Related papers: Exact Slope and Interpolating Functions in ABJM Th…

We obtain the planar correlation function of four half-BPS operators of arbitrary weights, up to three loops. Our method exploits only elementary properties of the integrand of the planar correlator, such as its symmetries and singularity…

Hypothesis testing for the slope function in functional linear regression is of both practical and theoretical interest. We develop a novel test for the nullity of the slope function, where testing the slope function is transformed into…

Integrable structure has played a very important role in the study of various non-perturbative aspects of planar ABJM theories. In this paper we showed that this remarkable structure survive after orbifold operation with discrete group…

We revisit the inverted pendulum problem with the goal of understanding and computing the true optimal value function. We start with an observation that the true optimal value function must be nonsmooth ($i.e.$, not globally $C^1$) due to…

We define the square amplitudes in planar Aharony-Bergman-Jafferis-Maldacena theory (ABJM), analogous to that in $\mathcal{N}{=}4$ super-Yang-Mills theory (SYM). Surprisingly, the $n$-point $L$-loop integrands with fixed $N{:=}n{+}L$ are…

We introduce two novel procedures to test the nullity of the slope function in the functional linear model with real output. The test statistics combine multiple testing ideas and random projections of the input data through functional…

We consider twist $J$ operators with spin $S$ in the $sl(2)$ sector of $\mathcal N=4$ SYM. The small spin expansion of their anomalous dimension defines the so-called slope functions. Much is known about the linear term, but the study of…

An important ``observable'' of planar N=4 SYM theory is the scaling function f(lambda) that appears in the anomalous dimension of large spin twist 2 operators and also in the cusp anomaly of light-like Wilson loops. The non-trivial relation…

Using the Ogata-Shiba wave function, the spectral functions of the one-dimensional infinite U Hubbard model are calculated for various concentrations. It is shown that the ``shadow band'' feature due to 2k_F fluctuations becomes more…

We study and compute supersymmetric observables for line defects in 3d $\mathcal{N}\ge4$ theories. Our setup is a novel supersymmetric configuration involving line operators and local operators living on a linked circle. The algebra of the…

We evaluate ABJM observables at two loops, for any value of the rank N of the gauge group. We compute the color subleading contributions to the four-point scattering amplitude in ABJM at two loops. Contrary to the four dimensional case, IR…

Calculations in field theory are usually accomplished by employing some variants of perturbation theory, for instance using loop expansions. These calculations result in asymptotic series in powers of small coupling parameters, which as a…

The exact localization result for the expectation value of the $1\over 2$ BPS circular Wilson loop in ${\cal N}=4$ SYM theory is given in the planar limit by the famous Bessel function expression: $\langle W\rangle = {2N\over \sqrt \lambda…

We consider the estimation of the value of a linear functional of the slope parameter in functional linear regression, where scalar responses are modeled in dependence of random functions. The theory in this paper covers in particular…

We study three-point correlation functions of local operators in planar $\mathcal{N}=4$ SYM at weak coupling using integrability. We consider correlation functions involving two scalar BPS operators and an operator with spin, in the so…

We compute one-point function of the glueball loop operator in the maximally confining phase of supersymmetric gauge theory using instanton calculus. In the maximally confining phase the residual symmetry is the diagonal U(1) subgroup and…

An extrapolation method in shell model calculations with deformed basis is presented, which uses a scaling property of energy and energy variance for a series of systematically approximated wave functions to the true one. Such approximated…

Using the gauge/gravity correspondence, we study the properties of 2-point correlation functions of finite-temperature strongly coupled gauge field theories, defined on a curved space of general spatial topology with a dual black hole…

We study the analytic continuation in the spin of the planar spectrum of ABJM theory using the integrability-based Quantum Spectral Curve (QSC) method. Under some minimal assumptions, we classify the analytic properties of the Q-functions…

Smoothing is omnipresent in astronomy, because almost always measurements performed at discrete positions in the sky need to be interpolated into a smooth map for subsequent analysis. Still, the statistical properties of different…