We revisit the D0 bound state problems, of the M/IIA duality, with the Orientifolds. The cases of O4 and O8 have been studied recently, from the perspective of five-dimensional theories, while the case of O0 has been much neglected. The computation we perform for D0-O0 states boils down to the Witten indices for $\mathcal N=16$ $O(m)$ and $Sp(n)$ quantum mechanics, where we adapt and extend previous analysis by the authors. The twisted partition function $Ω$, obtained via localization, proves to be rational, and we establish a precise relation between $Ω$ and the integral Witten index $\mathcal I$, by identifying continuum contributions sector by sector. The resulting Witten index shows surprisingly large numbers of threshold bound states but in a manner consistent with M-theory. We close with an exploration on how the ubiquitous rational invariants of the wall-crossing physics would generalize to theories with Orientifolds.
The aim of this paper is to study orientifolds of c=1 conformal field theories. A systematic analysis of the allowed orientifold projections for c=1 orbifold conformal field theories is given. We compare the Klein bottle amplitudes obtained at rational points with the orientifold projections that we claim to be consistent for any value of the orbifold radius. We show that the recently obtained Klein bottle amplitudes corresponding to exceptional modular invariants, describing bosonic string theories at fractional square radius, are also in agreement with those orientifold projections.
We analyse the problem of assigning sign choices to O-planes in orientifolds of type II string theory. We show that there exists a sequence of invariant $p$-gerbes with $p\geq-1$, which give rise to sign choices and are related by coboundary maps. We prove that the sign choice homomorphisms stabilise with the dimension of the orientifold and we derive topological constraints on the possible sign configurations. Concrete calculations for spherical and toroidal orientifolds are carried out, and in particular we exhibit a four-dimensional orientifold where not every sign choice is geometrically a…
We prove that the generating functions for the colored HOMFLY-PT polynomials of rational links are specializations of the generating functions of the motivic Donaldson-Thomas invariants of appropriate quivers that we naturally associate with these links. This shows that the conjectural links-quivers correspondence of Kucharski-Reineke-Stošić-Sułkowski as well as the LMOV conjecture hold for rational links. Along the way, we extend the links-quivers correspondence to tangles and, thus, explore elements of a skein theory for motivic Donaldson-Thomas invariants.
We consider the Witten-Reshetikhin-Turaev invariants or Chern-Simons partition function at or around roots of unity $q=e^{2πi \frac{1}{K}}$ with rational level $K=\frac{r}{s}$ where $r$ and $s$ are coprime integers. From the exact expression for the $G=SU(2)$ Witten-Reshetikhin-Turaev invariants of Seifert manifolds at other roots of unity obtained by Lawrence and Rozansky, we provide an expected form of the structure of the Witten-Reshetikhin-Turaev invariants in terms of the homological blocks at other roots of unity. Also, we discuss the asymptotic expansion of knot invariants around roots …
