Week 04.03.2024 – 10.03.2024

CANCELLED due to an unforeseen speaker emergency.

CANCELLED due to an unforeseen speaker emergency.

It is natural to expect that quantum gravity is not directly relevant at the low energies which experimentally accesible today, since the Planck scale is many orders of magnitude above the electroweak scale. However, mounting evidence coming from String Theory compactifications, general considerations based on black hole evaporation and holography suggest that there are some constraints that must be satisfied by low-energy effective field theories coupled to Einsteinian gravity. These constraints can in principle be used to rule out models at low energies or to connect with observations, an effort dubbed the "Swampland Program". I will review the program, its motivation, and recent advances.

QFT at finite temperature can be studied via compactifying the time direction. Placing CFTs on this non-trivial manifold, a subgroup of conformal symmetries is broken. Nonetheless, it is possible to derive broken Ward identities, which provide novel constraints on the theory. These constraints not only systematically reproduce all known results, including an implicit formulation of the generalized Cardy formula, but also relate the thermal energy spectrum with the conformal spectrum. Moreover, novel sum rules for one-point functions of operators are derived. They allow the computation of one-point functions for light operators in terms of zero temperature data, as well as their asymptotic behavior for heavy operators.

I will discuss a novel construction of field theories based on the idea that one has only a half boson degree of freedom per lattice site. Basically, instead of having a pair of canonical conjugate commuting variables at each site, one has only one degree of freedom and the non-trivial commutators arise from connections to the nearest neighbors. The construction is very similar to staggered fermions and naturally produces gapless systems with interesting topological properties. When considering gauging discrete translations on the phase space in one dimensional examples, one gets interesting critical spin chains, examples of which include the critical Ising model in a transverse magnetic field and the 3-state Potts model at criticality. I will explain how these staggered boson variables are very natural for describing non-invertible symmetries. These non-invertible symmetries are useful to describe the critical properties of these non-trivial spin chains. Models in higher dimensions obtained this way can automatically produce dynamical systems of gapless fractons.

In this talk, I provide an improved definition of new conserved quantities derived from the energy-momentum tensor in curved spacetime by introducing an additional scalar function. I find that the conserved current and the associated conserved charge become geometric under a certain initial condition of the scalar function, and show that such a conserved geometric current generally exists in curved spacetime. Furthermore, I demonstrate that the geometric conserved current agrees with the entropy current for the perfect fluid, thus the conserved charge is the total entropy of the system.