Related papers: Accessing Large Global Charge via the $\epsilon$-E…
We determine, for the first time, the scaling dimensions of a family of fixed-charge operators stemming from the critical $O(N)$ model in 4-$\epsilon$ dimensions to the leading and next to leading order terms in the charge expansion but to…
We compute observables in the interacting rank-one 6d $\mathcal{N}=(2,0)$ SCFT at large R-charge. We focus on correlators involving $\Phi^n$, namely symmetric products of the bottom component of the supermultiplet containing the…
We describe a highly efficient numerical scheme for finding two-sided bounds for the eigenvalues of the fractional Laplace operator (-Delta)^{alpha/2} in the unit ball D in R^d, with a Dirichlet condition in the complement of D. The…
Let $\{w_{i,j}\}_{1\leq i\leq n, 1\leq j\leq s} \subset L_m=F(X_1,...,X_m)[{\partial \over \partial X_1},..., {\partial \over \partial X_m}]$ be linear partial differential operators of orders with respect to ${\partial \over \partial…
We perform Monte-Carlo measurements of two and three point functions of charged operators in the critical O(2) model in 3 dimensions. Our results are compatible with the predictions of the large charge superfluid effective field theory. To…
We perform a model-independent analysis of $|\Delta b|=|\Delta d|=1$ processes to test the standard model and probe flavor patterns of new physics. Constraints on Wilson coefficients are obtained from global fits to $B^+ \to \pi^+…
We compute general higher-point functions in the sector of large charge operators $\phi^n$, $\bar\phi^n$ at large charge in $O(2)$ $(\bar \phi\phi)^2$ theory. We find that there is a special class of "extremal" correlators having only one…
We determine the scaling dimension $\Delta_n$ for the class of composite operators $\phi^n$ in the $\lambda \phi^4$ theory in $d=4-\epsilon$ taking the double scaling limit $n\rightarrow \infty$ and $\lambda \rightarrow 0$ with fixed…
We prove that the finite-difference based derivative-free descent (FD-DFD) methods have a capability to find the global minima for a class of multiple minima problems. Our main result shows that, for a class of multiple minima objectives…
In an arbitrary unitary 4D CFT we consider a scalar operator \phi, and the operator \phi^2 defined as the lowest dimension scalar which appears in the OPE \phi\times\phi with a nonzero coefficient. Using general considerations of OPE,…
Long-range forces up to next-to-leading order are computed in the framework of the Einstein-Maxwell-dilaton system by means of a semiclassical approach to gravity. As has been recently shown, this approach is effective if one of the masses…
An $(\epsilon,\phi)$-expander decomposition of a graph $G=(V,E)$ is a clustering of the vertices $V=V_{1}\cup\cdots\cup V_{x}$ such that (1) each cluster $V_{i}$ induces subgraph with conductance at least $\phi$, and (2) the number of…
We study cusped Wilson line operators in the Abelian Higgs model in $ d = 4 - \epsilon $ at large external charges. Using a double-scaling limit $ Q \to \infty $, $ \epsilon \to 0 $ with $ Q\epsilon $ fixed, we develop a semiclassical…
We investigate the analytic properties of the fixed charge expansion for a number of conformal field theories in different space-time dimensions. The models investigated here are $O(N)$ and $QED_3$. We show that in $d=3-\epsilon$ dimensions…
The present paper pioneers the study of the Dirichlet problem with $L^q$ boundary data for second order operators with complex coefficients in domains with lower dimensional boundaries, e.g., in $\Omega := \mathbb R^n \setminus \mathbb R^d$…
We consider the problem of finding an approximate solution to $\ell_1$ regression while only observing a small number of labels. Given an $n \times d$ unlabeled data matrix $X$, we must choose a small set of $m \ll n$ rows to observe the…
This article deals with maximal operators on ${\mathbb R}^n$ formed by taking arbitrary rotations of tensor products of a $d$-dimensional H\"ormander--Mihlin multiplier with the identity in $n-d$ coordinates, in the particular codimension 1…
We bootstrap the first-order correction in the curvature expansion of the Virasoro-Shapiro amplitude in AdS spacetime, for arbitrary Kaluza-Klein charges of external operators. By constructing a universal ansatz based on single-valued…
We study the fixed point that controls the IR dynamics of QED in $d = 4 - 2\epsilon$. We derive the scaling dimensions of four-fermion and bilinear operators beyond leading order in $\epsilon$-expansion. For the four-fermion operators, this…
In this Letter, we present for the first time a calculation of the complete next-to-leading order corrections to the $gg \to ZH$ process. We use the method of small mass expansion to tackle the most challenging two-loop virtual amplitude,…