Week 09.10.2021 – 17.10.2021


Quantum algebras in supersymmetric gauge theories: interfaces and stable envelopes

Regular Seminar Nikita Nekrasov (SCGP, Stony Brook and Center for Advanced Studies, Skoltech, Moscow)

13:20 IC
room B630

I will give an overview of a three decade long project of novel symmetries in quantum field theory, with the emphasis on the most recent development concerning the realisation of stable envelopes (proposed by A. Okounkov and collaborators) and R-matrices via supersymmetric interfaces in 1-2-3 dimensional supersymmetric gauge theories. Based on the recent paper arXiv:2109.10941 with Mykola Dedushenko.


Separation of variables and correlation functions in high-rank integrable systems

Regular Seminar Paul Ryan (KCL / Trinity College Dublin)

13:45 KCL
room K0.20

The spectral problem for N=4 Super Yang-Mills can be formulated as a set of quantisation conditions on a handful of functions called Q-functions. Recent analysis suggests that the Q-functions can be used as simple building blocks for 3-point correlation functions. This strongly resembles the situation in integrable spin chains where the wave functions factorise into a simple product of Q-functions in a special basis called Sklyanin’s separation of variables (SoV) basis which is one of the most powerful approaches for solving integrable systems. Unfortunately this framework has only been developed for the simplest integrable spin chains with sl(2) symmetry, far from the psu(2,2|4) needed to describe N=4 SYM. In this talk I will review recent advances in developing the SoV approach for higher rank integrable spin chains. I will explain how to construct the SoV basis in a systematic fashion and how it links to the representation theory of the system. Next, I will discuss a new approach for obtaining the measure in separated variables based on the famous Baxter TQ equation and how the approach naturally provides a large family of correlation functions as very simple determinants in Q-functions. I will briefly discuss how the approach can be applied directly to certain 4d QFTs, in particular the fishnet cousin of N=4 SYM.


Lessons and surprises from Kaluza-Klein spectra

Regular Seminar Gabriel Larios (UAM)

14:00 QMW
room zoom

[foor zoom link please email s.nagy@qmul.ac.uk] Infinite towers of massive modes arise for every compactification of higher dimensional theories. Understanding the properties of these Kaluza-Klein towers on non-trivial solutions with an AdS factor has been a longstanding issue with clear holographic interest, as they describe the spectrum of single-trace operators of the dual CFTs at strong coupling and large N. In this talk, I will focus on two classes of solutions of such kind. The first class consists of AdS4 solutions of D=11 and Type II supergravity that can be obtained from maximal gauged supergravities in D=4. For the later part, I will describe new families of solutions in N=(1,1) supergravity in D=6 which uplift from half-maximal supergravity in D=3. In both cases, the spectra can be computed using recent techniques from Exceptional Field Theory, and the information thus obtained leads to several unexpected conclusions.

Dynamical spin chains in 4D N = 2 SCFTs

Journal Club Elli Pomoni (DESY)

15:45 Other
room Zoom, instructions in abstract

In this talk we will revisit the study of spin chains capturing the spectral problem of 4d N = 2 SCFTs in the planar limit. At one loop and in the quantum plane limit, we will discover a quasi-Hopf symmetry algebra, defined by the R-matrix read off from the superpotential. This implies that when orbifolding the N = 4 symmetry algebra down to the N = 2 one and then marginaly deforming, the broken generators are not lost, but get upgraded to quantum generators. We will also demonstrate that these chains are dynamical, in the sense that their Hamiltonian depends on a parameter which is dynamically determined along the chain. At one loop we will show how to map the holomorphic SU(3) scalar sector to a dynamical 15-vertex model, which corresponds to an RSOS model, whose adjacency graph can be read off from the gauge theory quiver/brane tiling. One scalar SU(2) sub-sector is described by an alternating nearest-neighbour Hamiltonian, while another choice of SU(2) sub-sector leads to a dynamical dilute Temperley-Lieb model. These sectors have a common vacuum state, around which the magnon dispersion relations are naturally uniformised by elliptic functions. For the example of the ℤ_{2} quiver theory we study these dynamical chains by solving the one- and two-magnon problems with the coordinate Bethe ansatz approach. --- Part of the London Integrability Journal Club. If you are a new participant, please register at integrability-london.weebly.com. The link will be emailed on Tuesday.