Type IIB string theory on a 5-sphere gives rise to  = 8, SO(6) gauged supergravity in five dimensions. Motivated by the fact that this is the context of the most widely studied example of the AdS/CFT correspondence, we undertake an investigation of its critical points. The scalar manifold is an E 6(6) ∕USp(8) coset, and the challenge is that it is 42-dimensional. We take a Machine Learning approach to the problem using TensorFlow, and this results in a substantial increase in the number of known critical points. Our list of 32 critical points contains all five of the previously known ones, including an  = 2 supersymmetric point identified by Khavaev, Pilch and Warner.

Large dimensionless numbers, arising out of ratios of various physical constants, intrigued many scientists, especially Dirac. Relying on the coincidence of large numbers, Dirac arrived at the revolutionary hypothesis that the gravitational constant [Formula: see text] should vary inversely at the cosmic time [Formula: see text]. This hypothesis of Dirac, known as the Large Number Hypothesis (LNH), sparked off many speculations, arguments and new ideas in terms of applications. Works done by several authors with LNH as their basic platform are extensively reviewed in this work. Relationship between some of those works are pointed out here elaborately. Possibility of time variations of physical constants other than [Formula: see text] as well as large numbers in various realm of physical and biological sciences are also discussed.

We study the operator product expansion (OPE) of two identical scalar primary operators in the lightcone limit in a conformal field theory where a scalar is the operator with lowest twist. We see that in CFTs where both the stress tensor and a scalar are the lowest twist operators, the stress tensor contributes at the leading order in the lightcone OPE and the scalar contributes at the subleading order. We also see that there does not exist a scalar analogue of the average null energy condition (ANEC) for a CFT where a scalar is the lowest twist operator. arXiv:1908.06303v1 [hep-th]