Week 21.11.2021 – 27.11.2021

Live Tutorial. This lecture provides an introduction to duality symmetries in string theory. String theory was originally formulated as a theory of strings propagating in space time with interactions governed by the string coupling constant g. Scattering amplitudes for small g were constructed as a perturbation theory in g. Five consistent supersymmetric string theories were found, all in 10 spacetime dimensions with five distinct perturbation theories. This left many questions unanswered, such as why there should be five apparently consistent quantum theories of gravity and what happens to these theories as the coupling constant is increased. Such questions were answered by the developments in the mid-1990s that have been called the 2nd superstring revolution. Dualities proved to be the key to uncovering the non-perturbative structure of superstring theory and in particular its strong coupling behaviour. When g is large, one can analyse the theory as a perturbation theory in 1/g and seek a "dual theory" with coupling constant g' whose perturbative expansion in g' matches the behaviour of the original theory as a perturbation theory in 1/g on identifying g'=1/g. In some cases the dual theory is again a string theory, which might be a different string theory from the original one. In other cases, the dual theory isn't a string theory at all, but a new theory - M-theory. This leads to a picture in which all 5 string theories are related by dualities and so are all seen as different limits of M-theory. Duality transformation provide new symmetries of string/M theory and T,S and U-dualities. Remarkably, the theory that emerges is no longer just a theory of strings but one which includes both strings and branes which are higher dimensional extended objects. As the branes are related to strings by duality symmetries, they should be regarded as being on the same footing as the strings and of equal importance. The lecture explores all of these issues and discusses some examples. Please register at https://lonti.weebly.com/registration.html to receive joining instructions for this live session which will be held via Zoom.

Mathematical ideas introduced by Ramanujan a century ago in number theory and combinatorics have come to play a surprising role in understanding some deep and fundamental aspects of quantum gravity and quantum field theory in three very distinct contexts of holography, duality, and topology. In this colloquium, I shall first describe the fascinating history, physics, and mathematics behind this rich and fruitful connection focusing on the role (mock) modular forms have come to play in understanding quantum properties of black holes in string theory. I shall then elucidate briefly the manifestations of mock modularity in physics in its other avatars.

Almost all existing calculations that concern the Higgs mass are performed within the framework of an effective field theory. While sufficient for certain purposes, such calculations throw up problems to do with fine-tuning and naturalness in particular the famous hierarchy problem. This makes most attempts within field theory to understand the Higgs mass pretty much futile. Even most phenomenology done within string theory does not respect the full string symmetries that are responsible for many of the remarkable finiteness properties for which string theory is famous. Chief among these symmetries is worldsheet modular invariance, which is an exact symmetry of all perturtubative closed-string vacua. And yet if the UV is tamed by this symmetry then it should be exact even today! In this talk I will discuss the many things one can learn from this fact. For example that a gravitational modular anomaly generically relates the Higgs mass to the one-loop cosmological constant, yielding a string-theoretic connection between the two fundamental quantities which are known to suffer from hierarchy problems in the absence of spacetime supersymmetry. In addition one learns about the use and interpretation of modular invariant regulators in string theory, which in turn dictates how string theory arranges its UV/IR-mixing to make itself finite. Finally, I discuss how the effective field theory emerges showing that ultimately the Higgs mass can be understood as arising from an infinite “stringy” sum of Coleman-Weinberg effective potentials in such theories. The results can therefore serve as the launching point for a rigorous investigation of hierarchy problems in a UV complete theory.

Local observables in a de Sitter universe become conformal, if you wait long enough. Indeed, one can study the imprints of inflation by looking at conformal correlations in the sky. There’s an ongoing effort in the cosmology community to understand these late-time correlators from first principles, without invoking a specific Lagrangian. In this talk, I will discuss the late-time CFT living in de Sitter through the lens of a quantum field theorist. The CFT in question shares many features with its counterparts in flat space or AdS, but differs in crucial aspects: in particular, it can have complex scaling dimensions and correlation functions. I will nevertheless argue that de Sitter CFTs have good unitarity properties and can be constrained via conformal bootstrap equations. This observation should open up a new way to constrain cosmological correlation functions.

[there will be a pre-seminar for students at 1.30PM; for zoom link please email s.nagy@qmul.ac.uk] The characterization of measurements using the EFT framework is becoming prevalent, not just in its traditional realm of low-energy physics, but now also with LHC high-energy probes. At the LHC, the EFT approach is viewed as a way to transcend models, to exploit the huge range of LHC topologies, and even as a form of data preservation. In this talk we will review this state-of-affairs, point out challenges with this approach and also discuss some new opportunities that more data will bring.

We will have a new edition of the London Integrability Journal Club Gong Show, with six 10+5 mins talks by: Meer Ashwinkumar, Kavli Inst. Tokyo, "Three-dimensional WZW model and the R-matrix of the Yangian". Carlos Bercini, ICTP-SAIFR, "The Wilson Loop - Large Spin OPE Dictionary". Aleix Gimenez-Grau, DESY, "Bootstrapping holographic defect correlators". Himanshu Khanchandani, Princeton Univ., "CFT in AdS and Gross-Neveu BCFT". Levente Pristyak, Budapest Univ., "Current operators in the XYZ model". Xinyu Zhang, DESY, "Hidden symmetry in 4d N=2 quiver gauge theory". Abstracts and schedule can be found on the LIJC website, integrability-london.weebly.com . If you are not registered, please email Andrea Cavaglia at KCL for the Zoom link.