arXiv research

Quantized Coulomb branches linked to skein algebras.

We study quantized Coulomb branches of quiver gauge theories of Jordan type. We prove that the quantized Coulomb branch is isomorphic to the spherical graded Cherednik algebra in the unframed case, and is isomorphic to the spherical cyclotomic rational Cherednik algebra in the framed case. We also prove that the quanti…

Study of Hilbert schemes and Coulomb branches of hypertoric varieties.

Study quantized SL2-character variety of a once-punctured torus, finding three Coulomb branch isomorphisms.

Floer homology connects to quiver Hecke algebras in Coulomb branches.

This is an introduction to a provisional mathematical definition of Coulomb branches of $3$-dimensional $\mathcal N=4$ supersymmetric gauge theories, studied in arXiv:1503.03676, arXiv:1601.03586

Consider the $3$-dimensional $\mathcal N=4$ supersymmetric gauge theory associated with a compact Lie group $G_c$ and its quaternionic representation $\mathbf M$. Physicists study its Coulomb branch, which is a noncompact hyper-Kähler manifold with an $\mathrm{SU}(2)$-action, possibly with singularities. We give a math…

2d GLSM connects Berry connections to Coulomb branch via difference equations.

This is a companion paper of arXiv:1601.03586. We study Coulomb branches of unframed and framed quiver gauge theories of type $ADE$. In the unframed case they are isomorphic to the moduli space of based rational maps from ${\mathbb C}P^1$ to the flag variety. In the framed case they are slices in the affine Grassmannia…

This is an introduction to a provisional mathematical definition of Coulomb branches of $3$-dimensional $\mathcal N=4$ supersymmetric gauge theories, studied in arXiv:1503.03676, arXiv:1601.03586. This is an expanded version of an article arXiv:1612.09014 appeared in the 61st DAISUUGAKU symposium proceeding (2016), wri…

This is a supplement to [arXiv:1503.03676], where an approach towards a mathematically rigorous definition of the Coulomb branch of a $3$-dimensional $\mathcal N=4$ SUSY gauge theory was proposed. We ask questions on their expected properties, especially in relation to the corresponding Higgs branch, partly motivated b…

This is the third companion paper of arXiv:1601.03586. When a gauge theory has a flavor symmetry group, we construct a partial resolution of the Coulomb branch as a variant of the definition. We identify the partial resolution with a partial resolution of a generalized slice in the affine Grassmannian, Hilbert scheme o…

Consider the $3$-dimensional $\mathcal N=4$ supersymmetric gauge theory associated with a compact Lie group $G$ and its quaternionic representation $\mathbf M$. Physicists study its Coulomb branch, which is a noncompact hyper-Kähler manifold, such as instanton moduli spaces on $\mathbb R^4$, $SU(2)$-monopole moduli spa…

This is the second companion paper of arXiv:1601.03586. We consider the morphism from the variety of triples introduced in arXiv:1601.03586 to the affine Grassmannian. The direct image of the dualizing complex is a ring object in the equivariant derived category on the affine Grassmannian (equivariant derived Satake ca…

Monoidal categorifies genus zero skein algebra using K-theory.

New $G_2$-holonomy manifolds from 5d N=1 theories domain walls.

Study topological twists of massive SQCD with gauge group SU(2) and 3 or fewer fundamental hypermultiplets.

We study solutions of the Bogomolny equation on R^2\times S^1$ with prescribed singularities. We show that Nahm transform establishes a one-to-one correspondence between such solutions and solutions of the Hitchin equations on a punctured cylinder with the eigenvalues of the Higgs field growing at infinity in a particu…

Classifies theories with eight supercharges using pseudo-periodic maps and Riemann surfaces.

New connections found between knot invariants and Rozansky-Witten theory.

We calculate the free energy of Coulomb gas systems on Riemann surfaces.

The paper generalizes knot invariants and their connections to quivers and ideals.

Research characterizes intersection cohomology groups of gauge theories and cotangent bundles.

We establish existence and regularity results for normal Coulomb frames in the normal bundle of two-dimensional surfaces of disc-type embedded in Euclidean spaces of higher dimensions.

Proposes a Coulomb-like model for international trade flows, fitting real-world data.

Generative adversarial networks (GANs) evolved into one of the most successful unsupervised techniques for generating realistic images. Even though it has recently been shown that GAN training converges, GAN models often end up in local Nash equilibria that are associated with mode collapse or otherwise fail to model t…

Classifies instantons on ALF multi-Taub-NUT spaces and ties them to bow solutions.

Moduli spaces of doubly periodic monopoles, also called monopole walls or monowalls, are hyperkähler; thus, when four-dimensional, they are self-dual gravitational instantons. We find all monowalls with lowest number of moduli. Their moduli spaces can be identified, on the one hand, with Coulomb branches of five-dimens…

New method uses Coulomb gases for Monte Carlo integration with reduced errors.

The paper connects $G_2$-manifolds to Coulomb and Higgs phases of gauge theories.

The u-plane integral is the contribution of the Coulomb branch to correlation functions of N=2 gauge theory on a compact four-manifold. We consider the u-plane integral for correlators of point and surface observables of topologically twisted theories with gauge group SU(2), for an arbitrary four-manifold with (b1,b2+)…

Tripod spiders' energy control analyzed for Hooke and Coulomb potentials.

S-dual of Hamiltonian spaces connects to Langlands duality.

We introduce a novel class of localized atomic environment representations, based upon the Coulomb matrix. By combining these functions with the Gaussian approximation potential approach, we present LC-GAP, a new system for generating atomic potentials through machine learning (ML). Tests on the QM7, QM7b and GDB9 biom…

Math verifies Aganagic's proposal for Khovanov homology.

New gauge condition fixes $L^2$ metric divergence in hyperbolic monopole spaces.

In this paper we consider the existence and regularity problem for Coulomb frames in the normal bundle of two-dimensional surfaces with higher codimension in Euclidean spaces. While the case of two codimensions can be approached directly by potential theory, more sophisticated methods have to be applied for codimension…

Smooth Yang-Mills fields proved in supercritical dimensions.

We study the physics of globally consistent four-dimensional $\mathcal{N}=1$ supersymmetric M-theory compactifications on $G_2$ manifolds constructed via twisted connected sum; there are now perhaps fifty million examples of these manifolds. We study a rich example that exhibits $U(1)^3$ gauge symmetry and a spectrum o…

Study analyzes low-energy behavior of Schrödinger operators with Coulomb potentials.

New theorems in 2D and 4D for metrics with curvature or singularity.

Extends Coulomb gauge existence to non-associative gauge theory.

The study shows how to regularize weakly harmonic maps using Sobolev norms and Coulomb frames.

Study on Wasserstein gradient flow for MMD between Coulomb measures.

The paper recasts Penrose-Sparling's non-Hausdorff twistor space using noncommutative geometry.

Narasimhan and Ramadas showed that the Gribov ambiguity was maximal for the product SU(2) bundle over S^3. Specifically they showed that the holonomy group of the Coulomb connection is dense in the connected component of the identity of the gauge group. Instead of base manifold S^3, we consider here a base manifold wit…

When formulated in twistor space, the D-instanton corrected hypermultiplet moduli space in N=2 string vacua and the Coulomb branch of rigid N=2 gauge theories on $R^3 \times S^1$ are strikingly similar and, to a large extent, dictated by consistency with wall-crossing. We elucidate this similarity by showing that these…

Study evaluates topological contributions in massive SQCD on compact 4-manifolds.