Search for: All records

A<sc>bstract</sc> We make progress in understanding the geometry associated to the Generalized Toric Polygons (GTPs) encoding the Physics of 5d Superconformal Field Theories (SCFTs), by exploiting the connection between Hanany-Witten transitions and the mathematical notion of polytope mutations. From this correspondence, it follows that the singular geometry associated to a GTP is identical to that obtained by regarding it as a standard toric diagram, but with some of its resolutions frozen in way that can be determined from the invariance of the so-called period under mutations. We propose the invariance of the period as a new criterion for distinguishing inequivalent brane webs, which allows us to resolve a puzzle posed in the literature. A second mutation invariant is the Hilbert Series of the geometry. We employ this invariant to perform quantitative checks of our ideas by computing the Hilbert Series of the BPS quivers associated to theories related by mutation. Lastly, we discuss the physical interpretation of a mathematical result ensuring the existence of a flat fibration over ℙ¹interpolating between geometries connected by mutation, which we identify with recently introduced deformations of the corresponding BPS quivers. 

A<sc>bstract</sc> We introduce a class of 4-dimensional crystal melting models that count the BPS bound state of branes on toric Calabi-Yau 4-folds. The crystalline structure is determined by the brane brick model associated to the Calabi-Yau 4-fold under consideration or, equivalently, its dual periodic quiver. The crystals provide a discretized version of the underlying toric geometries. We introduce various techniques to visualize crystals and their melting configurations, including 3-dimensional slicing and Hasse diagrams. We illustrate the construction with the D0-D8 system on$${\mathbb{C}}$$⁴. Finally, we outline how our proposal generalizes to arbitrary toric CY 4-folds and general brane configurations. 

A<sc>bstract</sc> We investigate a class of mass deformations that connect pairs of 2d(0,2) gauge theories associated to different toric Calabi-Yau 4-folds. These deformations are generalizations to 2dof the well-known Klebanov-Witten deformation relating the 4dgauge theories for the ℂ²/ℤ₂× ℂ orbifold and the conifold. We investigate various aspects of these deformations, including their connection to brane brick models and the relation between the change in the geometry and the pattern of symmetry breaking triggered by the deformation. We also explore how the volume of the Sasaki-Einstein 7-manifold at the base of the Calabi-Yau 4-fold varies under deformation, which leads us to conjecture that it quantifies the number of degrees of freedom of the gauge theory and its dependence on the RG scale. 

We present a general formalism for deriving the thermodynamics of ferromagnets consisting of "atoms" carrying an arbitrary irreducible representation of and coupled through long-range two-body quadratic interactions. Using this formalism, we derive the thermodynamics and phase structure of ferromagnets with atoms in the doubly symmetric or doubly antisymmetric irreducible representations. The symmetric representation leads to a paramagnetic and a ferromagnetic phase with transitions similar to the ones for the fundamental representation studied before. The antisymmetric representation presents qualitatively new features, leading to a paramagnetic and two distinct ferromagnetic phases that can coexist over a range of temperatures, two of them becoming metastable. Our results are relevant to magnetic systems of atoms with reduced symmetry in their interactions compared to the fundamental case. 

The non-Abelian ferromagnet recently introduced by the authors, consisting of atoms in the fundamental representation of , is studied in the limit where becomes large and scales as the square root of the number of atoms . This model exhibits additional phases, as well as two different temperature scales related by a factor . The paramagnetic phase splits into a "dense" and a "dilute" phase, separated by a third-order transition and leading to a triple critical point in the scale parameter and the temperature, while the ferromagnetic phase exhibits additional structure, and a new paramagnetic-ferromagnetic metastable phase appears at the larger temperature scale. These phases can coexist, becoming stable or metastable as temperature varies. A generalized model in which the number of -equivalent states enters the partition function with a nontrivial weight, relevant, e.g., when there is gauge invariance in the system, is also studied and shown to manifest similar phases, with the dense-dilute phase transition becoming second-order in the fully gauge invariant case. 

We study the multiplicity of irreducible representations in the decomposition of 𝑛 fundamentals of 𝑆𝑈(𝑁) weighted by a power of their dimension in the large 𝑛 and large 𝑁 double scaling limit. A nontrivial scaling is obtained by keeping 𝑛∕𝑁2 fixed, which plays the role of an order parameter. We find that the system generically undergoes a fourth order phase transition in this parameter, from a dense phase to a dilute phase. The transition is enhanced to third order for the unweighted multiplicity, and disappears altogether when weighting with the first power of the dimension. This corresponds to the infinite temperature partition function of non-Abelian ferromagnets, and the results should be relevant to the thermodynamic limit of such ferromagnets at high temperatures. 

In this paper, we consider the Hamiltonian analysis of Yang–Mills theory and some variants of it in three space–time dimensions using the Schrödinger representation. This representation, although technically more involved than the usual covariant formulation, may be better suited for some nonperturbative issues. Specifically for the Yang–Mills theory, we explain how to set up the Hamiltonian formulation in terms of manifestly gauge-invariant variables and set up an expansion scheme for solving the Schrödinger equation. We review the calculation of the string tension, the Casimir energy and the propagator mass and compare with the results from lattice simulations. The computation of the first set of corrections to the string tension, string breaking effects, extensions to the Yang–Mills–Chern–Simons theory and to the supersymmetric cases are also discussed. We also comment on how entanglement for the vacuum state can be formulated in terms of the BFK gluing formula. This paper concludes with a discussion of the status and prospects of this approach.