Quantum Fields and Strings

We consider quantum field theory on a rigid de Sitter space. We show that the perturbative expansion of late-time correlation functions to all orders can be equivalently generated by a non-unitary Lagrangian on a Euclidean AdS geometry. We use this to infer the analytic structure of the spectral density that captures the conformal partial wave expansion of a late-time four-point function, to derive an OPE expansion, and to constrain the operator spectrum. Generically, dimensions and OPE coefficients do not obey the usual CFT notion of unitarity. Instead, unitarity of the de Sitter theory manifests itself as the positivity of the spectral density. We illustrate and check these properties by explicit calculations in a scalar theory by computing first tree-level, and then full one-loop-resummed exchange diagrams.

I discuss the question how string theory achieves a sum over bulk geometries with fixed asymptotic boundary conditions. I analyze this problem with the help of the tensionless string on AdS3xS3xT4 (with one unit of NS-NS flux) that was recently understood to be dual to the symmetric orbifold of T4. I argue that large stringy corrections around a fixed background can be interpreted as different semiclassical geometries, thus making a sum over semi-classical geometries superfluous.

Crossing symmetry asserts that particles are indistinguishable from anti-particles traveling back in time. In quantum field theory, this statement translates to the long-standing conjecture that probabilities for observing the two scenarios in a scattering experiment are described by one and the same function. Why could we expect it to be true? In this talk we examine this question in a simplified setup and take steps towards illuminating a possible physical interpretation of crossing symmetry. To be more concrete, we consider planar scattering amplitudes involving any number of particles with arbitrary spins and masses to all loop orders in perturbation theory. We show that by deformations of the external momenta, one can smoothly interpolate between the future and the past lightcones without encountering any singularities.

I will explain how to compute correlation functions of two heavy operators and a light BPS single-trace operator at strong coupling using a dual description of D-branes absorbing a supergravity mode. Our approach is inspired by the large charge expansion of CFT and resolves some confusions in the literature on the holographic computation involving heavy operators. In particular, we point out two important effects which are often missed; the first one is an average over classical configurations of the heavy state, which physically amounts to projecting the state to an eigenstate of quantum numbers. The second one is the contribution from wave functions of the heavy state. Time permitting I will also comment on possible applications to states dual to black holes and fuzzballs.

This talk will be about entanglement entropy in empty 4-dimensional de Sitter spacetime of a non-conformal QFT [1]. I will first briefly describe the set-up and show how a hydrodynamic plasma dilutes and falls out of equilibrium due to expansion towards empty de Sitter spacetime. Interestingly, in the empty setting we can show that extremal surfaces in the holographic dual of spherical entangling regions on the boundary QFT probe beyond the dual event horizon if and only if the entangling region is larger than the cosmological horizon.

[1] Jorge Casalderrey-Solana, Christian Ecker, David Mateos and WS, Strong-coupling dynamics and entanglement in de Sitter space, 2011.08194

I will give an introduction to the geometric aspects of Lie algebroids and show how they give the correct framework to discuss gauge theories. The analysis is solely based on geometry, and thus applies to every gauge theory, independently of their specific features and dynamics. By thoroughly re-formulating the physical content of gauge theories on Atiyah Lie algebroids, we will show that the BRST construction is part of the formalism, indicating a fascinating interplay between classical geometry and quantum physics. Time permitting, we will show how our setup encompasses gravitational theories too, once the frame bundle and solder form are added to the picture.