Brane Webs Research Articles

5d cubic prepotential and 5-brane webs

5d cubic prepotential and 5-brane webs

Quiver tails and brane webs

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.

The geometry of GTPs and 5d SCFTs

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 ℙ1 interpolating between geometries connected by mutation, which we identify with recently introduced deformations of the corresponding BPS quivers.

A tale of N cones

We study particular families of bad 3d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 quiver gauge theories, whose Higgs branches consist of many cones. We show the role of a novel brane configuration in realizing the Higgs moduli for each distinct cone. Through brane constructions, magnetic quivers, Hasse diagrams, and Hilbert series computations we study the intricate structure of the classical Higgs branches. These Higgs branches are both non-normal (since they consist of multiple cones) and non-reduced (due to the presence of nilpotent operators in the chiral ring). Applying the principle of inversion to the classical Higgs branch Hasse diagrams, we conjecture the quantum Coulomb branch Hasse diagrams. These Coulomb branches have several most singular loci, corresponding to the several cones in the Higgs branch. We propose the Hasse diagrams of the full quantum moduli spaces of our theories. The quivers we study can be taken to be 5d effective gauge theories living on brane webs. Their infinite coupling theories have Higgs branches which also consist of multiple cones. Some of these cones have decorated magnetic quivers, whose 3d Coulomb branches remain elusive.

3d \U0001d4a9 = 2 theories and plumbing graphs: adding matter, gauging, and new dualities

Recently, a large class of 3d \U0001d4a9 = 2 gauge theories with mixed Chern-Simons levels, corresponding to plumbing 3-manifolds, has been identified. In this paper we generalize these theories by including in their content chiral multiples, and analyze their properties. We find that the content of such theories can be encoded in graphs, which generalize plumbing graphs, and various operations in these theories can be represented in terms of transformations of such graphs. The operations in question include gauging global symmetries, integrating out gauge nodes, which for theories without chiral multiplets corresponds to Kirby moves, and ST-transformations that involve chiral multiplets. The dualities such as mirror triality and SQED-XYZ duality can be also represented in terms of graphs, and enable us to find many new dual theories by gauging global symmetries. In particular, we find that gauged SQED-XYZ duality leads to other dualities, which take the same form as operations of linking and unlinking discussed in the context of knots-quivers correspondence. We also find that the superpotential can be encoded in an interesting class of triangle graphs that satisfy certain consistency conditions, we discuss decoupling and Higgsing of chiral multiplets, as well as interpretation of various phenomena in terms of brane webs.

Twin theories, polytope mutations and quivers for GTPs

We propose a unified perspective on two sets of objects that usually arise in the study of bipartite field theories. Each of the sets consists of a polytope, or equivalently a toric Calabi-Yau, and a quiver theory. We refer to the two sets of objects as original and twin. In the simplest cases, the two sides of the correspondence are connected by the graph operation known as untwisting. The democratic treatment that we advocate raises new questions regarding the connections between these objects, some of which we explore.With this motivation in mind, we establish a correspondence between the mutations of the original polytope and the twin quiver. This leads us to propose that non-toric twin quivers are naturally associated to generalized toric polygons (GTPs) and we explore various aspects of this idea. Supporting evidence includes global symmetries, the ability of twin quivers to encode the generalized s-rule, and the connection between the mutations of polytopes and of configurations of webs of 5-branes suspended from 7-branes. We introduce three methods for constructing twin quivers for GTPs. We also investigate the connection between twin quivers obtained using different toric phases. Twin quivers provide a powerful new perspective on GTPs. The ideas presented in this paper may represent a step towards the generalization of brane tilings to GTPs.

3d defects in 5d: RG flows and defect F-maximization

We use a combination of AdS/CFT and supersymmetric localization to study codimension-2 defects in 5d SCFTs and their gauge theory deformations. The 5d SCFTs are engineered by (p, q) 5-brane webs, with defects realized by D3-branes ending on the 5-brane webs. We obtain the defect free energies and find that gauge theory descriptions of the combined 5d/3d systems can be connected to the UV defect SCFTs through a form of F-maximization which extremizes over different gauge theory defects. This leads to a match between the defect free energies obtained from supersymmetric localization in the gauge theories on the one hand and string theory results on the other. We extend this match to defect RG flows.

Symmetry TFTs from String Theory

We determine the d+1 dimensional topological field theory, which encodes the higher-form symmetries and their ’t Hooft anomalies for d-dimensional QFTs obtained by compactifying M-theory on a non-compact space X. The resulting theory, which we call the Symmetry TFT, or SymTFT for short, is derived by reducing the topological sector of 11d supergravity on the boundary partial X of the space X. Central to this endeavour is a reformulation of supergravity in terms of differential cohomology, which allows the inclusion of torsion in cohomology of the space partial X, which in turn gives rise to the background fields for discrete (in particular higher-form) symmetries. We apply this framework to 7d super-Yang Mills, where X= mathbb {C}^2/Gamma _{ADE}, as well as the Sasaki–Einstein links of Calabi–Yau three-fold cones that give rise to 5d superconformal field theories. This M-theory analysis is complemented with a IIB 5-brane web approach, where we derive the SymTFTs from the asymptotics of the 5-brane webs. Our methods apply to both Lagrangian and non-Lagrangian theories, and allow for many generalisations.

