hep-th

The R\'enyi quantum null energy condition conjectures that the second null shape variation of the sandwiched R\'enyi divergence (SRD) of an excited state relative to the vacuum is non-negative in local Poincar\'e-invariant quantum field theory, giving a one-parameter generalization of the quantum null energy condition (QNEC). We prove R\'enyi QNEC for all integer R\'enyi parameters $n\geq 2$ for von Neumann algebras carrying a half-sided modular inclusion structure. The only assumption on the excited state is finiteness of its SRD relative to the vacuum. Concretely, for any $\sigma$-finite von Neumann algebra with such an inclusion, we prove log-convexity, under the associated null-translation semigroup, of the Kosaki $L^n$ norm of any normal positive functional with finite $L^n$ norm.

The gravitational path integral produces an asymptotic expansion in $G_N$, a fact which is puzzling in the case of observables that are expected to fluctuate wildly. Wormholes appear to compute ensemble averages of functions of such observables, though in typical constructions of AdS/CFT, there are no parameters to average over except, in some examples, a single integer $N$. We introduce a procedure that we call ``Mellin averaging'' to define a sort of asymptotic average of a function of $N$. We argue that Mellin averaging over $N$ may suffice to reproduce the apparent randomness seen in wormhole physics, provided that the dual theory admits an analytic continuation in $N$ and the relevant observables fluctuate on superpolynomially small scales in $N$. As a test case, we consider the spectral form factor in the regime where the double cone is believed to dominate the gravitational path integral and compare to a random matrix theory in which $N$ behaves as a continuous variable. We also describe some toy models of analytic continuation in $N$: a qubit model that can be analytically continued in $N$, and an explicit construction of a deterministic function of $N$ that simulates a sequence of independent draws from a Gaussian ensemble.

We exploit the techniques of dynamical systems to study the cosmological evolution of cosmic fundamental strings and effective strings arising from branes wrapped on internal cycles. We also include the whole potential of the volume modulus characterised by an early time run-away towards a late time minimum. We analyse the overshoot problem with and without radiation, and find that the presence of an initial population of strings arising from NS5-branes wrapped around 4-cycles is enough to ensure that the modulus stabilises in its late time minimum, even in the absence of radiation. The reason is the transfer of energy between the modulus and the effective strings caused by the fact that their tension depends on the volume modulus. Interestingly, we find that the energy density of cosmic superstrings is generically very large when the modulus is oscillating around its minimum, opening up the possibility of a detectable gravitational wave signal. We also find no evidence of an efficient resonant enhancement of cosmic superstrings due to an oscillating tension in the late time minimum.