# 13th South East Mathematical Physics Seminar

The thirteenth meeting of the South East Mathematical Physics Seminar will be held on Thursday 21st February 2019 at King's College London in room Bush House (S) 2.01. The meeting is partially supported by supported by a London Mathematical Society Joint Research Groups grant.

There is no registation fee, and no need to register in advance, but currently all visitors to King's are required to sign in at reception, and it would be very helpful and speed matters up if we knew who was coming in advance. Please email Gerard Watts if you are likely to attend.

## Speakers, titles and abstracts

 Martin Wolf (Surrey) $$L_\infty$$ algebras, the BV formalism, and Classical Fields I will first review the Batalin-Vilkovisky formalism and its mathematical foundations with an emphasis on higher algebraic structures and classical field theories. I will then move on and discuss recent developments in formulating higher gauge theory with Lie quasi-groupoids as gauge structure. Finally, I will explain how all these ideas can be combined with those of twistor theory to formulate maximally superconformal gauge theories in four and six dimensions by means of quasi-isomorphisms. Imtak Jeon (KCL) Twisting and localization in supergravity: equivariant cohomology of BPS black holes I will talk about the formalism of supersymmetric localization in supergravity using the deformed BRST algebra defined in the presence of a supersymmetric background. The gravitational functional integral localizes onto the cohomology of a global supercharge $$Q_{eq}$$, obeying $$Q_{eq}^2=H$$, where $$H$$ is a global symmetry of the background. This construction naturally produces a twisted version of supergravity whenever supersymmetry can be realized off-shell. I will present the details of the twisted graviton multiplet and ghost fields for the superconformal formulation of four-dimensional N=2 supergravity. As an application of our formalism, we systematize the computation of the exact quantum entropy of supersymmetric black holes. In particular, we compute the one-loop determinant of the Qeq deformation operator for the off-shell fluctuations of the Weyl multiplet around the $$AdS_2\times S^2$$ saddle. Edoardo Lauria (Durham) 3d Abelian Gauge theories at the Boundary A four-dimensional abelian gauge theory can be coupled to a 3d CFT with a U(1) symmetry living on a boundary. This coupling gives rise to a continuous family of boundary conformal field theories (BCFTs) parametrized by the gauge coupling $$\tau$$ and by the choice of the CFT in the decoupling limit. Upon performing an Electric-Magnetic duality in the bulk and going to the decoupling limit in the new frame, one finds a different 3d CFT on the boundary, related to the original one by Witten's SL(2, Z) action. In particular the cusps on the real $$\tau$$ axis correspond to the 3d gauging of the original CFT. We study general properties of this family of BCFTs. We show how to express bulk one and two-point functions, and the hemisphere free-energy, in terms of the two-point functions of the boundary electric and magnetic currents. Finally, upon assuming particle-vortex duality (and its fermionic version), we show how to turn this machinery into a powerful computational tool to study 3d gauge theories. Cecilia de Fazio (City) Entanglement Content of Quantum Particle Excitations In the ﬁrst part of my talk I will give a brief introduction to the main features of the Entaglement Entropy of a bipartite system in Integrable Quantum Field Theories and Conformal Field Theories. Secondly I will discuss the results my collaborators and I obtained in our two papers. In particular, I will consider the Entaglement Entropy of a single connected region of a ﬁnite bipartite system in excited states described by one-dimensional massive free theories with ﬁnite numbers of particles. I will show that in the limit of large volume and large length of the region the excess of entanglement due to the presence of the particles with respect to the ground state takes a simple form and admits a "$$q$$-bit interpretation". Benjamin Doyon (KCL) Thermo/HydroDynamics of the classical Toda system and random matrix theory This will be presenting mainly some of my recent work, and also aspects of recent work of Herbert Spohn, both developed in parallel. The classical Toda system is a one-dimensional integrable many-body system, which can be seen either as a gas of particles or as a chain of degrees of freedom. Herbert has shown how the generalised Gibbs ensembles of the Toda chain can be obtained from a certain limit of the beta-ensemble in random matrix theory. Analysing and connecting the gas and chain viewpoints, I have obtained both the generalised Gibbs ensembles and generalised hydrodynamics from a quasiparticle scattering description. Thus we make a connection between quasiparticle scattering and random matrix theory.

## Practical Information

### Room

The meeting is in room Bush House (S)2.01, on the second floor of south wing of the central block of Bush House, the newly redeveloped building just across the road from the main King's Strand site. Here is a map of the campus [the Bush house building is labelled R in pink]. You can enter the building from either the Strand [south entrance] or Aldwych [north entrance],

#### Travel

Local travel information may also be found here.

London transport information is available here. The nearest tube station is Temple; other stations within walking distance are Embankment, Charing Cross, Covent Garden and Holborn.

Train information may be obtained from here. The nearest national rail stations are Charing Cross, Waterloo & Waterloo East, Blackfriars and City Thameslink.

