Related papers: Recursive Representations of Arbitrary Virasoro Co…

We prove a conjecture on uniqueness and existence of the irregular vertex operators of rank $r$ introduced in our previous paper. We also introduce ramified irregular vertex operators of the Virasoro algebra. As applications, we give…

AGT correspondence gives an explicit expressions for the conformal blocks of $d=2$ conformal field theory. Recently an explanation of this representation inside the CFT framework was given through the assumption about the existence of the…

In the context of Conformal Field Theory (CFT), many results can be obtained from the representation theory of the Virasoro algebra. While the interest in Logarithmic CFTs has been growing recently, the Virasoro representations…

We propose a new method to overcome the nodal plane problem for the tomographic reconstruction of molecular orbitals with twofold mirror antisymmetry in the length form based on high-order harmonic generation. It is shown that, by carrying…

Aspects of black hole thermodynamics and information loss can be derived as a consequence of Virasoro symmetry. To bolster the connection between Virasoro conformal blocks and AdS$_3$ quantum gravity, we study sl$(2)$ Chern-Simons Wilson…

In the limit of large central charge $c$ the 4-point Virasoro conformal block becomes a hypergeometric function. It is represented by a sum of chiral Nekrasov functions, which can also be explicitly evaluated. In this way the known proof of…

We study a family of fermionic oscillator representations of the Virasoro algebra via 2-point-local Virasoro fields on the Fock space $\mathit{F^{\otimes \frac{1}{2}}}$ of a neutral (real) fermion. We obtain the decomposition of…

We identify a link between regular matroids and torus representations all of whose isotropy groups have an odd number of components. Applying Seymour's 1980 classification of the former objects, we obtain a classification of the latter. In…

We study the Masur-Veech volumes $MV_{g,n}$ of the principal stratum of the moduli space of quadratic differentials of unit area on curves of genus $g$ with $n$ punctures. We show that the volumes $MV_{g,n}$ are the constant terms of a…

We investigate a relation between the super topological recursion and Gaiotto vectors for $\mathcal{N}=1$ superconformal blocks. Concretely, we introduce the notion of the untwisted and $\mu$-twisted super topological recursion, and…

Using the language of vertex operator algebras (VOAs) and vector-valued modular forms we study the modular group representations and spaces of 1-point functions associated to intertwining operators for Virasoro minimal model VOAs. We…

Spectral measurements of boundary localized in-gap modes are commonly used to identify topological insulators via the bulk-boundary correspondence. This can be extended to high-order topological insulators for which the most striking…

Topological Interlocking assemblies are arrangements of blocks kinematically constrained by a fixed frame, such that all rigid body motions of each block are constrained only by its permanent contact with other blocks and the frame. In the…

We construct a representation for the first AdS curvature correction to the Virasoro-Shapiro amplitude, as an integral over the Riemann sphere. The integrand is that of the Virasoro-Shapiro amplitude in flat space, with the extra insertion…

We revisit the critical two-dimensional Ashkin-Teller model, i.e. the $\mathbb{Z}_2$ orbifold of the compactified free boson CFT at $c=1$. We solve the model on the plane by computing its three-point structure constants and proving crossing…

In this paper, we study extensions between two finite irreducible conformal modules over the Schr\"odinger-Virasoro conformal algebra and the extended Schr\"odinger-Virasoro conformal algebra. Also, we classify all finite nontrivial…

We propose a reconstruction of vortex beams based on the implementation of quadratic transformations in the orbital angular momentum. The information is encoded in a superposition of Bessel-like nondiffracting beams. The measurement of the…

We prove the existence of a non-linear recursive relation for the volume of the moduli space of hyperbolic spheres with conical points or geodesic boundaries. This relation generalizes a result by Zograf, where the same was derived for…

We introduce a nonabelianization map for conformal blocks, which relates $c=1$ Virasoro blocks on a Riemann surface $C$ to Heisenberg blocks on a branched double cover $\widetilde{C}$ of $C$. The nonabelianization map uses the datum of a…

The explicit computation of higher-point conformal blocks in any dimension is usually a challenging task. For two-dimensional conformal field theories in Euclidean signature, the oscillator formalism proves to be very efficient. We…