We study fixed points with N scalar fields in $4 - \varepsilon$ dimensions to leading order $\varepsilon$ using a bottom-up approach. do so by analyzing O(N) invariants of the quartic coupling $\lambda_{ijkl}$ that describes such CFTs. In particular, we show $\lambda_{iijj}$ and $\lambda_{ijkl}^2$ are restricted specific domain, refining result Rychkov Stergiou. also averages one-loop anomalous...

We consider the problem of prescribing Gaussian and geodesic curvatures for a conformal metric on unit disk. This is equivalent to solving following P.D.E. $$\begin{aligned} {\left\{ \begin{array}{ll}-\Delta u=2K(z)e^u&{}\hbox {in}\;\mathbb {D}^2,\\ \partial _\nu u+2=2h(z)e^\frac{u}{2}&{}\hbox {on}\;\partial \mathbb {D}^2,\end{array}\right. } \end{aligned}$$ where K, h are prescribed curvatures...

We consider the dressed energy $\varepsilon$ of XXZ chain in massless antiferromagnetic parameter regime at $0 < \Delta 1$ and finite magnetic field. This function is defined as a solution Fredholm integral equation second kind. Conceived real over numbers it describes particle-hole excitations ground state fixed The extension to complex plane determines solutions Bethe Ansatz equations for eig...

Abstract We study map lattices coupled by collision and show how perturbations of transfer operators associated with the spatially periodic approximation model can be used to extract information about collisions per lattice unit. More precisely, we a on finite box L sites boundary conditions, collision. derive, via non-trivial first-order for leading eigenvalue rare event operator, formula firs...

We study algorithms for the sliding-window model, an important variant of data-stream in which goal is to compute some function a fixed-length suffix stream. extend smooth-histogram framework Braverman and Ostrovsky (FOCS 2007) almost-smooth functions, includes all subadditive functions. Specifically, we show that if can be \(\left( 1+{{\varepsilon }}\right) \)-approximated insertion-only strea...