5th ECR South East Mathematical Physics Seminars

Monday July 23rd, 2018

Mathematical Institute, Oxford; lecture room L5

The 5th ECR meeting of the South East Mathematical Physics Seminars (SEMPS) will be held on Monday 23rd July 2018 at the Mathematical Insitute, University of Oxford.

All talks will be in the lecture room L5 on the basement floor.

Coffee and tea will be served upstairs in the Maths Common Room. Ask at reception for access through the glass doors.

Registration

There is no registration fee, but please register here so we have sufficient coffee and cake.

Schedule

List of Speakers

Chris Beem - "Something for (almost) nothing: the SCFT/VOA correspondence in four dimensions"

Four-dimensional superconformal field theories with at least eight supercharges possess cohomological subsectors that take the form of vertex operator algebras (i.e., chiral algebras). The dictionary for relating four-dimensional quantities and vertex algebraic structures is by now quite extensive. In this talk, I will give a high level overview of this dictionary as it currently stands, using simple Argyres-Douglas SCFTs to demonstrate its various entries. I will then present an example of an SCFT about which ver little is a priori known, the rank-two H_0 F-theory SCFT. I will show how one can recover a surprising amount of information about this theory using the strong constraints of self-consistency for vertex algebras.

Andrea Cavaglià - "Correlators in N=4 SYM via the quantum spectral curve"

Integrability has led to an exact description of the spectrum of planar N=4 SYM through a powerful mathematical formulation, the Quantum Spectral Curve. Recently, we found strong evidence that the latter also encodes correlation functions at all orders in the 't Hooft coupling. 
The observable we consider is the structure constant of Wilson lines with 3 cusps with arbitrary angles in the so-called ladders limit. We find that the result can be expressed in an extremely simple form in terms of the key Quantum Spectral Curve ingredients, the Q-functions. We comment on a possible strategy to solve planar N=4 SYM. Based on 1802.04237.

Charles Strickland-Constable - "Finite heterotic deformations and holomorphic structures in generalised geometry"

Not long ago, it was found that the infinitesimal moduli of N=1 flux backgrounds of heterotic supergravity live in the cohomology of a particular holomorphic bundle over the spacetime manifold, which has the structure of a holomorphic Courant algebroid. In this talk I will present recent results examining the extension to small but finite deformations. Starting by expanding the superpotential functional in natural complex coordinates on the space of geometries, we find an expression which can be understood in terms of the natural operations of the holomorphic Courant algebroid, featuring elements of both Kodaira-Spencer gravity and holomorphic Chern-Simons theory. From this, we see that the deformations are described as the Maurer-Cartan set of a closely related L_3 algebra.

Simon Nakach - "Amplitudes in conformal higher spin theories: giving meaning to scattering higher derivative states"

In this talk, we will look at the higher derivative theory of Conformal Higher Spins (CHS), whose lower spin truncation is Conformal Gravity (CG). When scattering 2-derivative on-shell states, recent evidence shows that tree-level CHS amplitudes are trivial due to the underlying symmetry. However, the higher order equations of motion imply that there are many-more states in the theory. We will show how to obtain tree-level amplitudes containing these new states and characterise their "admissible" subsector (ie. the states that lead to finite scattering amplitudes). This will first be done in CG where we will see that some 3-point amplitudes involving massless spin 1 "ghosts" are finite and non-zero. We will see how this can be encoded in the language of "twistor-spinors", which allows us to generalise these results to CHS theory.

Clelia Pech - "Mirror symmetry for cominuscule homogeneous varieties"

In this talk reporting on joint work with K. Rietsch and L. Williams, I will explain a new version of the construction by Rietsch of a mirror for some varieties with a homogeneous Lie group action. The varieties we study include quadrics and Lagrangian Grassmannians (i.e., Grassmannians of Lagrangian vector subspaces of a symplectic vector space). The mirror takes the shape of a rational function, the superpotential, defined on a Langlands dual homogeneous variety. I will show that the mirror manifold has a particular combinatorial structure called a cluster structure, and that the superpotential is expressed in coordinates dual to the cohomology classes of the original variety. I will also explain how these properties lead to new relations in the quantum cohomology, and a conjectural formula expressing solutions of the quantum differential equation in terms of the superpotential. If time allows, I will also explain how these results should extend to a larger family of homogeneous spaces called cominuscule homogeneous spaces.

