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Two highly successful approaches to constructing 5d SCFTs are geometric engineering using M-theory on a Calabi-Yau 3-fold and the use of 5-brane webs suspended from 7-branes in Type IIB string theory. In the brane web realization, the extended Coulomb branch of the 5d SCFT can be studied by opening the web using rigid triple intersections of branes — i.e. configurations with no deformations. In this paper, we argue that the geometric engineering counterpart of these rigid triple intersections are the T-cones introduced in the mathematical literature. We extend the class of rigid brane webs to include locked superpositions of the minimal ones. These rigid brane webs serve as fundamental building blocks for supersymmetrically tessellating Generalized Toric Polygons (GTPs) from first principles. Interestingly, we find that the extended Coulomb branch generally exhibits a structure consisting of multiple cones intersecting at a single point. Hanany-Witten (HW) transitions in the web have been conjectured to correspond geometrically to flat fibrations over a line, where the central and generic fibers represent the geometries dual to the webs before and after the transition. We demonstrate this explicitly in an example, showing that for GTPs reducing to standard toric diagrams, the HW transition corresponds to a deformation of the BPS quiver that we map to the geometric deformation. 

We consider the vacuum wave function of a free scalar field theory in space partitioned into two regions, with the field obeying Robin conditions (of parameter $\kappa$) on the interface. A direct integration over fields in a subregion is carried out to obtain the reduced density matrix. This leads to a constructive proof of the Reeh-Schlieder theorem. We analyze the entanglement entropy as a function of the Robin parameter $\kappa$. We also consider a specific conditional probability as another measure of entanglement which is more amenable to analysis of the dependence on interface conditions. Finally, we discuss a direct calculation of correlation functions and how it gives an alternate route to the reduced density matrix. Published by the American Physical Society2025 

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. 

There are two sets of orbits of the Virasoro group which admit a Kähler structure. We consider the construction of coherent states for the orbit [Formula: see text] which furnishes unitary representations of the group. The procedure is analogous to geometric quantization using a holomorphic polarization. We also give an explicit formula for the Kähler potential for this orbit and comment on normalization of the coherent states. We further explore some of the properties of these states, including the definition of symbols corresponding to operators and their star products. Some comments which touch upon the possibility of applying this to gravity in [Formula: see text] dimensions are also given. 

Generalizing from previous work on the integer quantum Hall effect, we construct the effective action for the analog of Laughlin states for the fractional quantum Hall effect in higher dimensions. The formalism is a generalization of the parton picture used in two spatial dimensions, the crucial ingredient being the cancellation of anomalies for the gauge fields binding the partons together. Some subtleties which exist even in two dimensions are pointed out. The effective action is obtained from a combination of the Dolbeault and Dirac index theorems. We also present expressions for some transport coefficients such as Hall conductivity and Hall viscosity for the fractional states. Published by the American Physical Society2025 

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 discuss the realization of 2d (0,2) gauge theories in terms of branes focusing on Brane Brick Models, which are T-dual to D1-branes probing toric Calabi-Yau 4-folds. These brane setups fully encode the infinite class of 2d (0,2) quiver gauge theories on the worldvolume of the D1-branes and substantially streamline their connection to the probed geometries. We review various methods for efficiently generating Brane Brick Models. These algorithms are then used to construct 2d (0,2) gauge theories for the cones over all the smooth Fano 3-folds and two infinite families of Sasaki-Einstein 7-manifolds with known metrics. This note is based on the author’s talk at the Gauged Linear Sigma Models @ 30 conference at the Simons Center for Geometry and Physics. 

Generalized global symmetries, in particular non-invertible and categorical symmetries, have become a focal point in the recent study of quantum field theory (QFT). In this paper, we investigate aspects of symmetry topological field theories (SymTFTs) and anomalies of non-invertible symmetries for 2D QFTs from a string theory perspective. Our primary focus is on an infinite class of 2D QFTs engineered on D1-branes probing toric Calabi-Yau 4-fold singularities. We derive 3D SymTFTs from the topological sector of IIB supergravity and discuss the resulting 2D QFTs, which can be intrinsically relative or absolute. For intrinsically relative QFTs, we propose a sufficient condition for them to exist. For absolute QFTs, we show that they exhibit non-invertible symmetries with an elegant brane origin. Furthermore, we find that these non-invertible symmetries can suffer from anomalies, which we discuss from a top-down perspective. Explicit examples are provided, including theories for including theories for Y(p,k)(ℙ2), Y(2,0)(ℙ1×ℙ1), and ℂ4/ℤ4 geometries. 

A new type of quiver theories, denoted twin quivers, was recently introduced for studying 5d SCFTs engineered by webs of 5-branes ending on 7-branes. Twin quivers provide an alternative perspective on various aspects of such webs, including Hanany-Witten moves and the s-rule. More ambitiously, they can be regarded as a first step towards the construction of combinatorial objects, generalizing brane tilings, encoding the corresponding BPS quivers. This paper continues the investigation of twin quivers, focusing on their non-uniqueness, which stems from the multiplicity of toric phases for a given toric Calabi-Yau 3-fold. We find that the different twin quivers are necessary for describing what we call quiver tails, which in turn correspond to certain sub-configurations in the webs. More generally, the multiplicity of twin quivers captures the roots of the Higgs branch in the extended Coulomb branch of 5d theories.