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We study the size of the minimal gap between the first N eigenvalues of the Laplacian on a rectangular billiard having irrational squared aspect ratio $\alpha$, in comparison to the corresponding quantity for a Poissonian sequence. If…
We establish a structure result for the universal abelian variety over the moduli space A_5, in terms of discriminant curves of conic bundles over a del Pezzo surface. In particular, this gives a very simple unirational parametrization of…
We consider SU(2) Yang-Mills theory on $AdS_4$ by imposing various boundary conditions, which correspond to non-trivial deformations of its boundary $CFT$. We obtain classical solutions of Yang-Mills fields up to the first subleading order…
Let $P$ be a collection of $n$ points moving along pseudo-algebraic trajectories in the plane. One of the hardest open problems in combinatorial and computational geometry is to obtain a nearly quadratic upper bound, or at least a subcubic…
We investigate non-abelian branes in curved space. We discuss solutions to the equations of motion of the transverse scalars when they are constant along the world-volume directions and obey an $\mathfrak{su}(2)$ or an…
We analyze the psu(2,2|4) supersymmetry algebra of a superstring propagating in the AdS_5 x S^5 background in the uniform light-cone gauge. We consider the off-shell theory by relaxing the level-matching condition and take the limit of…
We determine the general structure of quantum anomalies for the $R$-multiplet of four dimensional $\mathcal{N}=1$ supersymmetric quantum field theories in the presence of background fields for an arbitrary number of Abelian flavor…
Superconformal sigma models with Calabi--Yau target spaces described as complete intersection subvarieties in toric varieties can be obtained as the low-energy limit of certain abelian gauge theories in two dimensions. We formulate mirror…
We show explicitly that the full structure of IIB string theory is needed to remove the non-localities that arise in boundary conformal theories that border hyperbolic spaces on AdS$_5$. Specifically, using the…
The anomalous dimension $\gamma_m =1$ in the infrared region near conformal edge in the broken phase of the large $N_f$ QCD has been shown by the ladder Schwinger-Dyson equation and also by the lattice simulation for $N_f=8$ for $ N_c=3$.…
It is a well known phenomenon that many classical minimal surfaces in Euclidean space also exist with higher dihedral symmetry. More precisely, these surfaces are solutions to free boundary problems in a wedge bounded by two vertical planes…
We establish the action of three-dimensional bosonization and particle-vortex duality in the presence of a boundary, which supports a non-anomalous two-dimensional theory. We confirm our prescription using a microscopic realization of the…
We study a general class of supersymmetric AdS_4 x Y_7 solutions of M-theory that have large N dual descriptions as N = 2 Chern-Simons-matter theories on S^3. The Hamiltonian function h_M for the M-theory circle, with respect to a certain…
We consider the anomalous dimension of a certain twist two operator in N=4 super Yang-Mills theory. At strong coupling and large-N it is captured by the classical dynamics of a spinning D5-brane. The present calculation generalizes the…
We study nonlocal minimal surfaces as a new approximation theory for the area functional, and more specifically in the context of Yau's conjecture on the existence of minimal surfaces in closed three-dimensional manifolds. This programme…
We study a novel non-Abelian matrix configuration of probe D-branes in AdS5. This configuration gives rise to a new D-brane phenomenon related to the known "Myers effect" in the context of holography. It is dual to a deformation of the…
It has been recently argued that an embedding of the SM into a consistent theory of quantum gravity may imply important constraints on the mass of the lightest neutrino and the cosmological constant $\Lambda_{4}$. The constraints come from…
The Shapley-Folkman theorem shows that Minkowski averages of uniformly bounded sets tend to be convex when the number of terms in the sum becomes much larger than the ambient dimension. In optimization, Aubin and Ekeland [1976] show that…
We propose dual pairs of $\mathcal{N}=(0,4)$ half-BPS boundary conditions for 3d $\mathcal{N}=4$ Abelian gauge theories related to mirror symmetry and S-duality by showing the matching of boundary 't Hooft anomalies and supersymmetric…
The theoretical understanding of density waves in disk galaxies starts from the classical WKB perturbative analysis of tight-winding perturbations, the key assumption being that the potential due to the density wave is approximately radial.…