arXiv research

We study knots in 3d Chern-Simons theory with complex gauge group $SL(N,\mathbb{C})$, in the context of its relation with 3d $\mathcal{N}=2$ theory (the so-called 3d-3d correspondence). The defect has either co-dimension 2 or co-dimension 4 inside the 6d $(2,0)$ theory, which is compactified on a 3-manifold $\hat{M}$. …

Proposes a new effective central charge for 3d N=2 theories.

New relations link knot theory to quiver representations in 3d physics.

We propose a new description of 3d $\mathcal{N}=2$ theories which do not admit conventional Lagrangians. Given a quiver $Q$ and a mutation sequence $m$ on it, we define a 3d $\mathcal{N}=2$ theory $\mathcal{T}[(Q,m)]$ in such a way that the $S^3_b$ partition function of the theory coincides with the cluster partition f…

Study 3d N=1 vacua from M-theory compactification on Spin(7) space.

3D gauge theories link knot polynomials to vortex partition functions.

In this paper we study supersymmetric co-dimension 2 and 4 defects in the compactification of the 6d $(2,0)$ theory of type $A_{N-1}$ on a 3-manifold $M$. The so-called 3d-3d correspondence is a relation between complexified Chern-Simons theory (with gauge group $SL(N, \mathbb{C})$) on $M$ and a 3d $\mathcal{N}=2$ theo…

New algorithm constructs characters of rational VOAs from knot complements.

Symmetrizes 4d and 3d BPS quivers for Argyres-Douglas theories.

The paper connects quivers to knot complements and studies their BPS states and 3d N=2 theories.

A class of 3d $\mathcal{N}=2$ supersymmetric gauge theories are constructed and shown to encode the simplicial geometries in 4-dimensions. The gauge theories are defined by applying the Dimofte-Gaiotto-Gukov construction in 3d/3d correspondence to certain graph complement 3-manifolds. Given a gauge theory in this class…

3D dual field theories for Virasoro minimal models constructed using Seifert fiber spaces.

The study connects knot complements to 3d theories via half-index calculations.

Study gauged supergravity, M5-branes, and class R theories, constraining supergravity coefficients and calculating partition functions.

The abstract discusses constructing 3d N=2 gauge theories using surgeries and M5-branes.

Study of IR phases in 3D class R theories linked to non-hyperbolic 3-manifolds.

Proposes categorification of Z-invariants for specific 3-manifolds.

We find and propose an explanation for a large variety of modularity-related symmetries in problems of 3-manifold topology and physics of 3d $\mathcal{N}=2$ theories where such structures a priori are not manifest. These modular structures include: mock modular forms, $SL(2,\mathbb{Z})$ Weil representations, quantum mo…

Study large N oscillations in 3D theories related to black hole physics.

Researchers map knot complements using 3d theories and half-index calculations.

Unified Higgs bundle vacua from M-theory on Spin(7) spaces.

Refined 3D index uses surgery and gradings to distinguish 3-manifolds.

We propose that a simple, Lagrangian 2d $\mathcal{N}=(0, 2)$ duality interface between the 3d $\mathcal{N}=2$ XYZ model and 3d $\mathcal{N}=2$ SQED can be associated to the simplest triangulated 4-manifold: the 4-simplex. We then begin to flesh out a dictionary between more general triangulated 4-manifolds with boundar…

Novel $A_{\infty}$-categories derived from gauge theories for manifold homologies.

New method uses resurgent analysis to determine growth rate of quantum field theory coefficients.

We propose a method to assign non-unitary TQFTs to certain SCFTs, deriving bounds and examples.

M-theory on compact eight-manifolds with $\mathrm{Spin}(7)$-holonomy is a framework for geometric engineering of 3d $\mathcal{N}=1$ gauge theories coupled to gravity. We propose a new construction of such $\mathrm{Spin}(7)$-manifolds, based on a generalized connected sum, where the building blocks are a Calabi-Yau four…

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

5D gauge theories are dual to 3D and 2D models via Floer homologies.

The study finds bounds on characterizing slopes for all knots.

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

Paper connects two invariants of 3D manifolds using Hopf algebras.

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

DECAF optimizes molecular graphs for ensemble properties, improving drug design accuracy.

Researchers mapped the moduli space of a specific group in 3D complex hyperbolic geometry.

For recovering 3D object poses from 2D images, a prevalent method is to pre-train an over-complete dictionary $\mathcal D=\{B_i\}_i^D$ of 3D basis poses. During testing, the detected 2D pose $Y$ is matched to dictionary by $Y \approx \sum_i M_i B_i$ where $\{M_i\}_i^D=\{c_i ΠR_i\}$, by estimating the rotation $R_i$, pr…

Quantizes moduli space of 3D gravity metrics.

3D BF theory on certain 3-manifolds evaluated via residues and large k limits.

In fivebrane compactifications on 3-manifolds, we point out the importance of all flat connections in the proper definition of the effective 3d N=2 theory. The Lagrangians of some theories with the desired properties can be constructed with the help of homological knot invariants that categorify colored Jones polynomia…

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…

We test the 3d-3d correspondence for theories that are labelled by Lens spaces. We find a full agreement between the index of the 3d ${\cal N}=2$ "Lens space theory" $T[L(p,1)]$ and the partition function of complex Chern-Simons theory on $L(p,1)$. In particular, for $p=1$, we show how the familiar $S^3$ partition func…

We provide a physical definition of new homological invariants $\mathcal{H}_a (M_3)$ of 3-manifolds (possibly, with knots) labeled by abelian flat connections. The physical system in question involves a 6d fivebrane theory on $M_3$ times a 2-disk, $D^2$, whose Hilbert space of BPS states plays the role of a basic build…

Teichmüller TQFT is a unitary 3d topological theory whose Hilbert spaces are spanned by Liouville conformal blocks. It is related but not identical to PSL(2,R) Chern-Simons theory. To physicists, it is known in particular in the context of 3d-3d correspondence and also in the holographic description of Virasoro conform…

Defines a map connecting 3d-index and skein module.

Study of symplectic Monge-Ampère equations using moment maps and contact structures.

Defines a new 3D TQFT from non-semisimple categories.

The paper explores the connection between 3d gravity and Chern-Simons theory using affine group connections.

Random Function Descent improves optimization in high dimensions.