Mathematical Physics Seminars 2018-2019

Upcoming seminars

Past seminars

  Wednesday 24 April 2019, 11:00, room 114

Reiko Toriumi (OIST, Okinawa) : The gravitational Wilson loop and the non-Abelian Stokes’ theorem

Finding suitable diffeomorphism-invariant observables to probe gravity at the Planck scale is essential in quantum gravity. The Wilson loop of the 4-dimensional Christoffel connection is a potentially interesting ingredient for the construction of such an observable. We have investigated to what extent and what form of curvature information of the underlying spacetime may be extracted from Wilson loops through a Stokes’ theorem-like relation. We present an expression for the conservation of geometric flux as the quantity related to the gravitational Wilson loop. This expression is surface-independent and it holds for a certain class of manifolds with global symmetries.

  Wednesday 10 April 2019, 11:00, room 114

Fidel Schaposnik Massolo (IHES, Bures-sur-Yvette) : On Phases Of Melonic Quantum Mechanics (arXiv:1903.06633)

In this talk I will discuss two melonic quantum mechanical systems, each of which can be formulated either as a tensor or a disordered model. Being inspired by the Sachdev-Ye-Kitaev model, the non-trivial IR behavior of their conformal phase bears relation to black-hole physics and nAdS2 / nCFT1 holography. I will present the techniques used to construct the phase diagrams, study both euclidean and real-time physics, and characterize chaos through Lyapunov exponents. Special attention will be given to a new low-energy ansatz, generalizing the one used in the literature for SYK and related models, spontaneously breaking SL(2,R) symmetry without creating a mass gap.

  Wednesday 6 March 2019, 11:00, room 114

Kenta Suzuki (CPHT, Ecole Polytechnique) : Emergence of Space-Time in the SYK Model

The Sachdev-Ye-Kitaev (SYK) model is a quantum mechanical many-body system with random all-to-all interactions on fermionic N sites (N>>1). This model is shown to saturate the known maximal chaos bound of many-body system and then based on this observation it is conjectured to be dual to a quantum black hole in the sense of the AdS/CFT correspondence. In this talk, we start from reviewing basis aspects of the SYK model in the large N limit, which is systematically described by a single bi-local field. We show that a propagator of the bi-local field, which is understood as a four-point function of the original fermions, predicts an infinite spectrum of the dual AdS_2 theory, but it has a divergent contribution from the zero mode at the critical IR fixed point of the model. Next, we show that the spectrum of the four-point integration SYK model can be interpreted as that of a single scalar field coupled to gravity in 3 space-time dimension. The scalar field lives on AdS_2 * I, where I is a finite interval, and subject to a delta function potential at the center of the interval. Through Kaluza-Klein procedure on the third direction, this scalar generates the spectrum predicted by the SYK bi-local propagator at strong coupling. Finally, we consider the question of identifying the bulk space-time of the SYK model. Focusing on the signature of emergent space-time of the (Euclidean) model, we explain the need for non-local (Radon-type) transformations on external legs of n-point Green’s functions. This results in a dual theory with Euclidean AdS signature with additional leg-factors. We speculate that these factors incorporate the coupling of additional bulk states similar to the discrete states of 2D string theory.

  Wednesday 30 January 2019, 11:00, room 114

Michele Levi (IPhT, CEA Saclay) : Effective Field Theories of Post-Newtonian Gravity

This talk presents the progress made in my research via the introduction of effective field theories (EFTs) into post-Newtonian (PN) Gravity. These have been put forward in the context of gravitational waves (GWs) from the compact binary inspiral. The setup and the strategy of a multi-stage EFT framework, which is deployed for the PN binary inspiral problem, is outlined. I then present in more detail the study of two effective theories at the intermediate scales of the problem. First, the EFT for a single rotating compact object is considered, from which I proceed to the EFT of a compact binary system, viewed as a composite particle with internal binding interactions. I conclude with the prospects of building on the field, and using further modern field theory insights and tools, to address the study of GWs, as well as to expand our fundamental understanding of QFTs and Gravity theories at all scales.

  Wednesday 12 December 2018, 11:00, room 114

Mikhail Isachenkov (IHES, Bures-sur-Yvette) : All-energy correlation functions in large N double-scaled SYK

I will review a method to evaluate correlation functions of certain large N statistical systems via chord diagrams and apply it to compute correlators in double-scaled version of SYK model at all energies, in particular to extract corrections to the maximal chaos exponent. Time permitting, I will comment on the suggested relation of this model to a Hamiltonian reduction of quantum particle moving on a non-compact quantum group SU_q(1,1).

  Wednesday 5 December 2018, 11:00, room 114

Ritam Sinha (IFT, UAM, Madrid) : Complex Fermionic Tensor models in 2-ϵ dimensions

Tensor models have proved to be an important playground for exploring a new large N limit, dominated by "melonic" diagrams. While they have been explored at length in 0+1-dimensions, it is unclear whether the melonic dominance makes sense in dimensions higher than 1. It is possible to make this idea firmer by exploring the range of all possible melonic CFTs in higher dimensions. In this context, we will review some work regarding certain large N boson and fermionic tensor models in d dimensions. We will especially focus on the large N behaviour of the fermionic tensor models that seem to flow to a weakly interacting fixed point in the IR in 2-ϵ dimensions. Motivated by this result, we will dwell upon the possibility of exploring the fixed point at finite N through a beta function calculation, and subsequently trying to study the one-dimensional fermionic tensor model at finite N via an ϵ expansion.

  Friday 30 November 2018, 11:00 and 14:00 (2 lectures), room 114

Joseph Ben Geloun (LIPN, Université Paris 13) : Counting in Tensor models

I will review the enumeration of observables in unitary tensor models and their topological field theory interpretation. Starting from the basics of group theory and its representation, I will make explicit the different counting formulae that we have for the moment. Gaussian correlators will be also computed in the same vein. Recent advances for the orthogonal tensor models will be sketched. Finally, as an invitation, I will list a few problems on the subject.