Week 15.05.2023 – 21.05.2023

Sigma models are maps from a domain to a target space T. The geometry of the target space is determined by the dimension of the domain and symmetries of the model. When it has isometries that can be gauged, the quotient space, i.e., the space of orbits under the isometries, supports a new sigma model. The target space geometry of the new model is the quotient of the T by the isometry group. This is first described for a bosonic sigma model and it is pointed out that we need to understand supersymmetric sigma models, their isometries and gauging as well as the quotient in order to apply the scheme to models with extended supersymmetry. We then look at these issues. The final goal is to construct new hyperkahler geometries from hyperkähler geometries with isometries, so making sure that the quotient construction preserves the symmetries etc. Ulf Lindstrom is Leverhulme Visiting Professor at Imperial College.

Recently, a relation was introduced connecting codes of various types with the space of abelian (Narain) 2d CFTs. We extend this relation to provide holographic description of code CFTs in terms of abelian Chern-Simons theory in the bulk. For codes over the alphabet Z_p corresponding bulk theory is, schematically, U(1)_p times U(1)_{-p} where p stands for the level. Furthermore, CFT partition function averaged over all code theories for the codes of a given type is holographically given by the Chern-Simons partition function summed over all possible 3d geometries. This provides an explicit and controllable example of holographic correspondence where a finite ensemble of CFTs is dual to "topological/CS gravity" in the bulk. The parameter p controls the size of the ensemble and "how topological" the bulk theory is. Say, for p=1 any given Narain CFT is described holographically in terms of U(1)_1^n times U(1)_{-1}^n Chern-Simons, which does not distinguish between different 3d geometries (and hence can be evaluated on any of them). When p approaches infinity, the ensemble of code theories covers the whole Narain moduli space with the bulk theory becoming "U(1)-gravity" proposed by Maloney-Witten and Afkhami-Jeddi et al.

TBA. If you are planning to attend, please send and email to pietro.benetti_genolini@kcl.ac.uk or alan.rios_fukelman@kcl.ac.uk so your name is added to the participants list in order to grant you access to the building.

The superconformal index of N=4 super Yang-Mills theory on a three-sphere is captured by a unitary matrix model with purely double trace operators in the action. The AdS/CFT correspondence predicts that this index should have exponential growth at large charges and large N, corresponding to the 1/16-BPS black hole (BH) in AdS5. I will show how the matrix model gives rise to this expected BH growth as well as an infinite number of new phases. In particular, I will introduce a deformation of the matrix model which allows us to solve it at large N. The deformation has interesting relations with the Bloch-Wigner dilogarithm, a function introduced by number theorists. I will then show how this matrix model can be expressed in terms of a system of free fermions in a certain ensemble. Integrating out the fermions and averaging over the ensemble leads to a convergent expansion as a series of determinants, showing how giant gravitons in the dual AdS5 are encoded in the gauge theory. . If you are planning to attend, please send and email to pietro.benetti_genolini@kcl.ac.uk or alan.rios_fukelman@kcl.ac.uk so your name is added to the participants list in order to grant you access to the building.

Dualities involving ensembles of theories represent a fascinating class of holographic correspondences. The inclusion of wormholes into a theory naturally motivates the study of ensembles, but doing so leads to many puzzles from the viewpoint of string theory. In this talk, I will discuss holographic dualities involving ensembles of 2D Narain conformal field theories. The bulk dual of such an ensemble is an Abelian Chern-Simons theory, but features a sum over 3D geometries. Generalizations of this correspondence lead to emergent ensemble symmetries – global symmetries that appear after averaging over the ensemble and are the vestiges of T-duality in the CFT. These symmetries are intimately related to the anyon data and 0-form symmetries of the bulk Chern-Simons theories. I will also discuss the relation of these emergent global symmetries with recent ideas in quantum gravity, and furthermore generally discuss the role of ensemble averaging in standard holography, the landscape, and the swampland. If you are planning to attend, please send and email to pietro.benetti_genolini@kcl.ac.uk or alan.rios_fukelman@kcl.ac.uk so your name is added to the participants list in order to grant you access to the building.

