PI Day

Quantum relative entropy is a measure of the indistinguishability of two quantum states in the same Hilbert space. I will discuss the relative entropy between a state with periodic boundary conditions and one with twisted boundary conditions for a free 1+1 CFT with c=1. I will also highlight the unresolved discrepancy between analytic and numeric results.

We investigate response functions near quantum critical points, allowing for finite temperature and a mild deformation by a relevant scalar. When the quantum critical point is described by a conformal field theory, we use conformal perturbation theory and holography to determine the two leading corrections to the scalar two-point function and to the conductivity. We build a bridge between the couplings fixed by conformal symmetry with the interaction couplings in the gravity theory. We construct a minimal holographic model that allows us to numerically obtain the response functions at all frequencies, independently confirming the corrections to the high-frequency response functions. In addition to probing the physics of the ultraviolet, the holographic model probes the physics of the infrared giving us qualitative insight into new physics scalings.

We describe the tunneling of a quantum mechanical particle with a Lorentzian (realtime) path integral. The analysis is made concrete by application to the inverted harmonic oscillator potential, where the path integral is known exactly. We apply Picard-Lefschetz theory to the time integral of the Feynmann propagator at fixed energy, and show that the Euclidean integration contour is obtained as a Lefschetz thimble, or a sum of them, in a suitable limit. Picard-Lefschetz theory is used to make the integral manifestly convergent and is also essential for the saddle point or semiclassical approximation. The very simple example of the inverted harmonic oscillator presents many interesting mathematical features, such as the Stokes phenomenon and multiple relevant complex saddles. We also attempt to construct a more realistic picture of the tunneling process, by allowing for spreading in energy and duration.

Extracting low energy universal data of quantum critical systems is a task whose difficulty increases with decreasing dimension. The increasing strength of quantum fluctuations can be tamed by using renormalization group (RG) schemes based on dimensional regularization close to the upper critical dimension of the system. By presenting a non-perturbative approach that allows the reliable extraction of the low energy universal data for the antiferromagnetic quantum critical metal in $2 \leq d < 3$-spatial dimensions, I will exemplify how an emergent non-commutativity between the low-energy limit and the dimensional limit preempts RG schemes based on dimensional regularization to access the correct low-energy universal data in integer dimensions.

I will introduce the idea that topological field theories describe the low-energy properties of gapped local quantum systems. This idea has proved fruitful in recent studies of gapped phases of matter.

A canonical analysis for general relativity is performed on a null surface without fixing the diffeomorphism gauge, and the canonical pairs of configuration and momentum variables are derived. Next to the well-known spin-2 pair, also spin-1 and spin-0 pairs are identified. The boundary action for a null boundary segment of spacetime is obtained, including terms on codimension two corners. FH, Laurent Freidel arXiv:1611.03096, Phys. Rev. D 95, 104006 (2017)

We give an introduction to cMERA, a continuous tensor networks ansatz for ground states of QFTs. We also explore a particular feature of it: an intrinsic length scale that acts as an ultraviolet cutoff. We provide evidence for the existence of this cutoff based on the entanglement structure of a particular family of cMERA states, namely Gaussian states optimized for free bosonic and fermionic CFTs. Our findings reflect that short distance entanglement is not fully present in the ansatz states, thus hinting at ultraviolet regularization.

Using Picard-Lefschetz theory we show that the Lorentzian path integral forms a good starting point for quantum cosmology which avoids the conformal factor problem present in Euclidean gravity. We study the Lorentzian path integral for a homogeneous and isotropic model with a positive cosmological constant. Applied to the “no-boundary” proposal, we show that this leads to the inverse of the result obtained by Hartle and Hawking. Including a inflation field, the Lorentzian path integral prefers to start at the 'top of the hill' leading to good initial conditions for slow roll inflation. However, when including gravitons the fluctuations seem to be unstable.

One of the defining features of holography is the geometerization of the renormalization group scale. This means that when a quantum field theory is holographically dual to a bulk gravity theory, then the direction normal to the boundary in the bulk (the `radial' direction) is to be interpreted as the energy scale of the dual quantum field theory. So this direction can be seen to be `emergent', and the evolution of bulk fields along this direction is equated with the renormalization group flow of sources or couplings of boundary operators. Given that gravitational theories are generally covariant, this emergent direction must be treated on equal footing as those of the space on which the boundary field theory lives. I will describe the precise integrability condition the renormalization group flow need satisfy which encodes this peculiar response of the quantum field theory under coarse graining so as to respect this property of covariance. In other words, this condition is `dual' to general covariance itself.

Entanglement entropy is now widely accepted as having deep connections with quantum gravity. It is therefore desirable to understand it in the context of causal sets, especially since they provide in a natural and covariant manner the UV cutoff needed to render entanglement entropy finite. Defining entropy in a causal set is not straightforward because the usual hypersurface data on which definitions of entanglement typically rely is not available. Instead, we appeal to a more global expression which, for a gaussian scalar field, expresses the entropy of a spacetime region in terms of the field’s correlation function within that region. In this talk I will present results from evaluating this entropy for causal sets sprinkled into a 1 + 1-dimensional causal diamond in flat spacetime, and specifically for a smaller causal diamond within a larger concentric one. In the first instance we find an entropy that obeys a (spacetime) volume law instead of the expected (spatial) area law. We find, however, that one can obtain the expected area law by following a prescription for truncating the eigenvalues of a certain “Pauli-Jordan” operator and the projections of their eigenfunctions on the Wightman function that enters into the entropy formula.

During past few decades, string theory has been used as a source of conjectural dualities in various areas of physics and mathematics. We have extended these applications of string dualities to the study of chiral algebras in 2d CFT. In this talk, I will sketch how to use S-duality of D3-D5-NS5 systems to shed some light on already known dual constructions of chiral algebras and generate huge amount of new dualities.

I will discuss two ways in which revising the notion of time at the Big Bang will lead to testable predictions. I will then contrast these predictions against standard ΛCDM scenario, and cosmological observations. The first model, Holographic Cosmology, is based on a 3d quantum field theory without time, suggesting the possibility of nonperturbative effects on large angles (l<30) in the CMB sky. The second model, Periodic Time Cosmology, relates (past and future) cosmic expansion history to the spectrum of cosmic perturbations by demanding consistency with an exactly periodic notion of time. Comparing this model to observations leads to surprising implications for dark energy and/or neutrino masses in cosmology.