We derive several no-go theorems in the context of massive type IIA string theory compactified to four dimensions in a way that, in the absence of fluxes, preserves $\mathcal{N}=1$ supersymmetry. Our derivation is based on the dilaton, Kähler and complex structure moduli dependence of the potential of the four-dimensional effective field theory, that is generated by the presence of $D6$-branes, $O6$-planes, RR fluxes, NSNS 3-form flux, and geometric fluxes. To demonstrate the usefulness of our theorems, we apply them to the most commonly studied class of toroidal orientifolds. We show that for all but two of the models in this class the slow-roll parameter $ϵ$ is bounded from below by numbers of order unity as long as the fluxes satisfy the Bianchi identities, ruling out slow-roll inflation and even the existence of de Sitter extrema in these models. For the two cases that avoid the no-go theorems, we provide some details of our numerical studies, demonstrating that small $ϵ$ can indeed be achieved. We stress that there seems to be an $\eta$-problem, suggesting that none of the models in this class are viable from a cosmological point of view at least at large volume, small string coupling, and leading order in the ${\alpha }^{\prime }$-expansion.

We work out all of the details required for implementation of the conformal bootstrap program applied to the four-point function of two scalars and two vectors in an abstract conformal field theory in arbitrary dimension. This includes a review of which tensor structures make appearances, a construction of the projectors onto the required mixed symmetry representations, and a computation of the conformal blocks for all possible operators which can be exchanged. These blocks are presented as differential operators acting upon the previously known scalar conformal blocks. Finally, we set up the bootstrap equations which implement crossing symmetry. Special attention is given to the case of conserved vectors, where several simplifications occur.Comment: 76 pages, v3 moved several details into appendices, expanded discussion of mixed symmetry projecto

We compute four-derivative corrections to the AdS supergravity actions arising from the near-horizon geometry of N M5-branes wrapped on either one or two Riemann surfaces. This setup features the novel presence of both gauged isometries as well as nontrivial hypermultiplets. We argue that the 5d Chern-Simons terms receive not only higher-derivative corrections but also contributions from Killing vector parameters, which we find must also be corrected. We check the central charges found by our supergravity methods against the dual field theory results and find perfect agreement at leading and subleading order in N. Along the way, we find higher derivative corrections to general AdS₅ and AdS₃ × Σ _g geometries.

In this paper we discuss gauging noninvertible zero-form symmetries in two dimensions. We specialize to certain gaugeable cases, specifically, fusion categories of the form $$ \textrm{Rep}\left(\mathcal{H}\right) $$ Rep H for $$ \mathcal{H} $$ H a suitable Hopf algebra (which includes the special case Rep(G) for G a finite group). We also specialize to the case that the fusion category is multiplicity-free. We discuss how to construct a modular-invariant partition function from a choice of Frobenius algebra structure on $$ {\mathcal{H}}^{\ast } $$ H ∗ . We discuss how ordinary G orbifolds for finite groups G are a special case of the construction, corresponding to the fusion category Vec(G) = Rep(ℂ[G]^*). For the cases Rep(S ₃), Rep(D ₄), and Rep(Q ₈), we construct the crossing kernels for general intertwiner maps. We explicitly compute partition functions in the examples of Rep(S ₃), Rep(D ₄), Rep(Q ₈), and $$ \textrm{Rep}\left({\mathcal{H}}_8\right) $$ Rep H 8 , and discuss applications in c = 1 CFTs. We also discuss decomposition in the special case that the entire noninvertible symmetry group acts trivially.

In this paper, we introduce a new set of modular-invariant phase factors for orbifolds with trivially-acting subgroups, analogous to discrete torsion and generalizing quantum symmetries. After describing their basic properties, we generalize decomposition to include orbifolds with these new phase factors, making a precise proposal for how such orbifolds are equivalent to disjoint unions of other orbifolds without trivially-acting subgroups or one-form symmetries, which we check in numerous examples.