New supersymmetric string theories from discrete theta angles

Abstract

We describe three previously unnoticed components of the moduli space of minimally supersymmetric string theories in d ≥ 7, describing in some detail their spectrum and duality properties. We find a new component in nine and eight dimensions, and two additional ones in seven dimensions. These theories were originally discovered in a bottom-up classification of possible F/M-theory singularity freezing patterns in the K3 lattice, described in a companion paper. The 9d/8d component can be understood as F/M-theory on a twisted fibration of the Klein bottle over a circle, while the new seven-dimensional components are described as IIB on Bieberbach manifolds with a duality bundle and RR-NSNS backgrounds turned on. All the new components can be obtained from previously known theories by turning on certain discrete theta angles; however, the spectrum of massive objects is very different, and most strikingly, they feature an incomplete lattice of BPS strings, showing that string BPS completeness is not true in general even with sixteen supercharges. In all cases we find non-BPS representatives for each value of the charge, so the Completeness Principle is satisfied. We also analyze analogous theta angles in nonsupersymmetric string theories, and provide a detailed explanation of why the Type I discrete θ angle proposed in 1304.1551 is unphysical, using this to clarify certain non-perturbative phenomena in O8 planes.

New supersymmetric string moduli spaces from frozen singularities

“…We argue that the later two are naturally identified with the frozen singularities Spin(32)/Z 2 and Spin(32), respectively, and are not connected one to another. This expectation matches an analysis of potential discrete theta angles in nine dimensional string compactifications with N = 1 [23]. Our results imply the existence of new string compactifications which do exist and are the subject of the companion paper [23].…”

“…This expectation matches an analysis of potential discrete theta angles in nine dimensional string compactifications with N = 1 [23]. Our results imply the existence of new string compactifications which do exist and are the subject of the companion paper [23].…”

“…Stringy descriptions of the new components predicted here turn out to exist and are given e.g. by turning on discrete theta angles in known string backgrounds; their construction and analysis is the subject of the companion paper [23].…”

Quantum gravity bounds on $$ \mathcal{N} $$ = 1 effective theories in four dimensions

“…8 Recently [55] has found examples of effective field theories in higher dimensions which violate the Completeness Conjecture for BPS strings; at the same time, there always exists another theory differing only at the massive level which does satisfy the BPS Completeness Conjecture. For our purpose of constraining the massless EFT spectra this would in fact be sufficient.…”

“…For our purpose of constraining the massless EFT spectra this would in fact be sufficient. It would be interesting to elucidate whether all counterexamples to the BPS string completeness conjecture have this property observed in [55].…”