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STP Board Talks – 29 & 30 May 2023

Speaker: Swapnamay Mondal
Title: Black hole microstates in String Theory
Abstract: Quantum mechanically a black hole emits thermal
radiation and has an entropy equalling a quarter of its surface area
in Planck units. This implies the existence of black hole microstates,
something inconceivable in classical gravity! In fact, the appearance
of Planck units suggests Quantum Gravity holds the key to the puzzle.

String theory, a candidate for thee theory of quantum gravity,
succeeds in explaining how black holes might have
microstates. Furthermore, it reproduces black hole entropy from
counting black hole microstates. I will discuss how this remarkable
feat is achieved, and will touuch upon my contribution in this field.

Speaker: Saki Koizumi
Title: Anomaly inflow of Rarita-Schwinger field in 3 Dimensions
Abstract: We study the anomaly inflow of the Rarita-Schwinger field with gauge symmetry in $3$ dimensions. We find that global anomalies of the Rarita-Schwinger field are obtained by the spectral flow, which is similar to Witten’s $SU(2)$ global anomaly for a Weyl fermion.

The Rarita-Schwinger operator is shown to be a self-adjoint Fredholm operator, and its spectral flow is determined by a path on the set of self-adjoint Fredholm operators with the gap topology.

From the spectral equivalence of the spectral flow, we find that the spectral flow of the Rarita-Schwinger operator is equivalent to that of the spin-$3/2$ Dirac operator.
From this fact, we confirm that the anomaly of the $3$-dimensional Rarita-Schwinger field is captured by the anomaly inflow.

Finally, we find that there are no global anomalies of gauge-diffeomorphism transformations on spin manifolds with any gauge group.
We also confirm that the anomalous phase of the partition function which corresponds to the generator of $\Omega_4^{{\rm Pin}^+}(pt)=\mathbb{Z}_{16}$ is $\exp(3i\pi /8)$ for the Rarita-Schwinger theory on unorientable ${\rm Pin}^+$ manifolds without gauge symmetry.

Speaker: Silvia Nagy
Title: Self-dual gravity in a curved background
Abstract: I will show that self-dual gravity in Euclidean four-dimensional Anti-de Sitter space (AdS4) can be described by a scalar field with a cubic interaction written in terms of a deformed Poisson bracket, providing a remarkably simple generalisation of the Plebanski action for self-dual gravity in flat space. This implies a novel symmetry algebra in self-dual gravity, notably an AdS4 version of the so-called kinematic algebra. This provides a concrete starting point for defining the double copy for Einstein gravity in AdS4 by expanding around the self-dual sector. Moreover, I will show that the new kinematic Lie algebra can be lifted to a deformed version of the $w_{1+\infty}$ algebra, which plays a prominent role in celestial holography.

Speaker: Constantin Teleman
Title: Character theory for compact group representations on 2-dimensional TQFTs
Abstract: Moore and Segal identified the representations of a
finite or compact group with the boundary conditions for 2D
topological gauge theory. Good control over representations comes from
the theory of characters. I will review the analogous theory in one
dimension higher: 2-dimensional gauge theories as boundary theories
for 3D topological gauge theory. Natural examples are gauged A-models
of symplectic manifolds. Surprisingly, there is a rigid holomorphic
theory of characters, which we now recognize as the general setting
for “3D Mirror Symmetry.” Time-permitting, I will review some
applications: Mirrors of flag varieties; the “Quantum GIT conjecture”
(now partially proven); and the construction of 3D “Coulomb branches”
from the 2-dimensional gauged linear sigma model.