We review the applications of the Quantum Spectral Curve (QSC) method to the Regge (BFKL) limit in N=4 supersymmetric Yang-Mills theory. QSC, based on quantum integrability of the AdS$_5$/CFT$_4$ duality, was initially developed as a tool for the study of the spectrum of anomalous dimensions of local operators in the N=4 SYM in the planar, $N_c\to\...
We study the double- and triple-scaling limits of a complex multi-matrix model, with $\mathrm{U}(N)^2\times \mathrm{O}(D)$ symmetry. The double-scaling limit amounts to taking simultaneously the large-$N$ (matrix size) and large-$D$ (number of matrices) limits while keeping the ratio $N/\sqrt{D}=M$ fixed. The triple-scaling limit consists in taking...
We investigate the existence and properties of a double asymptotic expansion in $1/N^{2}$ and $1/\sqrt{D}$ in $\mathrm{U}(N)\times\mathrm{O}(D)$ invariant Hermitian multi-matrix models, where the $N\times N$ matrices transform in the vector representation of $\mathrm{O}(D)$. The crucial point is to prove the existence of an upper bound $\chi(h)$ on...
In this paper we derive for the first time the NNNLO gravitational spin-orbit coupling at the quartic order in G in the post-Newtonian (PN) approximation. This represents the first computation in a spinning sector involving three-loop integration. We provide a comprehensive account of the topologies in the worldline picture for the computation, whi...
We analyze the stability of moduli fields at the quantum level in open-string theory realizing the spontaneous breaking of $\mathcal{N}=2$ supersymmetry in four dimensions. This is done by compactifying the type IIB orientifold theory on $T^2\times T^4/\mathbb{Z}_2$, with Scherk-Schwarz supersymmetry breaking implemented along $T^2$. Our analysis i...
We study a special class of four-point correlation functions of infinitely heavy half-BPS operators in planar N=4 SYM which admit factorization into a product of two octagon form factors. We demonstrate that these functions satisfy a system of nonlinear integro-differential equations which are powerful enough to fully determine their dependence on ...
We show that the introduction of two worldline parameters allows to drastically simplify computations in the effective field theory approach to the two-body problem in General Relativity, effectively removing half of the complexity in Feynman diagrams. These parameters obey a polynomial equation whose perturbative expansion recovers an infinite ser...
With one exception, all known non-supersymmetric AdS$_4$ and AdS$_5$ vacua of gauged maximal supergravities that descend from string and M theory have been shown to have modes with mass below the BF bound. The remaining non-supersymmetric AdS solution is perturbatively stable within gauged maximal supergravity, and hence appears to contradict recen...
We introduce a framework in noncommutative geometry consisting of a $*$-algebra $\mathcal A$, a bimodule $\Omega^1$ endowed with a derivation $\mathcal A\to \Omega^1$ and with a hermitian structure $\Omega^1\otimes \bar{\Omega}^1\to \mathcal A$, and a cyclic 1-cochain $\mathcal A\to \mathbb C$ whose coboundary is determined by the previous structur...
The notion of superconnection devised by Quillen in 1985 and used in gauge-Higgs field theory in the 1990's is applied to the spin factors (finite-dimensional euclidean Jordan algebras) recently considered as representing the finite quantum geometry of one generation of fermions in the Standard Model of particle physics.
