Triangle Seminars

Abstract:
This is the live session included as part of the LonTI lecture on Witten diagrams and the Mellin transform in AdS/CFT. Please register at https://lonti.weebly.com/registration.html to receive joining instructions for this live session which will be held via Zoom.AdS/CFT duality (or more general holographic principle) represents a major advance in understanding quantum gravity, and provides powerful tools for studying strongly coupled quantum field theories. This talk will give a basic introduction to AdS/CFT duality, with the focus on the computation of Witten diagrams and their Mellin transform. Witten diagrams, which play the role of Feynman diagrams, provide the means for computing correlation functions in AdS/CFT. We will show that CFT correlation functions obtained from Witten diagrams have much simpler structures after Mellin transform. Correlators in Mellin space are very analogous to the flat-space scattering amplitudes, and they are often called Mellin amplitudes. We will demonstrate the ideas by studying a few non-trivial examples.

Abstract:
​​Conformal blocks are the building blocks of conformal field theories, the key ingredients of correlation functions and knowledge of these blocks is central to the conformal bootstrap. This lecture covers some general results before quickly specialising to two-dimensions. It discusses the implications of global conformal invariance and then the larger and more constraining Virasoro algebra symmetry. It introduces various methods of calculation including brute force, differential equations, recursion relations and closed formulae - and some aspects of bootstrap techniques.

Abstract:
The AdS/CFT correspondence relates string theory on an Anti de Sitter (AdS) background to a dual conformal field theory (CFT) living on the boundary of AdS. One promising strategy for how to prove the duality is to consider the `tensionless' limit of string theory in which the dual CFT becomes weakly coupled. For the case of string theory on AdS3 we have recently identified a solvable world-sheet description for this tensionless limit. This opens the way towards proving the AdS/CFT correspondence, at least for this specific set-up.

Please contact Dionysios Anninos (dionysios.anninos@kcl.ac.uk) for the zoom link.

Abstract:
Recent developments on the black hole information paradox have shown that Euclidean wormholes — so called “replica wormholes’’ can dominate the von Neumann entropy as computed by a gravitational path integral, and that inclusion of these wormholes results in a unitary Page curve. This development raises some puzzles from the perspective of factorization, and has raised questions regarding what the gravitational path integral is computing. In this talk, I will focus on understanding the relationship between the gravitational path integral and the partition function via the gravitational free energy (more generally the generating functional). A proper computation of the free energy requires a replica trick distinct from the usual one used to compute the entropy. I will show that in JT gravity there is a regime where the free energy computed without replica wormholes is pathological. Interestingly, the inclusion of replica wormholes is not quite sufficient to resolve the pathology: an alternative analytic continuation is required. I will discuss the implications of this for various interpretations of the gravitational path integral (e.g. as computing an ensemble average) and also mention some parallels with spin glasses.

[please email a.held@imperial.ac.uk for zoom link or password]

Abstract:
Even in weakly coupled QFTs, perturbation theory breaks down
when one considers amplitudes with a large number \(n\) of legs. The series cleverly organizes as a double expansion in \(g^2\) and \(g^2n\).
I show how the series in \(g^2n\) can be fully captured by a semiclassical expansion around a non-trivial solution. Focussing on \(U(1)\) symmetric \(|\phi|^4\) theory in \(4\) and \(4-\epsilon\) dimension, I derive explicit and consistent all order results for the anomalous dimension of the complex operator \(\phi^n\). When restricting to the Wilson-Fisher fixed point and working on the cylinder, the dominant trajectory is seen to correspond to a superfluid phase for the conserved U(1). This creates a correspondence between, on one side, the spectrum of operators and fusion coefficients and and on the other the spectrum of hydrodynamics modes and their interactions. The results also nicely match Monte Carlo simulations in 3D, compatibly with the stunt of taking \(\epsilon=1\).

[please email alejandro.cabo_bizet@kcl.ac.uk for the Zoom link]

Abstract:
For zoom link please email s.nagyATqmul.ac.uk
There will be a pre-seminar for students at 13:30.
Abstract: I will discuss 2 recent results arising out of the recent resurgence in concrete tests / predictions of AdS/CFT over the last few years. The first is the precise identification of the CFT operators dual to single particle supergravity states (based on 2007.095395) and the second is a forthcoming work explicitly relating four-point correlators to a string effective action on AdSxS.

Abstract:
This Thursday we will have six speakers presenting a 10 mins talk each.
1) Stefano Baiguera (Niels Bohr Institute), "Non-relativistic near-BPS corners of N=4 super Yang-Mills with SU(1,1) symmetry".
2) Ilija Buric (Desy), "From Integrable Gaudin Models to Multipoint Conformal Blocks",
3) Julius Julius (King's College London), "Baxter Equation for Boundary Integrability",
4) Rob Klabbers (Nordita), "How coordinate Bethe ansatz works for Inozemtsev model",
5) Yuan Miao (University of Amsterdam), "On the Q-operator and the spectrum of the XXZ model at root of unity".
6) Anne Spiering (Trinity College Dublin), "Integrability and Quantum Chaos in N=4 SYM from the Spectral Rigidity".
Join us to hear the latest news in integrability!
Important: Please make sure your Zoom version is updated, in order to use the break-out rooms feature for discussions after the talks. See the journal club website for abstracts of the talks.
––––––––––––––- Part of the London Integrability Journal Club. New participants please register using the form which can be found on the webpage integrability-london.weebly.com. The link will be emailed.