation in terms of minimal tetrahedra with vertices on points in the toric diagram. A simple example is the C 4 /Z2 orbifold with action (1, 1, 1, 1) [1]. point in T CY 3 could be expanded into the third dimension.…”

UV completions for non-critical strings

“…This has been explored to some extent in certain cases such as references [12][13][14][15]. As a final motivation, there is also an intriguing connection between the supersymmetric quantum mechanics of M-theory on a (non-singular) K3-fibered Calabi-Yau fivefold and refined Gromov-Witten invariants of the base Calabi-Yau threefold [16] (see also [17]).…”