Related papers: Modular Forms and Three Loop Superstring Amplitude…

Unlike classical modular forms, there is currently no general way to implement the computation of Siegel modular forms of arbitrary weight, level and character, even in degree two. There is however, a way to do it in a unified way. After…

In the present paper we extend the Schwinger model of the nucleon to the inclusion of loop corrections. Starting from a chiral model of nucleon and delta for the mesons $\pi,\rho$ and $A_1$ we extend our nonperturbative sefconsistent…

Recently, various possible expressions for the vacuum-to-vacuum superstring amplitudes has been proposed at genus $g=3,4,5$. To compare the different proposals, here we will present a careful analysis of the comparison between the two main…

This paper studies the role of the axial gauge in the semiclassical analysis of simple supergravity about the Euclidean four-ball, when non-local boundary conditions of the spectral type are imposed on gravitino perturbations at the…

We prove an equidistribution statement for the Satake parameters of the local representations attached to Siegel cusp forms of degree $2$ of increasing level and weight, counted with a certain arithmetic weight. We then apply this to…

We show that the central charges that group theory allows in the (2,0) supersymmetry translations algebra arise from a string and a 3-brane by commuting two supercharges. We show that the net force between two such parallel strings…

We study Soergel modules for arbitrary Coxeter groups. For infinite Coxeter groups, we show that the homomorphisms between Soergel modules are in general more than those coming from morphisms of Soergel bimodules. This result provides a…

We undertake a detailed study of the lowest weight modules for the Hermitian symmetric pair (G,K), where G=Sp_4(R) and K is its maximal compact subgroup. In particular, we determine K-types and composition series, and write down explicit…

We construct superconformal gauged sigma models with extended rigid supersymmetry in three dimensions. Those with N>4 have necessarily flat targets, but the models with N \leq 4 admit non-flat targets, which are cones with appropriate…

We show that within any strong orbit equivalent class, there exist minimal subshifts with arbitrarily low superlinear complexity. This is done by proving that for any simple dimension group with unit $(G,G^+,u)$ and any sequence of positive…

Let $K$ denote a simply connected compact Lie group and let $G=K^{\mathbb C}$, the complexification. It is known that there exists an $LK$ bi-invariant probability measure on a natural hyperfunction completion of the complex loop group…

Scattering amplitudes computed by superstring perturbation theory are known to holomorphically split into chiral half integrands at fixed internal loop momentum. It is established by direct computation that upon reduction to the ordinary…

We analyse the Weak Gravity Conjecture for chiral four-dimensional F-theory compactifications with N=1 supersymmetry. Extending our previous work on nearly tensionless heterotic strings in six dimensions, we show that under certain…

We study skein modules of 3-manifolds by embedding them into the Hilbert spaces of 4d ${\cal N}=4$ super-Yang-Mills theories. When the 3-manifold has reduced holonomy, we present an algorithm to determine the dimension and the list of…

The notion of formal Siegel modular forms for an arithmetic subgroup $\Gamma$ of the symplectic group of genus $n$ is a generalization of symmetric formal Fourier-Jacobi series. Assuming an upper bound on the affine covering number of the…

In this PhD thesis we study holomorphic and non-holomorphic elliptic analogues of multiple zeta values, namely elliptic multiple zeta values and modular graph functions. Both classes of functions have been discovered very recently, and are…

We prove that the graded ring of modular forms of weight divisible by 3 is naturally isomorphic to a certain log canonical ring of the corresponding elliptic modular surface.

We show that the ring of modular forms with characters for $\mathrm{O}(2,4;\mathbb{Z})$ is generated by forms of weights 4, 4, 6, 8, 10, 10, 12, and 30 with three relations of weights 8, 20, and 60. The proof is based on the study of a…

As open N=2 or 4 strings describe self-dual N=4 super Yang-Mills in 2+2 dimensions, the corresponding closed (heterotic) strings describe self-dual ungauged (gauged) N=8 supergravity. These theories are conveniently formulated in a chiral…

We revisit Beukers' modular-form proof of the irrationality of $\zeta(3)$ from the point of view of the auxiliary weight two modular form. For the Fricke group $\Gamma_0(6)^\star$, we show that Beukers' choice is not isolated: it belongs to…