DE-type little strings from glued brane webs

We propose brane web configurations for D-type and E-type mathcal{N} =(1,0) little string theories based on a trivalent or quadrivalent gluing of 5-brane web diagrams. Tri-/quadri-valent gluing is a powerful way of computing 5d/6d partition functions for supersymmetric gauge theories based on the topological vertex. We generalize the gluing techniques to little string theories by introducing a new compact direction and compute their supersymmetric partition functions on Omega-deformed ℝ4×T2. As concrete examples, we consider little string theories arising from Type IIB NS5-branes probing D4 or D5 singularity. Their effective gauge theory descriptions as the affine D4 or D5 quiver gauge theory can be realized with quadrivalent or trivalent gluing, respectively. Based on these gluings of 5-brane webs, we compute their refined partition functions and compare them with the known results. We extend the computation of the partition function to little string theory engineered from IIB NS5-branes probing E6 singularity based on a trivalent gluing. We also discuss the generalization to higher rank cases and the symmetries of the partition functions.

Holographic duals of N=1 quivers in 5d and their nonrelativistic limits

We explore nonrelativistic limits of $\mathcal{N}=1$ quiver gauge theories in 5d. The stringy counterpart of these Super Conformal Field Theories (SCFTs) is characterized by torsional string Newton-Cartan (TSNC) sigma models which are defined over non-Lorentzian manifolds. We further show that under transverse T duality, these TSNC sigma models are mapped into another new class of nonrelativistic sigma models which are defined over a T-dual TSNC background. Considering nonrelativistic limits of various field theory observables in a holographic setup, we further estimate corresponding entities in the TSNC limit of $\mathcal{N}=1$ quivers. We carry out a parallel analysis on holomorphic functions and the associated pole structures in the nonrelativistic limit of ($p$, $q$) five brane webs. In particular, we investigate the generic structure of various loop operators in a nonrelativistic setup and explore their properties under S duality. Finally, we comment on the large $c$ limit of Ramond-Ramond (RR) fields and discuss the associated S-duality transformation rules in the nonrelativistic limit of $\mathcal{N}=1$ quivers.

Brain webs for brane webs

We propose a new technique for classifying 5d Superconformal Field Theories arising from brane webs in Type IIB String Theory, using technology from Machine Learning to identify different webs giving rise to the same theory. We concentrate on webs with three external legs, for which the problem is analogous to that of classifying sets of 7-branes. Training a Siamese Neural Network to determine equivalence between any two brane webs shows an improved performance when webs are considered equivalent under a weaker set of conditions. This therefore suggests that the conjectured classification of 7-brane sets is not complete.

Higgs branches of U/SU quivers via brane locking

We solve a long standing problem on the computation of the Higgs branch mathcal{H} of linear quivers with 8 supercharges and with both unitary and special unitary gauge nodes. The solution uses the concept of magnetic quivers, where components of mathcal{H} are described as 3d mathcal{N} = 4 Coulomb branches. When the starting quiver is good, there is a single component in mathcal{H} and the magnetic quiver is a 3d mirror. The magnetic quivers are obtained from studying the brane web for an auxiliary 5d theory (with only special unitary gauge groups), constrained by a new notion called brane locking, where some branes are required to move together. We view this as a computational tool rather than an operation in 5d. A detailed algorithm is provided.

Refined topological vertex with ON-planes

We propose refined topological vertex formalism for 5-brane systems with ON-planes by introducing a new vertex associated with reflection over an ON-plane, which gives rise to new vertex and edge factors. We test our proposal against various 5d \U0001d4a9 = 1 gauge theories which can be realized as 5-brane webs with ON-planes, which include D-type quiver theories. In particular, we compute the refined partition functions for 6d E-string theory on a circle as well as 5d SU(3) theory at the Chern-Simons level 9, which can be realized as 5-brane webs with two ON-planes. Our results completely agree with the known results.

3d mathcal{N} = 2 brane webs and quiver matrices

We discuss 3d brane webs and effective Chern-Simons levels for 3d mathcal{N} = 2 gauge theories. We find that turning on real masses for chiral multiplets leads to various equivalent brane webs that are related by flipping positions of D5-branes. We interpret flips as ST-transformations for chiral multiplets. ST-transformations could turn abelian theories into dual theories with mixed Chern-Simons levels that are interpreted as quiver matrices Cij encoding DT-invariants. We notice that each brane web corresponds to a quiver matrix. ST-transformations of holomorphic blocks are discussed to verify results. We also discuss the movement of flavor D5-branes, which leads to double-layer brane webs and manifests fiber-base duality. In the second part, we compute refined vortex partition functions of nonabelian theories with the gauge group U(N) and find corresponding quiver matrices. The computation shows that on Higgs branch nonabelian groups are broken to abelian groups.

