January 2021

Date: January 14

Time: 17:30 IST (UTC + 5:30)

Speaker: Suvankar Dutta (IISER Bhopal)

Title: From 2d droplets to 2d Yang-Mills

• Abstract: In this talk we shall discuss a connection between time evolution of free Fermi droplets and partition function of generalised q-deformed Yang-Mills theories on Riemann surfaces. Classical phases of $(0+1)$ dimensional unitary matrix models can be characterised by free Fermi droplets in two dimensions. We quantise these droplets and find that the modes satisfy an abelian Kac-Moody algebra. The Hilbert spaces $\cH_+$ and $\cH_-$ associated with the upper and lower free Fermi surfaces of a droplet admit a Young diagram basis in which the phase space Hamiltonian is diagonal with eigenvalue, in the large $N$ limit, equal to the quadratic Casimir of $u(N)$. We shall discuss an exact mapping between states in $\cH_\pm$ and geometries of droplets. In particular, coherent states in $\cH_\pm$ correspond to classical deformation of upper and lower Fermi surfaces. We shall see that correlation between two coherent states in $\cH_\pm$ is equal to the chiral and anti-chiral partition function of $2d$ Yang-Mills theory on a cylinder. Using the fact that the full Hilbert space $\cH_+ \otimes \cH_-$ admits a composite basis, we see that correlation between two classical droplet geometries is equal to the full $U(N)$ Yang-Mills partition function on a cylinder. We shall also discuss a connection between higher point correlators in $\cH_\pm$ and higher point correlators in $2d$ Yang-Mills on Riemann surface. There are special states in $\cH_\pm$ whose transition amplitudes are equal to the partition function of $2d$ \emph{q}-deformed Yang-Mills and in general character expansion of Villain action.

VIDEO: Click here

Date: January 21

Time: 17:30 IST (UTC + 5:30)

Speaker: Nava Gaddam (Utrecht University)

Title: Black hole eikonal and the information paradox

• Abstract: In this talk, I will show that there is a remarkable phase of quantum gravity where gravitational collision energies near the horizon satisfy E << \gamma M_Pl, with \gamma = M_Pl/M_BH. In this phase, scattering amplitudes are unitary suggesting a resolution of the information paradox; I will sketch the explicit derivation of the scattering matrix. Owing to the low energies of collisions, there are no firewalls experienced by infalling observers. A consequence of our results is that the information paradox is an emergent one at low energies and does not require detailed ultra-violet physics for a resolution.

VIDEO: Click here