arXiv research

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

Topological twists for 4d N=2 theories depend on spacetime type, gerbe connections, and generalized spin-c structures.

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…

We propose a method for determining the spins of BPS states supported on line defects in 4d $\mathcal{N}=2$ theories of class S. Via the 2d-4d correspondence, this translates to the construction of quantum holonomies on a punctured Riemann surface $\mathcal{C}$. Our approach combines the technology of spectral networks…

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

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

M-theory compactified on $G_2$-holonomy manifolds results in 4d $\mathcal{N}=1$ supersymmetric gauge theories coupled to gravity. In this paper we focus on the gauge sector of such compactifications by studying the Higgs bundle obtained from a partially twisted 7d super Yang-Mills theory on a supersymmetric three-cycle…

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

New invariant measures knotted surfaces in 4D, revealing unknottedness.

Geometrically computes superpotentials for certain 4D N=2 theories.

New geometric approach realizes 5D bulk theories with 4D edge modes.

The paper explores gauge theory invariants and their duals via topological-holomorphic twist.

New $\mathcal{C}$-connection characterizes 4D spaces conformal to Einstein spaces.

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

Study of complex structures on product twistor spaces for 4D manifolds.

We show that the smooth geometry of a hyperbolic 3-manifold emerges from a classical spin system defined on a 2d discrete lattice, and moreover show that the process of this "dimensional oxidation" is equivalent with the dimensional reduction of a supersymmetric gauge theory from 4d to 3d. More concretely, we propose a…

We study the twisted index of 4d $\mathcal{N}$ = 2 class S theories on a closed hyperbolic 3-manifold $M_3$. Via 6d picture, the index can be written in terms of topological invariants called analytic torsions twisted by irreducible flat connections on the 3-manifold. Using the topological expression, we determine the …

The paper classifies noncollapsed translators in 4D space.

Geometric interpretation of 2d-4d wall-crossing formulas.

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

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…

Geometric formulation of 4D supergravity for mathematicians.

In this paper we investigate the relation between complexified Fenchel-Nielsen coordinates and spectral network coordinates on Seiberg-Witten moduli space. The main technique is the comparison of exact expressions for the expectation value of 't Hooft defects in certain 4D $SU(2)$ $\mathcal{N}=2$ gauge theories. We der…

A theorem connects two Willmore energies in 4D.

We consider compactification of type IIA supergravity on nearly Kaehler manifolds. These represent a simple class of SU(3) structure manifolds which includes S^6 and CP^3. We exhibit for the first time an explicit reduction ansatz in this context, obtaining an N=2 gauged supergravity in 4d with a single vector and hype…

We explore 4d Yang-Mills gauge theories (YM) living as boundary conditions of 5d gapped short/long-range entangled (SRE/LRE) topological states. Specifically, we explore 4d time-reversal symmetric pure YM of an SU(2) gauge group with a second-Chern-class topological term at $θ=π$ (SU(2)$_{θ=π}$ YM), by turning on backg…

Enhances Hantzsche's theorem for 3-manifolds in 4D.

We use the conformal invariance and the holographic correspondence to fully specify the dependence of entanglement entropy on the extrinsic geometry of the 2d surface $Σ$ that separates two subsystems of quantum strongly coupled ${\mathcal{N}}=4$ SU(N) superconformal gauge theory. We extend this result and calculate en…

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

Study the singularities of Gauss map components of surfaces in 4D.

Explains how knots relate to 4D shapes.

S-dual of Hamiltonian spaces connects to Langlands duality.

Study classifies hypersurfaces in 4D Lorentz-Minkowski space using specific operators.

We explain how, starting with a stack of D4-branes ending on an NS5-brane in type IIA string theory, one can, via T-duality and the topological-holomorphic nature of the relevant worldvolume theories, relate (i) the lattice models realized by Costello's 4d Chern-Simons theory, (ii) links in 3d analytically-continued Ch…

After a review of exotic statistics for point particles in 3d BF theory, and especially 3d quantum gravity, we show that string-like defects in 4d BF theory obey exotic statistics governed by the 'loop braid group'. This group has a set of generators that switch two strings just as one would normally switch point parti…

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

We construct ${\cal N}=2$ supersymmetric Yang-Mills theory on 4D manifolds with a Killing vector field with isolated fixed points. It turns out that for every fixed point one can allocate either instanton or anti-instanton contributions to the partition function, and that this is compatible with supersymmetry. The equi…

In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge group, this generalization involves a gauge '2-group'. We focus on 6 examples. First, every abelian Lie group gives a Lie 2-gr…

Study of surface defects in gauge theories leads to duality and separation of variables.

We study integrable non-degenerate Monge-Ampere equations of Hirota type in 4D and demonstrate that their symmetry algebras have a distinguished graded structure, uniquely determining the equations. This is used to deform these heavenly type equations into new integrable PDE of the second order with large symmetry pseu…

New invariant measures complexity of 2-knots in 4D space.

Local classification of 4D Ricci solitons with specific algebra properties.

Approaches 4D Schoenflies via pseudo-isotopy.

New theory classifies knotted spheres in 4D space.

Refines knot defect measurement in 3D and 4D.

The question we address here is of whether phenomena of collective bankruptcies are related to self-organized criticality. In order to answer it we propose a simple model of banking networks based on the random directed percolation. We study effects of one bank failure on the nucleation of contagion phase in a financia…

Compactification of M- / string theory on manifolds with $G_2$ structure yields a wide variety of 4D and 3D physical theories. We analyze the local geometry of such compactifications as captured by a gauge theory obtained from a three-manifold of ADE singularities. Generic gauge theory solutions include a non-trivial g…

We study S-dualities in analytically continued SL(2) Chern-Simons theory on a 3-manifold M. By realizing Chern-Simons theory via a compactification of a 6d five-brane theory on M, various objects and symmetries in Chern-Simons theory become related to objects and operations in dual 2d, 3d, and 4d theories. For example,…