Fall 2015

The AdS/CFT correspondence is applied to a close analogue of the little hierarchy problem in AdS_{d+1} with d>2. The new mechanism requires a Maxwell gauge field that gauges U(1)_R symmetry in a bulk supergravity theory with a negative cosmological constant. Supersymmetry is explicitly broken by a boundary term, and the SUSY breaking deformation engendered is exactly marginal. SUSY breaking effects are computed exactly using the U(1) Ward identity. Conformal dimensions and thus masses of scalar and spinor partners are split simply because they carry different R-charges. However SUSY breaking effects cancel to all orders for R-neutral .fields, even in diagrams with internal R-charged loops. SUSY breaking corrections can be explicitly calculated to all loop orders. Graviton loops do not introduce any further SUSY breaking corrections.

The conformal bootstrap gives a powerful and rigorous way to learn about strongly-interacting conformal field theories and critical phenomena. I will discuss recent results from the conformal bootstrap in 3 and 4 dimensions, making precise predictions in known CFTs such as the 3D Ising, O(N) vector, and Gross-Neveu models, as well as giving exciting evidence for possible new conformal field theories.

I will review recent developments in the non-linear theory of massive gravitons, or spin-2 fields.  On de Sitter space, there exists a special value for the mass of a graviton for which the linear theory propagates 4 rather than 5 degrees of freedom. If a fully non-linear version of the theory exists and can be coupled to known matter, it would have interesting properties and could solve the cosmological constant problem. I will describe evidence for and obstructions to the existence of such a theory, and recent developments.

 In quantum field theory, the entropy of a region is nonzero, even in the vacuum state, due to entanglement between the fields inside and outside the region.  But in field theories with gravitational anomalies, the entropy of a region is no longer invariant under a Lorentz boost near the boundary.  Thus there is an anomaly in the entanglement entropy, even on backgrounds on which the gravitational anomaly vanishes.  I will show how this effect can be derived by physical arguments based on the propagation of chiral modes, and from the path integral, in various dimensions.  Based on arXiv:1509.04325.

Despite the seemingly vast possibilities offered by the string landscape, it has been argued that not all consistent low energy quantum field theories can be ultraviolet completed into string theory.  The space of consistent low-energy effective theories which cannot be completed to a full theory with gravity was dubbed the ``swampland”.  In this talk, we revisit this ``swampland” proposal in theories with axion-like fields. We describe how quantum gravity can limit the axion field range, which is otherwise unconstrained in the low energy effective theories. These constraints have interesting implications to axion inflation models, and the prospects of such models in generating detectable primordial gravitational waves.

We consider Lorentzian correlators of local operators. In perturbation theory, singularities occur when we can draw a position-space Landau diagram with null lines. In theories with gravity duals, we can also draw Landau diagrams in the bulk. We argue that certain singularities can arise only from bulk diagrams, not from boundary diagrams. As has been previously observed, these singularities are a clear diagnostic of bulk locality. We analyze some properties of these perturbative singularities and discuss their relation to the OPE and the dimensions of double-trace operators. In the exact nonperturbative theory, we expect no singularity at these locations. We prove this statement in 1+1 dimensions by CFT methods.