Title: Effective Modular Hamiltonians 

The question of whether entanglement entropy in gauge theories is BRST invariant has an odd answer: two different representatives of a BRST cohomology class have different entanglements, but the replica trick path integral commonly used to calculate entanglement is invariant under BRST transformations. After short introductions to entanglement in gauge theories and Hamiltonian BRST quantisation, I will explain why this is so and how it evades the usual arguments about the equivalence between the path integral and the Hamiltonian pictures. Finally, I will comment on the possibility of a prescription to "fix" the Hamiltonian calculation -- to make it BRST-invariant and equal to the answer given by the replica trick.

One of the main frontiers of Nuclear Physics is searching for violations of fundamental symmetries such as parity and time reversal. These symmetries have to be broken at the level above the Standard Model prediction, otherwise it will be hard to explain the observed amount of nuclear matter in the Universe. Measurements of the electric dipole moment (EDM) of nucleon, nuclei, and atoms are the most promising ways to observe CP-symmetry violations in the quark-gluon sector. Several experiments plan to improve the bound on the neutron EDM by two orders of magnitude in the next decade. Another vital condition for the baryogenesis is the violation of the baryon number, which, despite extensive several decade-long searches for proton decays and neutron oscillations, has never been observed. Interpreting these experimental limits in terms of fundamental particles and their interactions requires robust theoretical understanding of hadron structure. Thanks to mature numerical methods of solving QCD on a lattice, we can now investigate effects of non-Standard Model quark-gluon interactions on the properties of protons and neutrons. I will present our recent progress in calculations of nucleon EDM induced by quark-gluon color-electric dipole interaction (quark chromo-EDM) performed in QCD with physical masses of quarks and discretization preserving chiral symmetry. In addition, I will present results for the neutron-antineutron oscillation amplitudes and its implications for BSM phenomenology.

Recently, a number of exciting connections have been made between large gauge transformations (eg. BMS) and infrared physics (eg. Weinberg's soft graviton theorem). One of the more exciting explorations in this vein was Hawking-Perry-Strominger's (HPS) investigation of the consequences of these new symmetries for black hole physics. I will show very concretely that the Ward identity for the BMS-like large U(1) gauge transformations discussed by HPS fixes the low energy black hole absorption rate for photons. Time permitting, I will discuss broader implications and future extensions.

Abstract: I will discuss how to count the identities of a quantum state. The result implies a new form of quantum uncertainty principle and provides for interesting novel ways to characterize quantum states. As an application, I argue that the physics of localization, in any of its current incarnations, is a manifestation of quantum (un)certainty and should be quantitatively characterized in those terms.

It is known that thermalization in a CFT corresponds to black hole formation in AdS space. For a system to thermalize it must interact. To address black hole formation in string theory we look for thermalization in the D1D5 CFT which has an AdS dual. Thermalization should occur through interactions caused by twist operators which deform the theory off of its free point. The twist operators can join and unjoin ‘strings’ in the CFT. No clear evidence of thermalization was identified at first order in the twist deformation. We therefore compute interactions at second order in the twist deformation with an initial excitation propagating on one of the strings. We consider transitions of the initial excitation to three lower energy excitations in the final state. This yields preliminary evidence for thermalization.