The Higgs branch of Heterotic ALE instantons

Abstract

We begin a study of the Higgs branch of six-dimensional $(1,0)$ little string theories governing the worldvolumes of heterotic ALE instantons. We give a description of this space by constructing the corresponding magnetic quiver. The latter is a three-dimensional $\mathcal{N}=4$ quiver gauge theory that flows in the infrared to a fixed point whose quantum corrected Coulomb branches is the Higgs branch of the six-dimensional theory of interest. We present results for both types of heterotic strings, and mostly for ${\mathbb{C}}^2/{\mathbb{Z}}_k$ ALE spaces. Our analysis is valid both in the absence and in the presence of small instantons. Along the way, we also describe small $SO(32)$ instanton transitions in terms of the corresponding magnetic quiver, which parallels a similar treatment of the small $E_8$ instanton transitions in the context of the $E_8\times E_8$ heterotic string.

arXiv comment48 pages, 3 figures; v2: typos fixed, citations added; v3: improved introduction, updated references, version published in JHEP

References in corpus (71)

• Heterotic and Type I String Dynamics from Eleven Dimensions
• Eleven-Dimensional Supergravity on a Manifold with Boundary
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Evidence for F-Theory
• N=2 dualities
• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• Mirror Symmetry in Three Dimensional Gauge Theories
• Small Instantons in String Theory
• Matrix Description of M-theory on $T^5$ and $T^5/Z_2$
• Small $E_8$ Instantons and Tensionless Non-critical Strings
• 6d Conformal Matter
• On Mirror Symmetry in Three Dimensional Abelian Gauge Theories
• Symplectic singularities
• Mirror Symmetry in Three-Dimensional Gauge Theories, Quivers and D-branes
• A brief review of "little string theories"
• Branes and Six Dimensional Supersymmetric Theories
• Anomalies, Dualities, and Topology of D=6 N=1 Superstring Vacua
• Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories
• Mirror Symmetry in Three-Dimensional Gauge Theories, SL(2,Z) and D-Brane Moduli Spaces
• Mirrors of 3d Sicilian theories
• Branes at Orbifolds versus Hanany Witten in Six Dimensions
• Towards a mathematical definition of Coulomb branches of $3$-dimensional $\mathcal{N}=4$ gauge theories, II
• Tinkertoys for Gaiotto Duality
• New Phases of String Theory and 6d RG Fixed Points via Branes at Orbifold Singularities
• Point-like Instantons on K3 Orbifolds
• Supersymmetry enhancement by monopole operators
• Generalized Global Symmetries of $T[M]$ Theories. I
• Consistency Conditions for Branes at Orbifold Singularities
• RG Fixed Points in Six Dimensions via Branes at Orbifold Singularities
• Top Down Approach to 6D SCFTs
• Issues on Orientifolds: On the brane construction of gauge theories with SO(2n) global symmetry
• Coulomb Branch and The Moduli Space of Instantons
• Exceptional Indices
• 3d Coulomb branch and 5d Higgs branch at infinite coupling
• Quiver Subtractions
• $E_8$ instantons on type-A ALE spaces and supersymmetric field theories
• Instanton Operators and the Higgs Branch at Infinite Coupling
• Point-like Instantons and the Spin(32)/Z2 Heterotic String
• M-Theory Origin of Mirror Symmetry in Three Dimensional Gauge Theories
• Universal Features of BPS Strings in Six-dimensional SCFTs
• Discrete Gauging in Six Dimensions
• Magnetic Quivers, Higgs Branches, and 6d N=(1,0) Theories -- Orthogonal and Symplectic Gauge Groups
• M&m's
• Fission, Fusion, and 6D RG Flows
• The frozen phase of F-theory
• Revisiting the classifications of 6d SCFTs and LSTs
• Exploring the landscape of heterotic strings on T^d
• A new twist on heterotic string compactifications
• Monopoles in String Theory
• Small instanton transitions for M5 fractions
• Comments on Non-invertible Symmetries in Argyres-Douglas Theories
• General Prescription for Global U(1)'s in 6D SCFTs
• On The Universality Class Of Little String Theories
• Classification of chiral fermionic CFTs of central charge $\le 16$
• Balanced B and D-type orthosymplectic quivers -- Magnetic quivers for product theories
• Pursuing the double affine Grassmannian I: transversal slices via instantons on A_k-singularities
• Charges and holography in 6d (1,0) theories
• Heterotic String Conformal Field Theory And A-D-E Singularities
• Back to Heterotic Strings on ALE Spaces: Part I -- Instantons, 2-groups and T-duality
• The moduli space of instantons on an ALE space from 3d $\mathcal{N}=4$ field theories
• Hierarchy of RG flows in 6d $(1,0)$ orbi-instantons
• Compactified Little String Theories and Compact Moduli Spaces of Vacua
• Probing 7-branes on Orbifolds
• Hierarchies of RG flows in 6d $(1,0)$ massive E-strings
• Minimally Unbalanced Quivers
• Little String Origin of Surface Defects
• 3D String Theory and Umbral Moonshine
• Heterotic String Corrections from the Dual Type II String
• Heterotic Little String Theories and Holography
• Critical Wilson Lines in Toroidal Compactifications of Heteroric Strings
• The minimal degeneration singularities in the affine Grassmannians

Cited by in corpus (7)

• Higgs branch RG-flows via Decay and Fission
• Decay and Fission of Magnetic Quivers
• Non-minimal Elliptic Threefolds at Infinite Distance II: Asymptotic Physics
• Orthosymplectic Quotient Quiver Subtraction
• Quotient Quiver Subtraction
• Atomic Higgsings of 6D SCFTs
• Quiver Polymerisation