S-foldings of 5d SCFTs

We explore the ℤ2,3,4,6 S-foldings of some 5d superconformal field theories from the (p, q) 5-brane web perspective. The S-folding involves both a spatial quotient and an SL(2, ℤ) transformation on 5-branes simultaneously. The ℤ2,3,4,6 S-foldings are achieved by the insertion of the D4, E6, E7, E8 7-branes, respectively. The deficit angles and monodromies of these 7-branes are exactly those necessary for the S-foldings. We explore the details of the S-folding process, especially the enhancement of global flavor symmetry in various simple cases. The characteristic of the S-folding depends sharply on whether the fixed point of the discrete symmetry is at the center of a compact face (or surface), at a 5-brane, or at a crossing point of 5 branes. The analysis of the prepotential greatly supports this view of the discrete gauging.

Exploring the orthosymplectic zoo

We study the Higgs branch of the SCFT limit of 5d SO(6) and SO(8) gauge theory with hypermultiplets in the spinor and vector representations. In the case of SO(6) gauge theories, we contrast the magnetic quivers obtained with those of SU(4) gauge theory with hypermultiplets in the fundamental and second rank antisymmetric representations. Since SU(4) gauge theories admit several different values of the Chern-Simons level, we make some observations about how to distinguish those theories from the brane webs of the SO(6) theories. In the case of SO(8) gauge theories, we use SO(8) triality to propose (naively) inequivalent magnetic quivers, which will turn out to have the same moduli spaces of vacua, at least locally around their most singular loci. We encounter several interesting new phenomena occurring in the magnetic quivers, such as hypermultiplets between neighbouring symplectic gauge nodes and matter in two-index representations of unitary nodes. We also give a prescription for computing the local Coulomb branch Hilbert series for quivers involving bad USp(2) gauge nodes.

Gauging discrete symmetries of TN-theories in five dimensions

We study the gauging of a discrete ℤ3 symmetry in the five-dimensional superconformal TN theories. We argue that this leads to an infinite sequence of five-dimensional superconformal theories with either E6× SU(N) or SU(3) × SU(N) global symmetry group. In the M-theory realisation of TN theories as residing at the origin in the Calabi-Yau orbifolds frac{{mathbb{C}}^3}{{mathbb{Z}}_Ntimes {mathbb{Z}}_N} we identify the ℤ3 symmetry geometrically and the new theories arise from M-theory on the non-Abelian orbifolds left(frac{{mathbb{C}}^3}{{mathbb{Z}}_Ntimes {mathbb{Z}}_N}right)/{mathbb{Z}}_3 . On the other hand, in the (p, q) 5-brane web description in Type IIB theory, the symmetry combines the U-duality symmetry with a rotation in space, defining a so-called U-fold background, where the E6 symmetry is manifest.

Non-supersymmetric AdS6 and the swampland

We discuss infinite families of non-supersymmetric AdS6 solutions in Type IIB string theory. They are siblings of supersymmetric solutions which are associated with (p, q) 5-brane webs and holographically dual to 5d SCFTs engineered by those brane webs. The non-supersymmetric backgrounds carry identical 5-brane charges and are connected to the supersymmetric ones by RG flows. We study the stability of the non-supersymmetric solutions, identifying perturbative and non-perturbative decay channels for all the backgrounds explicitly available. We also identify likely decay mechanisms for solutions that have not been constructed explicitly but may be expected to exist based on brane web considerations. Finally, we exclude scale separation by constructing universal spin 2 modes with masses comparable to the mass-scale of the cosmological constant.

Refined topological vertex for a 5D Sp(N) gauge theories with antisymmetric matter

We consider type IIB 5-brane web diagrams for a 5D $Sp(N)$ gauge theory with an antisymmetric hypermultiplet and ${N}_{f}$ fundamental hypermultiplets. The corresponding 5-branes can be obtained by Higgsing a 5-brane web for quiver gauge theory. We use the refined topological vertex formalism to compute Nekrasov partition functions of 5D $Sp(2)$ theories with one antisymmetric hypermultiplet and flavors. Our results agree with the known results obtained from the Atiyah-Drinfeld-Hitchin-Manin method. We also discuss a particular tuning of K\"ahler parameters associated with this Higgsing.

Magnetic quivers from brane webs with O7+-planes

We consider the Higgs branch of 5d fixed points engineered using brane webs with an O7+-plane. We use the brane construction to propose a set of rules to extract the corresponding magnetic quivers. Such magnetic quivers are generically framed non-simply-laced quivers containing unitary as well as special unitary gauge nodes. We compute the Coulomb branch Hilbert series of the proposed magnetic quivers. In some specific cases, an alternative magnetic quiver can be obtained either using an ordinary brane web or a brane web with an O5-plane. In these cases, we find a match at the level of the Hilbert series.