arXiv subjects

Mario Carcamo

Publications and source records attributed to Mario Carcamo.

3 recordsLinked to original sources

arXiv2026

Crystal Melting, Triality and Partition Functions for Toric Calabi-Yau Fourfolds

We extend the study of the recently introduced crystal melting models associated to toric Calabi-Yau 4-folds in several directions. In particular, we investigate in greater detail the structure of these models for general toric CY 4-folds and flavor configurations, using the explicit example of $Q^{1,1,1}$ to illustrate our ideas. To this end, we develop an efficient algorithm for constructing crystals based on periodic quivers. A central goal of this work is to understand the behavior of crystals and their partition functions under triality. We analyze the evolution of crystals along periodic triality cascades and generate detailed data for these systems, including Hasse diagrams, partition functions, and the multiplicities of melting configurations. We introduce the notion of stable variables and show that they lead to the stabilization of the partition functions along cascades. Finally, we define the profile of the crystal partition function and observe that, when expressed in terms of stable variables, it displays interesting behavior. A further motivation for this work is to generate empirical data that may guide the search for a physically motivated generalization of cluster algebras associated with $2d$ (0,2) quiver theories and their triality transformations.

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arXiv2025

Relevant Deformations, Brane Brick Models and Triality

We extend the study of relevant deformations connecting 2d (0,2) gauge theories on D1-branes probing toric Calabi-Yau 4-folds beyond pure mass deformations. The underlying geometry provides powerful insights when field-theoretic tools are still lacking. We observe that the volume of the Sasaki-Einstein base of the Calabi-Yau 4-fold grows towards the IR, signaling the relevance of deformations. We exploit the map between gauge theory fields and GLSM fields to compute scaling dimensions directly from divisor volumes, allowing for a sharper determination of whether terms in the Lagrangian are relevant or irrelevant. Moreover, this map provides a systematic way to determine the precise set of terms needed to realize a given deformation. We also explore the interplay between general relevant deformations and triality, studying cases where non-mass deformations are mapped to mass deformations in a dual theory, and resolving puzzles that seem to require non-holomorphic couplings in one of the dual phases. Finally, we present evidence that when the Hilbert series of the mesonic moduli space is refined only under the U(1) R-symmetry, it becomes invariant even under non-mass relevant deformations of the brane brick models corresponding to toric Calabi-Yau 4-folds related by a birational transformation, extending previous results to a broader class of deformations.

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arXiv2025

Charting the Triality Webs for All Smooth Fano 3-Folds

We determine all toric phases for the $2d$ $(0,2)$ theories on D1-branes probing the complex cones over the 18 smooth Fano 3-folds, whose toric diagrams correspond to the regular reflexive polytopes in 3 dimensions. These results significantly expand the list of explicitly known gauge theories on D1-branes over toric CY 4-folds. We go beyond the classification of toric phases and map the corresponding triality webs, establishing how the toric phases are connected by triality. The size and complexity of the webs constructed in this work far surpass any previously known examples, both in the contexts of Calabi-Yau 3-folds and 4-folds-with several of these CY 4-folds exhibiting hundreds of toric phases. We propose various new approaches for characterizing triality webs. Our work lays the foundation for a comprehensive exploration of the structure of triality webs.

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