Week 14.11.2021 – 20.11.2021

Lonti Autumn 2021 Series: Lecture 4. Live Tutorial. Please register at https://lonti.weebly.com/registration.html to receive joining instructions for this live session which will be held via Zoom. Gauge theories are ubiquitous in theoretical physics, not to mention that the standard model is one. It is therefore of utmost importance to know what the observables of these theories are, quantities that can be calculated and measured. I start with a long discussion based on the most familiar gauge theory, Maxwell's electromagnetism, where a lot of computations can be done explicitly. I then take the lessons from that to non-abelian gauge theories. The observables covered are local, Wilson loops, and briefly 't Hooft loops and surface operators.

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. The lecture is available here: https://youtube.com/playlist?list=PLlva4MroG-KHsP0WGLxRk9ZWsmAHUklMT

In this talk I will give an overview of recent and ongoing work regarding rotating black holes in dynamical Chern-Simons (dCS) gravity. dCS gravity is a well motivated modified theory of gravity which has been extensively studied in gravitational and cosmological contexts. I will first discuss unique geometric structures, `the Chern-Simons caps,' which slowly rotating black holes in dCS gravity were recently found to possess. Motivated by the dCS caps, I will then discuss superradiance in the context of slowly rotating dCS black holes and show that there are corrections to the usual solution for a Kerr black hole. Lastly, I will comment on the observable implications for these corrections and point towards avenues for future work.

It is known that the classical O(N) model in dimension d > 3 at its bulk critical point admits three boundary universality classes: the ordinary, the extraordinary and the special. The extraordinary fixed point corresponds to the bulk transition occurring in the presence of an ordered boundary, while the special fixed point corresponds to a boundary phase transition between the ordinary and the extra-ordinary classes. While the ordinary fixed point survives in d = 3, it is less clear what happens to the extraordinary and special fixed points when d = 3 and N is greater or equal to 2. I'll show that formally treating N as a continuous parameter, there exists a finite range 2 < N < N_c where the extra-ordinary universality class survives, albeit in a modified form: the long-range boundary order is lost, instead, the order parameter correlation function decays as a power of log r. I'll discuss recent Monte-Carlo simulations and numerical bootstrap results that confirm the above picture and indicate that the critical value N_c > 3. Based on arXiv:2009.05119, 2111.03613, 2111.03071

The Bethe-Gauge Correspondence (BGC) of Nekrasov and Shatashvili, which relates 1d quantum integrable spin chains to two-dimensional supersymmetric gauge theories with \mathcal{N}=2 supersymmetry, is one of the instances of the deep connection between supersymmetric gauge theories and integrable models. The question that will be the main content of the talk is the origin of this correspondence. I will explain how the BGC could be naturally realized within superstring theory. Toward this aim, I will first explain The Bethe Side (noncompact rational integrable \mathfrak{gl}(m|n) superspin chains) and the corresponding Gauge Side of the BGC. I will then discuss the brane setup for the realization of The Gauge Side. Using string dualities, this brane setup will be mapped to another setup, which realizes The Bethe Side of the correspondence. An important role in this duality frame is played by the 4d Chern-Simons Theory of Costello which explains the integrability of The Bethe Side. If time permits, I will also explain the story for the compact rational integrable \mathfrak{gl}(m|n) superspin chains. This talk is based on the joint work (arXiv:2110.15112) with Nafiz Ishtiaque, Surya Raghavendran, and Junya Yagi.

The Euler-scale power-law asymptotics of space-time correlation functions in many-body systems, quantum and classical, can be obtained by projecting the observables onto the hydrodynamic modes admitted by the model and state. This is the Boltzmann-Gibbs principle; it works for integrable and non-integrable models alike. However, certain observables, such as some order parameters in thermal of generalised Gibbs ensembles, do not couple to any hydrodynamic mode: the Boltzmann-Gibbs principle gives zero. I will explain how hydrodynamics can still give the leading exponential decay of order parameter correlation functions. With the examples of the quantum XX chain and the sine-Gordon model, I will explain how large deviations of the spin and U(1) current fluctuations are related to such exponential decay. Exact predictions are given by the ballistic fluctuation theory based on generalised hydrodynamics. In the XX model, this is in agreement with results obtained previously by a more involved Fredholm determinant analysis and other techniques, and even gives a new formula for a parameter regime not hitherto studied. In the sine-Gordon model, these are new results, inaccessible by other techniques. Works in collaboration with Giuseppe Del Vecchio Del Vecchio, and Márton Kormos. ---- 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.

Modulo some vitally important ansätze, subtleties, provisos, and work in progress, all topological quantum field theories are gauge theories for higher finite groups. [for zoom link please contact jung-wook(dot)kim(at)qmul(dot)ac(dot)uk]