13 papers found.

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We study various geometrical quantities for Calabi–Yau varieties realized as cones over Gorenstein Fano varieties, obtained as toric varieties from reflexive polytopes in various dimensions. Focus is made on reflexive polytopes up to dimension 4 and the minimized volumes of the Sasaki–Einstein base of the corresponding Calabi–Yau cone are calculated. By doing so, we conjecture...

We introduce a new duality for \( \mathcal{N} \) = 1 supersymmetric gauged matrix models. This 0d duality is an order 4 symmetry, namely an equivalence between four different theories, hence we call it Quadrality. Our proposal is motivated by mirror symmetry, but is not restricted to theories with a D-brane realization and holds for general \( \mathcal{N} \) = 1 matrix models. We...

We compute the elliptic genus of abelian 2d (0, 2) gauge theories corresponding to brane brick models. These theories are worldvolume theories on a single D1-brane probing a toric Calabi-Yau 4-fold singularity. We identify a match with the elliptic genus of the non-linear sigma model on the same Calabi-Yau background, which is computed using a new localization formula. The...

We introduce Orbifold Reduction, a new method for generating 2d (0, 2) gauge theories associated to D1-branes probing singular toric Calabi-Yau 4-folds starting from 4d \( \mathcal{N}=1 \) gauge theories on D3-branes probing toric Calabi-Yau 3-folds. The new procedure generalizes dimensional reduction and orbifolding. In terms of T-dual configurations, it generates brane brick...

Brane brick models are Type IIA brane configurations that encode the 2d \( \mathcal{N}=\left(0,2\right) \) gauge theories on the worldvolume of D1-branes probing toric Calabi-Yau 4-folds. We use mirror symmetry to improve our understanding of this correspondence and to provide a systematic approach for constructing brane brick models starting from geometry. The mirror...

We provide a brane realization of 2d (0, 2) Gadde-Gukov-Putrov triality in terms of brane brick models. These are Type IIA brane configurations that are T-dual to D1-branes over singular toric Calabi-Yau 4-folds. Triality translates into a local transformation of brane brick models, whose simplest representative is a cube move. We present explicit examples and construct their...

We introduce brane brick models, a novel type of Type IIA brane configurations consisting of D4-branes ending on an NS5-brane. Brane brick models are T-dual to D1-branes over singular toric Calabi-Yau 4-folds. They fully encode the infinite class of 2d (generically) \( \mathcal{N}=\left(0,2\right) \) gauge theories on the worldvolume of the D1-branes and streamline their...

We study the moduli spaces of k U(N ) vortices which are realized by the Higgs branch of a U(k) supersymmetric gauge theory. The theory has 4 supercharges and lives on k D1-branes in a N D3- and NS5-brane background. We realize the vortex moduli space as a \( {\mathbb{C}}^{*} \) projection of the vortex master space. The Hilbert series is calculated in order to characterize the...

The algebraic structure of moduli spaces of 3d \( \mathcal{N}=2 \) supersymmetric gauge theories is studied by computing the Hilbert series which is a generating function that counts gauge invariant operators in the chiral ring. These U(N c ) theories with N f flavors have Aharony duals and their moduli spaces receive contributions from both mesonic and monopole operators. In...

We initiate a systematic study of 2d (0, 2) quiver gauge theories on the world-volume 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...

We study renormalization group flows among \( \mathcal{N}=1 \) SCFTs realized on the worldvolume of D3-branes probing toric Calabi-Yau singularities, thus admitting a brane tiling description. The flows are triggered by masses for adjoint or vector-like pairs of bifundamentals and are generalizations of the Klebanov-Witten construction of the \( \mathcal{N}=1 \) theory for the...

We study chiral gauge-invariant operators on moduli spaces of G instantons for any classical group G on A-type ALE spaces using Hilbert Series (HS). Moduli spaces of instantons on an ALE space can be realized as Higgs branches of certain quiver gauge theories which appear as world-volume theories on Dp branes in a Dp-D(p + 4) system with the D(p + 4) branes (with or without O(p...