This series consists of talks in the area of Quantum Fields and Strings.
The Monster CFT is a (1+1)d holomorphic CFT with the Monster group global symmetry. The symmetry twisted partition functions exhibit the celebrated Monstrous Moonshine Phenomenon. From a modern point of view, topological defects generalize the notion of global symmetries. We argue that the Monster CFT has a Kramers-Wannier duality defect that is not associated with any global symmetry.
It is a curious numerology that the dynamical scale associated with the instanton of the electroweak SU(2) gauge group is approximately the energy scale of dark energy. We revisit this electroweak quintessence axion scenario, taking into account observational as well as swampland constraints.
Defining entanglement in a continuum field theory is a subtle challenge, because the Hilbert space does not naively factorize into local products.
Behind certain marginally trapped surfaces one can construct a geometry containing an extremal surface of equal, but not larger area. This construction underlies the Engelhardt-Wall proposal for explaining the Bekenstein-Hawking entropy as a coarse-grained entropy. The construction can be proven to exist classically but fails if the Null Energy Condition is violated. Here we extend the coarse-graining construction to semiclassical gravity. Its validity is conjectural, but we are able to extract an interesting nongravitational limit.
The AdS/CFT correspondence provides a remarkably useful tool
for asking questions in quantum gravity, as it formulates a theory of
quantum gravity in terms of an ordinary non-gravitational quantum field
theory. Fruitfully exploiting this correspondence therefore requires
understanding how to translate the language of CFT into gravity; a key
insight that has emerged over the past decade is that the entanglement
structure of the CFT must be intimately tied to the emergence of the
There is a fundamental tension between what string theory computes (S-matrix elements) and what you can compute in QFT on a time-dependent backgrounds (real time operator expectation values). The prescription for computing time dependent expectation values in QFT involves a path integral defined on a closed time path, known as the Keldysh contour. In this talk, we'll discuss how a worldsheet formulation of string theory must perceive the Keldysh contour and how this modifies critical string theory at tree level in the string coupling.
The relative entropy is a measure of the distinguishability of two quantum states. A great deal of progress has been made in the study of the relative entropy between an excited state and the vacuum state of a conformal field theory (CFT) reduced to a spherical region. For example, when the excited state is a small perturbation of the vacuum state, the relative entropy is known to have a universal expression for all CFT’s. Specifically, the perturbative relative entropy can be written as the symplectic flux of a certain scalar field in an auxiliary AdS-Rindler spacetime.
I will describe an example in which ER=EPR can be understood as a worldsheet string duality, by finding the Lorentzian continuation of the FZZ duality. The result is that string perturbation theory around the thermofield double state in a disconnected spacetime with a condensate of entangled folded strings is equivalent to string theory in a connected two sided black hole spacetime. Important ingredients are the Lorentzian interpretation of time winding vertex operators, and string theory with target space Schwinger-Keldysh contours.
In this talk, I will describe some of the recent progress on computing holographic correlators using analytic bootstrap techniques combined with supersymmetric localization. From taking a certain flat space limit of the holographic correlators, one can obtain scattering amplitudes of gravitons in string theory, and one can then reproduce some of the known results for these scattering amplitudes. I will focus mostly on the case of the 4d {\cal N} = 4 super-Yang-Mills theory, but I will also mention related work in the 3d ABJM theory.
The averaged null energy condition (ANEC) can be used to put constraints on the scaling dimensions of operators in a local CFTs. In some cases these are stronger than the unitarity bounds. I will consider four dimensional N=1 superconformal field theories (SCFTs) and discuss bounds on generic long and protected multiplets with spin (j,0). Some of them can be obtained analytically and others can be studied by means of a simple semidefinite programming problem. I will also briefly mention the consequences for N=2,4 SCFTs. Based on [1905.09293].