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Type IIB supergravity enjoys a discrete non-Abelian duality group, which has potential quantum anomalies. In this paper we explicitly compute these, and present the bordism group that controls them, modulo some physically motivated assumptions. Quite surprisingly, we find that they do not vanish, which naively would signal an inconsistency of F-theory. Remarkably, a subtle modification of the standard 10d Chern-Simons term cancels these anomalies, a fact which relies on the ***specific*** field content of type IIB supergravity. We also discover other ways to cancel this anomaly, via a topological analog of the Green-Schwarz mechanism. These alternative type IIB theories have the same low energy supergravity limit as ordinary type IIB, but a different spectrum of extended objects. They could either be part of the Swampland, or connect to the standard theory via domain walls.
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A recent arXiv manuscript, arXiv:1801.03278, claims that a cosmic background radiation with a black body temperature of $T_{rm BB}$ ~ 500 K (440 F) was just barely visible to human eyes, thus fixing the onset of the Dark Ages at about 5 million years post recombination. This claim presents an insurmountable biophysical challenge, since even hotter bodies, such as 450 F pizzas, do not seem to be glowing in the dark. As volunteer referees we show that this claim is the result of employing an incorrect assumption. Via a corrected analysis we find that the Dark Ages must have had a significantly earlier start. A second, more descriptive claim, that a cosmic background radiation with $T_{rm BB}$ of 1545 K was as blinding to humans as is our own Sun, is based on the same assumption and may have to be revised.
We construct a finitely generated group that does not satisfy the generalized Burghelea conjecture.
Spacetime theories obtained from perturbative string theory constructions are automatically free of perturbative anomalies, but it is not settled whether they are always free of global anomalies. Here we discuss a possible $mathbb{Z}_{24}$-valued pure gravitational anomaly of heterotic compactifications down to two spacetime dimensions, and point out that it can be shown to vanish using the theory of topological modular forms, assuming the validity of the Stolz-Teichner conjecture.
We present a simple general proof that Casimir force cannot originate from the vacuum energy of electromagnetic (EM) field. The full QED Hamiltonian consists of 3 terms: the pure electromagnetic term $H_{rm em}$, the pure matter term $H_{rm matt}$ and the interaction term $H_{rm int}$. The $H_{rm em}$-term commutes with all matter fields because it does not have any explicit dependence on matter fields. As a consequence, $H_{rm em}$ cannot generate any forces on matter. Since it is precisely this term that generates the vacuum energy of EM field, it follows that the vacuum energy does not generate the forces. The misleading statements in the literature that vacuum energy generates Casimir force can be boiled down to the fact that $H_{rm em}$ attains an implicit dependence on matter fields by the use of the equations of motion and the illegitimate treatment of the implicit dependence as if it was explicit. The true origin of the Casimir force is van der Waals force generated by $H_{rm int}$.
The early history of the Vogt-Russell theorem is retraced following its route starting at the realization of a correlation between mass and luminosity of binary and pulsating stars, through the embossing of this observation into a theorem, and finally to the emerging first signs of its failure to serve as a theorem in the strict mathematical sense of the word.
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