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Search: authors:"Amihay Hanany"

26 papers found.
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Quiver theories and formulae for nilpotent orbits of Exceptional algebras

We treat the topic of the closures of the nilpotent orbits of the Lie algebras of Exceptional groups through their descriptions as moduli spaces, in terms of Hilbert series and the highest weight generating functions for their representation content. We extend the set of known Coulomb branch quiver theory constructions for Exceptional group minimal nilpotent orbits, or reduced...

Nilpotent orbits and the Coulomb branch of T σ (G) theories: special orthogonal vs orthogonal gauge group factors

Coulomb branches of a set of 3d \( \mathcal{N} \) = 4 supersymmetric gauge theories are closures of nilpotent orbits of the algebra \( \mathfrak{so}(n) \). From the point of view of string theory, these quantum field theories can be understood as effective gauge theories describing the low energy dynamics of a brane configuration with the presence of orientifold planes [1]. The...

Algebraic properties of the monopole formula

The monopole formula provides the Hilbert series of the Coulomb branch for a 3-dimensional \( \mathcal{N}=4 \) gauge theory. Employing the concept of a fan defined by the matter content, and summing over the corresponding collection of monoids, allows the following: firstly, we provide explicit expressions for the Hilbert series for any gauge group. Secondly, we prove that the...

On three-dimensional quiver gauge theories of type B

We study three-dimensional supersymmetric quiver gauge theories with a nonsimply laced global symmetry primarily focusing on framed affine B N quiver theories. Using a supersymmetric partition function on a three sphere, and its transformation under S-duality, we study the three-dimensional ADHM quiver for SO(2N + 1) instantons with a half-integer Chern-Simons coupling. The...

Branes and the Kraft-Procesi transition

The Coulomb and Higgs branches of certain 3d \( \mathcal{N}=4 \) gauge theories can be understood as closures of nilpotent orbits. Recently, a new theorem by Namikawa suggests that this is the simplest possible case, thus giving this class a special role. In this note we use branes to reproduce the mathematical work by Kraft and Procesi. It studies the classification of all...

Coulomb branches for rank 2 gauge groups in 3d \( \mathcal{N}=4 \) gauge theories

The Coulomb branch of 3-dimensional \( \mathcal{N}=4 \) gauge theories is the space of bare and dressed BPS monopole operators. We utilise the conformal dimension to define a fan which, upon intersection with the weight lattice of a GNO-dual group, gives rise to a collection of semi-groups. It turns out that the unique Hilbert bases of these semi-groups are a sufficient, finite...

Quiver theories for moduli spaces of classical group nilpotent orbits

We approach the topic of Classical group nilpotent orbits from the perspective of the moduli spaces of quivers, described in terms of Hilbert series and generating functions. We review the established Higgs and Coulomb branch quiver theory constructions for A series nilpotent orbits. We present systematic constructions for BCD series nilpotent orbits on the Higgs branches of...

Instanton operators and the Higgs branch at infinite coupling

The richness of 5d \( \mathcal{N}=1 \) theories with a UV fixed point at infinite coupling is due to the existence of local disorder operators known as instanton operators. By considering the Higgs branch of SU(2) gauge theories with N f ≤ 7 flavours at finite and infinite coupling, we write down the explicit chiral ring relations between instanton operators, the glueball...

Highest weight generating functions for hyperKähler T ⋆(G/H) spaces

We develop an efficient procedure for counting holomorphic functions on a hyperKahler cone that has a resolution as a cotangent bundle of a homogeneous space by providing a formula for computing the corresponding Highest Weight Generating function.

Construction and deconstruction of single instanton Hilbert series

Many methods exist for the construction of the Hilbert series describing the moduli spaces of instantons. We explore some of the underlying group theoretic relationships between these various constructions, including those based on the Coulomb branches and Higgs branches of SUSY quiver gauge theories, as well as those based on generating functions derivable from the Weyl...

Chiral theories of class \( \mathcal{S} \)

We study a class of four-dimensional \( \mathcal{N}=1 \) superconformal field theories obtained from the six-dimensional (1, 0) theory, on M5-branes on \( {\mathrm{\mathbb{C}}}^2/{\mathrm{\mathbb{Z}}}_k \) orbifold singularity, compactified on a Riemann surface. This produces various quiver gauge theories whose matter contents are chiral. We classify the building blocks...

4d \( \mathcal{N}=1 \) from 6d \( \mathcal{N}=\left(1,0\right) \) on a torus with fluxes

Compactifying \( \mathcal{N}=\left(1,0\right) \) theories on a torus, with additional fluxes for global symmetries, we obtain \( \mathcal{N}=1 \) supersymmetric theories in four dimensions. It is shown that for many choices of flux these models are toric quiver gauge theories with singlet fields. In particular we compare the anomalies deduced from the description of the six...

Highest weight generating functions for Hilbert series

We develop a new method for representing Hilbert series based on the highest weight Dynkin labels of their underlying symmetry groups. The method draws on plethystic functions and character generating functions along with Weyl integration. We give explicit examples showing how the use of such highest weight generating functions (“HWGs”) permits an efficient encoding and analysis...

Hilbert series and moduli spaces of k U(N ) vortices

We study the moduli spaces of k U(N ) vortices which are realized by the Higgs branch of a U(k) supersymmetric gauge theory. The theory has 4 supercharges and lives on k D1-branes in a N D3- and NS5-brane background. We realize the vortex moduli space as a \( {\mathbb{C}}^{*} \) projection of the vortex master space. The Hilbert series is calculated in order to characterize the...

Hilbert series for theories with Aharony duals

The algebraic structure of moduli spaces of 3d \( \mathcal{N}=2 \) supersymmetric gauge theories is studied by computing the Hilbert series which is a generating function that counts gauge invariant operators in the chiral ring. These U(N c ) theories with N f flavors have Aharony duals and their moduli spaces receive contributions from both mesonic and monopole operators. In...

T ρ σ (G) theories and their Hilbert series

We give an explicit formula for the Higgs and Coulomb branch Hilbert series for the class of 3d \( \mathcal{N}=4 \) superconformal gauge theories T ρ σ (G) corresponding to a set of D3 branes ending on NS5 and D5-branes, with or without O3 planes. Here G is a classical group, σ is a partition of G and ρ a partition of the dual group G ∨. In deriving such a formula we make use of...

Coulomb branch and the moduli space of instantons

The moduli space of instantons on ℂ2 for any simple gauge group is studied using the Coulomb branch of \( \mathcal{N}=4 \) gauge theories in three dimensions. For a given simple group G, the Hilbert series of such an instanton moduli space is computed from the Coulomb branch of the quiver given by the over-extended Dynkin diagram of G. The computation includes the cases of non...

Monopole operators and Hilbert series of Coulomb branches of 3d \( \mathcal{N} \) = 4 gauge theories

This paper addresses a long standing problem - to identify the chiral ring and moduli space (i.e. as an algebraic variety) on the Coulomb branch of an \( \mathcal{N} \) = 4 superconformal field theory in 2+1 dimensions. Previous techniques involved a computation of the metric on the moduli space and/or mirror symmetry. These methods are limited to sufficiently small moduli spaces...