Related papers: Generating Functions for Giant Graviton Bound Stat…
We present an overview of the role of generating functions in quantum mechanical contexts, mainly in the modern theory of polarization and in the study of quantum phase transitions. Generating functions enable the derivation of moments and…
We generalize generating functions for hypergeometric orthogonal polynomials, namely Jacobi, Gegenbauer, Laguerre, and Wilson polynomials. These generalizations of generating functions are accomplished through series rearrangement using…
We study the normal approximation of functionals of Poisson measures having the form of a finite sum of multiple integrals. When the integrands are nonnegative, our results yield necessary and sufficient conditions for central limit…
We study spin chains with boundaries that are dual to open strings suspended between systems of giant gravitons and dual giant gravitons. The anomalous dimensions computed in the gauge theory are in complete quantitative agreement with…
In this paper we consider composition operator generated by nonsingular measurable transformation between two different Grand Lebesgue Spaces (GLS); we investigate the boundedness, compactness and essential norm of composition operators.
We propose a generating functional for nonrelativistic gauge invariant actions. In particular, we consider actions without the usual magnetic term. Like in the Born-Infeld theory, there is an upper bound to the electric field strength in…
We study the giant graviton integrated correlator in SU$(N)$ $\mathcal{N}=4$ super Yang-Mills at finite complexified coupling $\tau$. Despite the formidable complexity arising from the heavy nature of the operators considered, the large-$N$…
Let $M$ be a discrete-time normal martingale that has the chaotic representation property. Then, from the space of square integrable functionals of $M$, one can construct generalized functionals of $M$. In this paper, by using a type of…
We argue that existing methods for the perturbative computation of anomalous dimensions and the disentanglement of mixing in N = 4 gauge theory can be considerably simplified, systematized and extended by focusing on the theory's dilatation…
We present differential double-copy relations between gluon and graviton three-point functions in (A)dS$_{d+1}$. We introduce a set of differential operators in (A)dS that naturally generalize on-shell kinematics of scattering amplitudes in…
We study integrable non-diagonal open boundary conditions for spin chains arising from holographic gauge theories. Their dual description is in terms of open strings stretching between giant gravitons intersecting at arbitrary angles inside…
Anomalous dimensions of high-twist Wilson operators in generic gauge theories occupy a band of width growing logarithmically with their conformal spin. We perform a systematic study of its fine structure in the autonomous SL(2) subsector of…
The recently constructed Lunin-Maldacena deformation of $AdS_{5}\times S^{5}$ is known to support two inequivalent Penrose limits that lead to BPS pp-wave geometries. In this note, we construct new giant graviton solutions on these…
We study graviton non-Gaussianities in the EFT of Inflation. At leading (second) order in derivatives, the graviton bispectrum is fixed by Einstein gravity. There are only two contributions at third order. One of them breaks parity. They…
We reformulate MHV scattering amplitudes in 4D gauge theory and supergravity as correlation functions of bilinear operators in a supersymmetric gaussian matrix model. The model retains the symmetries of an S(4) of radius L and the matrix…
We compute the generating function of random planar quadrangulations with three marked vertices at prescribed pairwise distances. In the scaling limit of large quadrangulations, this discrete three-point function converges to a simple…
In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical…
We develop bootstrap methods for mixed heavy-light four-point correlators $\langle GGOO\rangle$ in $\mathcal N=4$ super-Yang--Mills theory at large $N$, where $O\equiv {\cal O}_2$ is the chiral primary operator in the stress-tensor…
We treat quantum creation of gravitons by small scale factor oscillations around the average of an expanding universe. Such oscillations can arise in standard general relativity due to oscillations of a homogeneous, minimally coupled scalar…
In this paper, we consider situations in which a given logical function is realized by a multithreshold threshold function. In such situations, constant functions can be easily obtained from multithreshold threshold functions, and…