Participants

Practical Information

Funding

Limited funds are available to help with travel expenses of participants with no other source of funding. We hope this will encourage postgraduate students and postdocs to attend the meeting. Please email one of the organisers in advance if you would like to apply for funding.

Travel Information and venue

Local travel information can be found here.

Organising Committee: Anthony Ashmore and Carlo Meneghelli

Previous Meeting

Monday July 11th, 2016

Mathematical Institute, Oxford; lecture room L3 (L5 in the afternoon)

The 7^th meeting of the South East Mathematical Physics Seminars (SEMPS) was held on Monday 11th July 2016 at the Mathematical Insitute, University of Oxford.

Schedule

List of Speakers

Philip Candelas - "Heterotic Geometry"

The simplest compactifications of heterotic string theory on a Calabi-Yau manifold make use of the "standard embedding" in which the background gauge field is identified with the spin connection. These lead to N=2 supersymmetry in spacetime and the moduli spaces of these compactifications are described by special geometry. There has been recent progress on the more general case, where the background gauge field is different from the spin connection. These compactifications correspond to N=1 supersymmetry in spacetime and the moduli spaces are characterised by what we term heterotic geometry. A key role, in deriving this geometry, is played by the anomaly cancellation condition. This talk will be based on joint work with X. de la Ossa and J. McOrist, part of which is reported in arXiv:1605.05256 .

Martyna Kostacinska - "Two-loop form factors: from N=4 super Yang-Mills to QCD"

The study of form factors in maximally supersymmetric Yang-Mills theory has recently been shown to bear relevance for calculations of QCD Higgs + gluon amplitudes in the effective Lagrangian description. With this phenomenological application in mind, we investigate two-loop form factors and remainder functions of non-protected operators belonging to the SU(2|3) closed subsector of N=4 SYM. In the process, we uncover certain hints of universality: firstly, regarding the coincidence of the maximally transcendental part of the result to that of a half-BPS operator and secondly (more surprisingly), across different sectors of the theory. Finally, we use our results to resolve the mixing problem and reconstruct the two-loop dilatation operator in the SU(2|3) sector. The talk is based on the recent work, reported in https://arxiv.org/abs/1606.08682.

Kai Roehrig - "Perturbative N=4 SYM in twistor space"

I will review the developments driving the reformulation of N=4 SYM scattering amplitudes in twistor space. An amazing result of this is a closed form expression for all tree level scattering amplitudes, the RSV-Witten formula. After introducing the relevant mathematical background to understanding this formula, we will take a peak at its
extension loop level.

Jennifer Ashcroft - "Scattering Sheep: Kink Collisions in the Presence of False Vacua"

We investigate numerically head-on kink collisions in a 1+1 dimensional scalar field theory with multiple vacua. The lowest minimum of the potential is called the true vacuum, and any local minima with higher energy are called false vacua. We consider kinks interpolating between false and true vacua, and form four distinct initial configurations from combinations of these kinks. A rich variety of scattering outcomes is found in which, depending on the initial kink set-up and impact velocities, kinks can repel each other, annihilate, form true or false domain walls and reflect off each other.

Jin-Mann Wong - "M5-branes on $M_4$ $\times$ $S^2$"

Antonio Pittelli - "T-Self Duality and Integrability of AdS$_2$ Superstrings"

Dual superconformal symmetry underlies $N=4$ SYM amplitude/Wilson loop duality and, via AdS/CFT, corresponds to the invariance of the AdS$_5$ $\times$ S$^5$ superstring under specific T-dualities. We show that T-self duality holds also for AdS$_2$ $\times$ S$^2$ $\times$ S$^2$ $\times$ T$^4$ superstrings, implying dual superconformal symmetry of the dual CFT$_1$ and giving insights about ABJM’s. We then focus on AdS$_2$ $\times$ S$^2$ $\times$ T$^6$ superstrings and discuss their peculiar integrable worldsheet S-matrix, as well as the infinite dimensional symmetry of the model: the Y[gl$_c$(1|1)] yangian.

Organising Committee: Andrea Ferrari, Yvonne Geyer, Mark Van Loon, Prof. Lionel Mason