Related papers: Linking disks, spinning vortices and exponential n…
Twisted torus knots and links are given by twisting adjacent strands of a torus link. They are geometrically simple and contain many examples of the smallest volume hyperbolic knots. Many are also Lorenz links. We study the geometry of…
We study the quiver with relations of the endomorphism algebra of an APR tilting module. We give an explicit description of the quiver with relations by graded quivers with potential (QPs) and mutations. The result also implies that…
We extend our 2+1 dimensional discrete growth model (PRE 79, 021125 (2009)) with conserved, local exchange dynamics of octahedra, describing surface diffusion. A roughening process was realized by uphill diffusion and curvature dependence.…
We perform a Hodge theoretic study of parameter dependent families of D-branes on compact Calabi-Yau manifolds in type II and F-theory compactifcations. Starting from a geometric Gauss-Manin connection for B type branes we study the…
We introduce constructions of exact Lagrangian cobordisms with cylindrical Legendrian ends and study their invariants which arise from Symplectic Field Theory. A pair $(X,L)$ consisting of an exact symplectic manifold $X$ and an exact…
We study the quantum broadening (width) of k-strings. We generalise an old result by Luscher, Munster and Weisz to the case of a k-string, by using the gauge/gravity correspondence. When the fundamental QCD-string is replaced by a bound…
We establish a congruence formula between $p$-adic logarithms of Heegner points for two elliptic curves with the same mod $p$ Galois representation. As a first application, we use the congruence formula when $p=2$ to explicitly construct…
The physics of M5 branes placed near an M9 plane on an A-type ALE singularity exhibits a variety of phenomena that introduce additional massless degrees of freedom. There are tensionless strings whenever two M5 branes coincide or whenever…
We study D-branes extended in T^2/Z_4 using the mirror description as a tensor product of minimal models. We describe branes in the mirror both as boundary states in minimal models and as matrix factorizations in the corresponding…
We consider quiver forms that appear in the motivic Donaldson-Thomas generating series or characters of conformal field theories and relate them to 3d $\mathcal{N}=2$ theories on $D^2 \times_q S^1$ with certain boundary conditions…
A generalized augmented link of a knot $K$ is a link obtained by adding trivial components to $K$ that bound $n$-punctured disks. In this paper we consider that $K$ is given by a positive braid with at least one full twist. We characterize…
To a quiver with involution, we study the Coulomb branch of the 3d $\mathcal{N} = 4$ involution-fixed part of the quiver gauge theory. We show that there is an algebra homomorphism from the corresponding shifted twisted Yangian to the…
We study two-dimensional SQED viewed as the world-volume theory of a D-string in the presence of D5-branes with non-zero background fields that induce attractive forces between the branes. In various approximations, the low-energy dynamics…
We produce the first examples relating non-orientable exact Lagrangian fillings of Legendrian links to cluster theory, showing that the ungraded augmentation variety of certain max-tb representatives of Legendrian $2$-bridge links is…
We study (2,2) supersymmetric field theories on two-dimensional worldsheet with boundaries. We determine D-branes (boundary conditions and boundary interactions) that preserve half of the bulk supercharges in non-linear sigma models, gauged…
We study the BPS particle spectrum of five-dimensional superconformal field theories (SCFTs) on $\mathbb{R}^4\times S^1$ with one-dimensional Coulomb branch, by means of their associated BPS quivers. By viewing these theories as arising…
In this paper we find and explore the correspondence between quivers, torus knots, and combinatorics of counting paths. Our first result pertains to quiver representation theory -- we find explicit formulae for classical generating…
We establish a twistor correspondence between a cuspidal cubic curve in a complex projective plane, and a co-calibrated homogeneous $G_2$ structure on the seven--dimensional parameter space of such cubics. Imposing the Riemannian reality…
M2 branes suspended between adjacent parallel M5 branes lead to light strings, the `M-strings'. In this paper we compute the elliptic genus of M-strings, twisted by maximally allowed symmetries that preserve 2d (2,0) supersymmetry. In a…
We investigate a holographic description of k-strings in higher representations via D5 branes with worldvolume fluxes. The D-brane configurations are embedded in supergravity backgrounds dual to confining field theories in 3 and 4…