Related papers: Comments on the slope function

The effective action of N=2 gauge multiplets in general includes higher-dimension UV finite nonholomorphic corrections integrated with the full N=2 superspace measure. By adding a hypermultiplet in the adjoint representation we study the…

We define a switch function to be a function from an interval to $\{1,-1\}$ with a finite number of sign changes. (Special cases are the Walsh functions.) By a topological argument, we prove that, given $n$ real-valued functions, $f_1,…

The sum of proper divisors function $s(n)$ has been studied for more than 2000 years. In this paper we study statistical properties of the related function $S_s(n) := \sum_{d \mid n} s(d)$. This function arises from a generalization of the…

This is a tutorial paper that gives the complete proof of a result of Frolov [2] that shows the optimal order of convergence for numerical integration of functions with bounded mixed derivatives. The presentation follows Temlyakov [8], see…

We take an $L_1$-dense class of functions $\Cal F$ on a measurable space $(X,\Cal X)$ together with a sequence of independent, identically distributed $X$-space valued random variables $\xi_1,\dots,\xi_n$ and give a good estimate on the…

Consider an $s$-dimensional function being evaluated at $n$ points of a low discrepancy sequence (LDS), where the objective is to approximate the one-dimensional functions that result from integrating out $(s-1)$ variables. Here, the…

We construct, to the first two non-trivial orders, the next conserved charge in the su(2|3) sector of N=4 Super Yang-Mills theory. This represents a test of integrability in a sector where the interactions change the number of sites of the…

The spectrum of Supersymmetric Yang-Mills Quantum Mechanics (SYMQM) in D=4 dimensions for SU(2) gauge group is computed for a maximal number of bosonic quanta $B\le60$ in the two-fermion sector with the angular momentum $j=0$. We analyse…

We develop a new approach to extracting the physical consequences of S-duality of four-dimensional $\mathcal{N}=4$ super Yang-Mills (SYM) and its string theory dual, based on $SL(2,\mathbb{Z})$ spectral theory. We observe that CFT…

Anomalous dimension and higher conserved charges in the $sl(2)$ sector of ${\cal N}=4$ SYM for generic spin $s$ and twist $L$ are described by using a novel kind of non-linear integral equation (NLIE). The latter can be derived under…

We investigate the interaction between systolic geometry and positive scalar curvature through spinorial methods. Our main theorem establishes an upper bound for the two-dimensional stable systole on certain high-dimensional manifolds with…

We prove the local existence of unique smooth solutions of the Donaldson geometric flow on the space of symplectic forms on a closed smooth four-manifold, representing a fixed cohomology class. It is a semiflow on the Besov space…

We use high-low frequency methods developed in the context of decoupling to prove sharp (up to $C_\epsilon R^\epsilon$) square function estimates for the moment curve $(t,t^2,\ldots,t^n)$ in $\mathbb{R}^n$. Our inductive scheme incorporates…

We develop the derivative expansion of the one-loop ${\cal N}=4$ SYM effective action depending both on ${\cal N}=2$ vector multiplet and on hypermultiplet background fields. We get a new derivation of the complete ${\cal N}=4$…

Continuing the program of math.SG/0012067 and math.SG/0310450, we introduce refinements of the Donaldson-Smith standard surface count which are designed to count nodal pseudoholomorphic curves and curves with a prescribed decomposition into…

We take our first step toward getting finite results from the alpha'-corrected D=4 N=4 SYM theory with emphasis on the field theory techniques. Starting with the classical action of N=4 SYM with the leading alpha'-corrections, we examine…

We analyze the one-loop correction to the three-point function coefficient of scalar primary operators in N=4 SYM theory. By applying constraints from the superconformal symmetry, we demonstrate that the type of Feynman diagrams that…

We derive normal approximation results for a class of stabilizing functionals of binomial or Poisson point process, that are not necessarily expressible as sums of certain score functions. Our approach is based on a flexible notion of the…

The gauge fixing procedure for N=1 supersymmetric Yang-Mills theory (SYM) is proposed in the context of the stochastic quantization method (SQM). The stochastic gauge fixing, which was formulated by Zwanziger for Yang-Mills theory, is…

Let $R,r$ be as in the classical Gromov non-squeezing theorem, and let $\epsilon = (\pi R ^{2} - \pi r ^{2})/ \pi r ^{2} $. We first conjecture that the Gromov non-squeezing phenomenon persists for deformations of the symplectic form on the…