arXiv research

Study of 5D SYM theory on toric surfaces yields refined Vafa-Witten invariants.

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

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…

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…

This work is a continuation of our previous paper arXiv:1812.06473 where we have constructed ${\cal N}=2$ supersymmetric Yang-Mills theory on 4D manifolds with a Killing vector field with isolated fixed points. In this work we expand on the mathematical aspects of the theory, with a particular focus on its nature as a …

Novel gauge-theoretic Floer homologies defined from 5d N=2 theory, linking 4, 3, and 2-manifolds.

5D SCFTs can have confining vacua with strings and unbroken symmetries.

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

Extract anomalies from 5D SCFTs using extra-dimensional η-invariants.

We continue our research work started in "Kinematic Quantities and Raychaudhuri Equations in a $5D$ Universe" (Eur. Phys. J. C, 2015), and obtain in a covariant form, the equations of motion with respect to the $(1+1+3)$ threading of a $5D$ universe $(\bar{M}, \bar{g})$. The natural splitting of the tangent bundle of $…

A new algebraic method extracts symmetry anomalies from 5D SCFTs.

New insights connect strong coupling SYM amplitudes to hyperkähler geometry.

Let $X$ be a compact connected Riemann surface of genus $g$, with $g \geq 2$. For each $d <η(X)$, where $η(X)$ is the gonality of $X$, the symmetric product $\text{Sym}^d(X)$ embeds into $\text{Pic}^d(X)$ by sending an effective divisor of degree $d$ to the corresponding holomorphic line bundle. Therefore, the restrict…

In 5D, integrability is linked to curvature constraints of subconformal structures.

Revisits SYM theory to compute Donaldson invariants using mock modular forms.

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

Study topological correlators for $SU(2)$ SYM on four-manifolds, deriving explicit formulae and confirming S-duality.

Derive K-theoretic Donaldson invariants for various 4-manifolds using path integrals and topological twists.

Categorifies Stokes coefficients in Chern-Simons theory models.

Sym-NCO leverages symmetricities to improve DRL-NCO performance.

Defines discrete symmetry of manifolds and proves bounds on its value.

Let $M^2_{g,k}$ and $M^2_{g',k'}$ be compact Riemann surfaces with punctures ($g,g'\ge 0$ - genuses, $k,k'\ge 1$ - number of punctures). For any Hausdorff space $X$ the quotient space $\mathrm{Sym}^nX := X^n/S_n$ is the $n$-th symmetric product of $X, \ n\ge 2$. It is well known, that $\mathrm{Sym}^n M^2_{g,k}$ is a sm…

In this paper we use the anholonomic frames method to construct exact solutions for vacuum 5D gravity with metrics having off-diagonal components. The solutions are in general anisotropic and possess interesting features such as an anisotropic warp factor with respect to the extra dimension, or a gravitational scaling/…

New hyperbolic links have more symmetries than their complements.

We give an immersion formula, the Sym-Bobenko formula, for minimal surfaces in the 3-dimensional Heisenberg space. Such a formula can be used to give a generalized Weierstrass type representation and construct explicit examples of minimal surfaces.

The paper connects link symmetries to finite subgroups of O(3).

On a five dimensional simply connected Sasaki-Einstein manifold, one can construct Yang-Mills theories coupled to matter with at least two supersymmetries. The partition function of these theories localises on the contact instantons, however the contact instanton equations are not elliptic. It turns out that these equa…

It is formulated a new 'anholonomic frame' method of constructing exact solutions of Einstein equations with off--diagonal metrics in 4D and 5D gravity. The previous approaches and results are summarized and generalized as three theorems which state the conditions when two types of ansatz result in integrable gravitati…

Humans take advantage of real world symmetries for various tasks, yet capturing their superb symmetry perception mechanism with a computational model remains elusive. Motivated by a new study demonstrating the extremely high inter-person accuracy of human perceived symmetries in the wild, we have constructed the first …

We briefly review the current situation with various relations between knot/braid polynomials (Chern-Simons correlation functions), ordinary and extended, considered as functions of the representation and of the knot topology. These include linear skein relations, quadratic Plucker relations, as well as "differential" …

The paper connects orbifold singularities to higher symmetries in SQFTs.

Study new ECS structures in 5D Minkowski compactifications of M-theory.

We construct a new class of exact solutions describing spacetimes possessing Lie algebroid symmetry. They are described by generic off-diagaonal 5D metrics embedded in bosonic string gravity and possess nontrivial limits to the Einstein gravity. While we focus on nonholonomic vielbein transforms of the Schwarzschild me…

GyroSwin models plasma turbulence with neural nets, reducing costs and capturing neglected nonlinearities.

Let $X$ be a compact connected Riemann surface of genus $g\geq 0$, and let ${\rm Sym}^d(X)$, $d \ge 1$, denote the $d$-fold symmetric product of $X$. We show that ${\rm Sym}^d(X)$ admits a Hermitian metric with negative Chern scalar curvature if and only if $g \geq 2$, and positive Chern scalar curvature if and only if…

Paper explores geometry of covariance matrices using associated bundles.

The Bergman space and conformally flat 2-disk operads are linked to vertex operator algebras.

Inequality found for a specific equation on 5D manifolds.

The study classifies all compact 5D polytopes with 9 facets.

Paper shows rigidity of rotationally symmetric minimal hypersurfaces in 5D spaces.

New algebraic rules for 5D shapes based on 3D cocycles.

We construct modular invariants on the moduli space of quantum vacua of N=2 SYM with gauge group SU(2). We also introduce a nonchiral function K which is expressed in terms of the Seiberg-Witten and Poincare' metrics. It turns out that K has all the expected properties of the next to leading term in the Wilsonian effec…

Estimates Kähler metrics on compactified hyperbolic surfaces and their symmetric products.

Study duality of zero mean curvature surfaces in Heisenberg group.

There are two different approaches to exhibit submaximal symmetric rank 2 distributions in 5D via Monge equations. In this note we establish precise relations between these models, find auto-equivalences of one family, and treat two special equations.

Paper derives a formula for renormalized area of minimal hypersurfaces in 5D Poincaré-Einstein spaces.

Neural surrogates speed up 5D gyrokinetic simulations of plasma turbulence.

Considering the kinematics of the moving frame associated with a constant mean curvature surface immersed in S^3 we derive a linear problem with the spectral parameter corresponding to elliptic sinh-Gordon equation. The spectral parameter is related to the radius R of the sphere S^3. The application of the Sym formula …