Week 05.12.2021 – 11.12.2021

Cosmological inflation predicts the existence of a stochastic background of gravitational waves (GW), whose features depend on the model of inflation under consideration. There exist well motivated frameworks leading to an enhancement of the primordial GW spectrum at frequency scales testable with GW experiments, with specific features as parity violation, anisotropies, and non-Gaussianity. I will explain the properties of such scenarios, and their distinctive predictions for what respect GW observables. I will then discuss perspectives for testing these predictions with future GW experiments.

Recently in their celestial holography programme, Strominger and coworkers attempt to provide a holographic description of conventional 4d gravity. In their investigations, they uncovered a hidden w-infinity symmetry in their `celestial soft OPEs' for graviton scattering. This talk will explain the origin of this symmetry in terms of old ideas of Newman and Penrose based on light-cone cuts of null infinity and their description in terms of asymptotic twistors and certain sigma models in asymptotic twistor space. W_n symmetries were introduced by Zamolodchikov as higher spin symmetries in 2d conformal field theories. These were given a geometric interpretation for n=infinity as area-preserving diffeomorphisms of the plane. I will explain how the corresponding loop algebra becomes a hidden symmetry of self-dual gravity via Penrose's nonlinear graviton construction. The action of this symmetry on the tree-level S-matrix of full gravity beyond the self-dual sector will then be obtained from its action on a sigma model in the asymtotic twistor space of a general space-time. This talk is based on https://arxiv.org/abs/2110.06066 and https://arxiv.org/abs/2103.16984.

The strongly coupled Argyres-Douglas field theories have particular significance among four-dimensional N=2 SCFTs. In this talk, we describe new AdS5 solutions in 11d supergravity and identify them as the gravity duals of a large class of Argyres-Douglas theories, engineered via a stack of M5-branes wrapping a sphere. A notable feature of the gravity solutions is an internal M5-brane source, which is dual to an irregular puncture on the sphere. We explain how the holographic data (including central charges) match the data of the dual Argyres-Douglas field theories

It is well known that the most general renormalizable quantum field theory one can write down for a finite spectrum of spin-0, 1/2, and 1 particles is a gauge theory, with possible spontaneously broken symmetries. The existence of Lie group structures in such a theory is dictated by perturbative unitarity of the on-shell scattering amplitudes. Armed with new tools developed for scattering amplitudes, we demonstrate very explicitly how broken symmetries emerge from the constraints of tree unitarity. We review the on-shell spinor helicity formalism, using which we enumerate all possible 3-pt and 4-pt tree amplitudes of massive spin-0, 1/2 and 1 particles satisfying unitarity constraints. We show in these amplitudes how massive vectors and scalars need to be in the same representation of some Lie group, and how the longitudinal components of these massive vectors are equivalent to scalars in the high energy limit. We will also comment on an extended color-kinematics duality that can be hiding in such a general theory.

It is well understood how the 2d free scalar CFT emerges from 3d Chern-Simons theory with chiral boundary conditions. Adapting a recent proposal of Costello and Stefanski, I will show how bosonic string theory can be obtained from this description by coupling to a dynamical Beltrami differential in the 3d theory. In particular, I will show how this Beltrami differential restores worldsheet diffeomorphism and Weyl invariance in the 2d theory, and recover the Polyakov action explicitly. By rewriting the theory in the BV formalism, I will show how the bc ghost system arises from the 3d perspective. Finally, if there is sufficient time, I will provide the 3d realization of vertex operators. This talk is based on work in progress with Kevin Costello and Bogdan Stefanski. ----------- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.

[there will be a pre-seminar for students at 13:30. For zoom link please email s.nagy@qmul.ac.uk] Following a proposal by H. Sati, we have recently stated a hypothesis about the mathematical home of the quantum charges in M-theory. This “Hypothesis H” refines the traditional proposal for quantization of D-brane charge from K-theory to the non-abelian cohomology theory known as 4-Cohomotopy, whose classifying space is the 4-sphere. Besides its motivation from homotopy-theoretic re-analysis of 11d supergravity and of the old brane scan, Hypothesis H is currently justified by its rigorous implication of a list of long-conjectured M-theoretic consistency conditions on C-field flux and M-brane charges – such as shifted C-field flux quantization, dual Page charge quantization and M2/M5-brane tadpole cancellation. But if Hypothesis H is a correct assumption about the nature of M-theory, this suggests that quantum states of full M-theory should be reflected in the positive cohomology of the moduli space of Cohomotopy cocycles, much like quantum states of non-perturbative Chern-Simons theory are in the Dolbeault cohomology of moduli spaces of (flat) connections. In this talk I discuss how, in the topological sector of D6/D8-brane intersections, such quantum states according to Hypothesis H are identified with *weight systems* on *horizontal chord diagrams*, and how these do reflect a range of phenomena expected from the traditional approaches to understanding these brane intersections, such as non-abelian DBI-theory, the BMN matrix model, Rozansky-Witten theory and Hanany-Witten theory. Specifically, we have proven that the sl(2,C)-weight system satisfies the positivity condition that characterizes physical (i.e. non-ghost) quantum states. Under the above identification, this quantum state corresponds to an elementary fuzzy funnel configuration and/or to the elementary transverse M5-brane state in the BMN matrix model – both as expected for D6/D8-brane intersections. Besides possible implications for the elusive formulation of M-theory, this result may provide a unifying explanation for the plethora of unexpected appearances that chord diagrams are recently making in fundamental high energy physics, notably in discussion of holographic entanglement entropy. Slides and further pointers available at: https://ncatlab.org/schreiber/show/Some+Quantum+States+of+M-Branes+under+Hypothesis+H