Abstract: The Nambu-Goto string, being purely geometrical and exhibiting diffeomorphism invariance, can be seen as a toy model for (quantum) gravity. I present an effective field theory approach to its quantization, based on perturbation theory around non-trivial classical solutions. It employs the BRST formalism (to deal with diffeomorphism invariance) and renormalization methods developed for QFT on curved space-times. It can be seen as the string theory analog of perturbative quantum gravity. Using rotating classical solutions as the starting point of perturbation theory, one can compute semi-classical corrections to the energy. Several deviations from standard quantum strings are found. For example, the theory is consistent, as an effective field theory, for any dimension of the target space. Furthermore, the semi-classical limit of standard quantum strings does not coincide with that of our perturbative approach. The origin of these deviations will be briefly discussed. The talk is partly based on joint work with D. Bahns and K. Rejzner.

Abstract: It is well known that the diffeomorphism invariance of gravitational theories makes it impossible to define local and gauge-invariant observables in perturbative (quantum) gravity, except at linear order. While in flat space on can study the S-Matrix, which is a gauge-invariant global observable, no analogue exists in a general curved space. Relational observables (i.e., the value of one field at the point where a second field has a prescribed value) are natural candidates for observables in (quantum) gravity, but they are not local when constructed around flat space or around a cosmological (FLRW) background spacetime due to the high symmetry of the latter. We present two different approaches to this problem: a) correlation functions at fixed geodesic distance, and b) a construction of invariant coordinates, for which explicit and fully renormalized results for one-graviton-loop corrections to two- point functions and coupling constants have been obtained.

Abstract: I will discuss the following topics: 1) The classical lattice gauge field model. 2) Quantization, field and observable algebras. 3) Dynamics. 4) The thermodynamical limit. 5) Towards finding the vacuum.

Abstract: Classical Yang-Mills theory is background-independent in the sense that splitting the gauge connection into a background connection and a dynamical vector potential is a symmetry of the theory. I will talk about a definition of background independence in (perturbative) quantum YM theory, that is the preservation of this symmetry at the quantum level. In a geometrical formulation, we define background-independent observables as flat sections of an algebra bundle over the manifold of background configurations, with respect to a flat connection which implements background variations. However, background independence at the quantum level is in general violated by potential obstructions. I will discuss such obstructions for YM theory and will remark on perturbative quantum gravity. (Joint work with Jochen Zahn).

Abstract: We investigate four-Fermi theories on 3-dimensions. These include Gross-Neveu and Thirring models with a varying numbers of flavours Nf. These theories are renormalizable in the 1/Nf-expansion and possess an interacting continuum limit. Gross-Neveu models undergo a second order phase transition for all values of Nf. We present results for the critical behaviour of the lattice theories. Contrary to previous works we use chiral fermions. Thirring models with current-current interaction and U(2Nf) chiral symmetry are closely related to 3d QED and other models used to describe properties of graphene. The critical flavour number, below which the model shows chiral symmetry breaking, has been obtained with different methods over the last years but so far, the results are not conclusive ranging from 2 to ∞. Via simulations with chiral fermions we relate parameters of the effective potential to chirally invariant observables. We show that there is no spontaneous chiral symmetry breaking for integer Nf. For half-integer Nf there is a discrete parity-breaking phase transition up to some critical flavour number.

Abstract: Entanglement is the nonlocal correlation of states of quantum theory and entanglement entropy quantifies the entanglement of the state across the respective subsystems. In quantum field theory, bipartite systems are described by local algebras on causally disconnected spacetime regions. If the regions touches each other, then the entropy density will be infinite and there does not exist any separable normal states. Therefore we are forced to leave some finite separation between the regions and then the restriction of any global pure state across the bipartite system is necessarily mixed. A widely studied entanglement measure is the von Neumann entropy of the reduced density operators. It is attractive due to the fact that every entanglement measure of a pure state is equal to the von Neumann entanglement entropy, up to some normalization constant. But this uniqueness is lost for mixed states, inevitable for quantum field theories. An alternative entanglement measure is the relative entanglement entropy, exhibiting desirable properties to be a “good entanglement measure”. We study the relative entanglement entropy of quasifree states for Dirac field in a globally hyperbolic spacetime of signature difference 1, 2, 6, 7, 8 mod 8. In particular, we compute an upper bound of relative entanglement entropy for the ground state of Dirac field on a Lorentzian static spacetime of dimensions 3, 4, 8, 9, 10 in a coordinate free fashion.

Abstract: The aim of the project is to look at “Hawking-effect tunnelling” for quantum fields in the setting of Moretti-Pinamonti paper (https://arxiv.org/abs/1011.2994), and pursue extensions of it to local versions of horizons. This talk will concern itself with the former aspect, placing the concepts of Isolated horizon and Dynamic horizon in a mathematically precise setting. To be succinct, the following will be discussed: (a) Raychaudhari’s equation (b) Concept of an event horizon and its global nature (c) The quasi local formalisms: Hayward’s trapped surface, Isolated horizon, Dynamic horizon (d) Applications: Black hole thermodynamics. A few other, possibly interesting, topics are omitted in favour of ones which are necessary for my work.

Abstract: In applications in numerical relativity we would ideally like to be able to include future null-infinity in the computational domain. This would have a number of advantages, not least that gravitational waves are unambiguously defined in this limit. In my talk I will discuss a new strategy, based on the use of dual-frames, to achieve this goal.