The global anomalies of (2,0) superconformal field theories in six dimensions

We compute the global gauge and gravitational anomalies of the A-type (2,0) superconformal quantum field theories in six dimensions, and conjecture a formula valid for the D- and E-type theories. We show that the anomaly contains terms that do not contribute to the local anomaly but that are crucial for the consistency of the global anomaly. A side result is an intuitive picture for the appearance of Hopf-Wess-Zumino terms on the Coulomb branch of the (2,0) theories.Comment: 35 pages, 2 figures. v2: typos corrected, some clarifications added in the introduction and in Section 4.6, version to be published in JHE

Higher abelian Dijkgraaf-Witten theory

Dijkgraaf-Witten theories are quantum field theories based on (form degree 1) gauge fields valued in finite groups. We describe their generalization based on $p$-form gauge fields valued in finite abelian groups, as field theories extended to codimension 2.Comment: 12 pages. v3: minor corrections, simplification of the main proo

Finite higher spin transformations from exponentiation

We study the exponentiation of elements of the gauge Lie algebras ${\rm hs}(\lambda)$ of three-dimensional higher spin theories. Exponentiable elements generate one-parameter groups of finite higher spin symmetries. We show that elements of ${\rm hs}(\lambda)$ in a dense set are exponentiable, when pictured in certain representations of ${\rm hs}(\lambda)$, induced from representations of $SL(2,\mathbb{R})$ in the complementary series. We also provide a geometric picture of higher spin gauge transformations clarifying the physical origin of these representations. This allows us to construct an infinite-dimensional topological group $HS(\lambda)$ of finite higher spin symmetries. Interestingly, this construction is possible only for $0 \leq \lambda \leq 1$, which are the values for which the higher spin theory is believed to be unitary and for which the Gaberdiel-Gopakumar duality holds. We exponentiate explicitly various commutative subalgebras of ${\rm hs}(\lambda)$. Among those, we identify families of elements of ${\rm hs}(\lambda)$ exponentiating to the unit of $HS(\lambda)$, generalizing the logarithms of the holonomies of BTZ black hole connections. Our techniques are generalizable to the Lie algebras relevant to higher spin theories in dimensions above three.Comment: 34 pages. v3: references added. Added a discussion of the Euclidean higher spin symmetry group. Unlike what was claimed in a previous version, the formalism developed here can be applied to the Euclidean case as wel

D-branes in Lie groups of rank > 1

We consider a low-energy effective action for the gauge field on Wess-Zumino-Witten D-branes in a compact simple Lie group, in the limit of large k. We prove that the effective action is bounded from below, and study stability of various D-brane configurations, including some class of non-maximally symmetric ones. We show that for Lie groups of rank higher than one, the D-brane ground state breaks the Kac-Moody symmetry of the boundary theory. We then give arguments hinting that the "fuzzy sphere" D2-brane which is known to be the stable brane configuration in the case of SU(2), may also correspond to the ground state in other compact simple Lie groups.Comment: 17 pages. Misplaced sum sign fixed in eq.2, normalization corrected in eq.16, table and text slightly modified accordingl