We consider vacuum transitions by bubble nucleation among vacua with different values and signs of the cosmological constant Lambda, including both up and down tunnelings. Following the Hamiltonian formalism in four dimensions, we explicitly compute the decay rates for all possible combinations of initial and final values of Lambda and find that up-tunneling may be allowed starting not only from pure dS spacetime but also from pure AdS and Minkowski spacetimes. We trace the difference with the Euclidean approach, for which these transitions are found not to be allowed, to the difference of assigning either vanishing or infinite entropy to both pure AdS and Minkowski. We find that, in all allowed cases, detailed balance is satisfied. Also in the formal limit Lambda -> -infinity, the transition rates for AdS to dS agree with the Hartle-Hawking and Vilenkin amplitudes for the creation of dS from nothing. This is consistent with a proposal of Brown and Dahlen to define 'nothing' as AdS in this limit. We generalise our results to include black hole backgrounds for which transitions are allowed only in certain regimes of the black hole mass M but detailed balance is not satisfied, except for Schwarzschild de Sitter (SdS) to another SdS for which the transition is allowed and detailed balance satisfied. We compute the bubble trajectory after nucleation and find that, contrary to the M = 0 case, the trajectory is not a geodesic for the open universe slicing of dS. We briefly discuss the relevance of our results to the string landscape.

Matrix models offer non-perturbative descriptions of quantum gravity in simple settings, allowing us to study large-N dualities between gauge and string theories. However, the large-N expansions of matrix models lead to divergent series, only defined as asymptotic series. By fine-tuning the couplings of the matrix model we obtain models of pure gravity coupled to minimal conformal field theories. The free energy for the simplest of these "minimal models" is 2d gravity also admits an asymptotic expansion which formally satisfies the Painlevé I equation. These asymptotic properties are connected to the existence of exponentially small contributions not captured by a perturbative analysis and whose physical interpretation can be elusive. The emerging structure can be accurately described by means of a resurgent transseries, capturing this perturbative/non-perturbative connection and its consequences. This talk will focus on the essential role of this resurgent transseries for the cases of Painlevé I and the quartic matrix model: together with exponentially accurate numerical and summation methods, one can show how to go beyond the asymptotic results and obtain (analytically and numerically) non-perturbative data. If you are planning to attend, please send and email to pietro.benetti_genolini@kcl.ac.uk or alan.rios_fukelman@kcl.ac.uk so your name is added to the participants list in order to grant you access to the building.

For a weakly nonlinear classical system, the kinetic equation for waves governs the evolution of the occupation number of a given wavevector. It is like the Boltzmann equation, but for waves instead of particles. As has been known for half a century, in addition to thermal equilibrium, the kinetic equation has another stationary solution: a turbulent state, describing a cascade of energy. Wave turbulence is observed in a wide range of physical contexts, most notably in surface gravity waves in the ocean. Higher order terms in the kinetic equation, going beyond leading order in the nonlinearity, have never been computed. We describe a method, based on quantum field theory, for computing such terms. We show that higher order terms can exhibit UV divergences. We sum the most divergent diagrams (bubble diagrams) to derive a kind of renormalized kinetic equation. Based on 2203.08168, 2212.02555, and work in progress with G. Falkovich. If you are planning to attend, please send and email to pietro.benetti_genolini@kcl.ac.uk or alan.rios_fukelman@kcl.ac.uk so your name is added to the participants list in order to grant you access to the building.

I give an overview of work characterizing radiation in generic four-dimensional conformal field theories. I argue that for theories with conformal scalars, the radiated energy is not positive definite and the radiated power is not Lorentz invariant. I then determine the coupling dependence of radiation, for N=2 superconformal field theories in the planar limit. This involves a purely combinatorial solution of certain matrix models, in terms of tree graphs. If you are planning to attend, please send and email to pietro.benetti_genolini@kcl.ac.uk or alan.rios_fukelman@kcl.ac.uk so your name is added to the participants list in order to grant you access to the building.