#### Funds

Limited funds are available to help with travel expenses of participants with no other source of funding. We hope that this will encourage postgraduate students and postdocs to attend the meeting. Please email Clare Dunning (tcd at kent.ac.uk) in advance if you would like to apply for support. A claim form is available here

# 9th South East Mathematical Physics Seminar

The ninth meeting of the South East Mathematical Physics Seminar will be held on Monday 17th July 2017 at King's College London in room K3.11. The meeting is partially supported by supported by a London Mathematical Society Joint Research Groups grant.

There is no registation fee, and no need to register in advance, but currently all visitors to King's are required to sign in at reception, and it would be very helpful and speed matters up if we knew who was coming in advance. Please email Gerard Watts if you are likely to attend.

## Speakers, titles and abstracts

 Mario Collura (Oxford) Non-equilibrium transport in the XXZ spin-1/2 chain: Domain-Wall analytic solution Juan P Garrahan (Nottingham) Boundary driven open quantum chains: fluctuating hydrodynamics, large deviations and hyperuniformity I will consider the problem of quantum chains driven by dissipative interactions at the boundaries - and subject to dissipation at the bulk - in order to study the interplay between coherent and dissipative processes in their transport. I will discuss how dynamics on large scales can be described in terms of fluctuating hydrodynamics, in analogy with what is done in classical exclusion processes. This is an important simplification as it allows to apply the methods of macroscopic fluctuation theory to compute the large deviation statistics of time-integrated currents and dynamical activities. For the case of fermionic chains, singularities in large deviation functions indicate the existence of distinct dynamical phases and phase transitions between them at the fluctuation level, manifested in singular changes in the structure of dynamical trajectories. I will discuss how these results fit more broadly in the application of classical ideas to open quantum non-equilibrium systems. Eva-Maria Graefe (Imperial) PT-symmetric random matrix ensembles using split-quaternionic numbers Random matrices play a crucial role in various fields of mathematics and physics. In particular in the field of quantum chaos Hermitian random matrix ensembles represent universality classes for spectral features of Hamiltonians with classically chaotic counterparts. In recent years the study of non-Hermitian but PT-symmetric quantum systems has attracted a lot of attention. These are non-Hermitian systems that have an anti-unitary symmetry, which is often interpreted as a balance of loss and gain in a system. In this talk the question of whether and how the standard ensembles of Hermitian quantum mechanics can be modified to yield PT-symmetric counterparts is addressed. In particular it is argued that using split-complex and split-quaternionic numbers two new PT-symmetric random matrix ensembles can be constructed. These matrices have either real or complex conjugate eigenvalues, the statistical features of which are analysed for 2 × 2 matrices.

## Practical Information

### Room

The meeting is in room K3.11, on the third floor of the King's building. Here is a map of the campus [the King's building is in red] and a map of the second floor of the King's building

#### Travel

Local travel information may also be found here.

London transport information is available here. The nearest tube station is Temple; other stations within walking distance are Embankment, Charing Cross, Covent Garden and Holborn.

Train information may be obtained from here. The nearest national rail stations are Charing Cross, Waterloo & Waterloo East, Blackfriars and City Thameslink.

#### Funds

Limited funds are available to help with travel expenses of participants with no other source of funding. We hope that this will encourage postgraduate students and postdocs to attend the meeting. Please email Clare Dunning (tcd at kent.ac.uk) in advance if you would like to apply for support. A claim form is available here

# 2nd South East Mathematical Physics Seminar

The second meeting of the South East Mathematical Physics Seminar will be held on Thursday 15th May 2014 at King's College London in room K2.31. The meeting is partially supported by supported by a London Mathematical Society Joint Research Groups grant.
There is no registatrion or fee, but it would be helpful for ordering the right amount of coffee if you could email Gerard Watts if you are likely to go

## Provisional timetable

 11.00 - 11.30 Coffee 11.30 - 12.30 Leron Borsten A magic pyramid of supergravities 12.30 - 13.30 lunch 13.30 - 14.30 Paul Sutcliffe Magnetic vortex rings 14.30 - 15.30 Vidas Regelskis Twisted Yangians for symmetric pairs of types B, C, D 15.30 - 16.00 Tea & Biscuits 16.00 - 16.45 Abera Muhamed Moduli spaces of lumps on the projective plane RP^3 16.45 - 17.30 Craig Lawrie Box Graphs and Singular Fibers

## Speakers, titles and abstracts

Twisted Yangians for symmetric pairs of types B, C, D
 Leron Borsten (Imperial) A magic pyramid of supergravities The octonions occupy a privileged position as the largest of the division algebras A (reals R, complexes C, quaternions H and octonions O) and provide an intuitive basis for the exceptional Lie groups. Efforts to understand the exceptional groups geometrically in terms of octonions resulted in the Freudenthal-Rozenfeld-Tits magic square; a symmetric four-by-four (A1, A2) array of semi-simple Lie algebras. The octonionic row (A1= O, A2 = R, C, H, O) is exceptional: F4, E6, E7, E8. We begin with an elementary introduction to division algebras and magic squares. Then we will give a R, C, H, O description of D = 3 Yang-Mills with N = 1, 2, 4, 8. Tensoring left and right Yang-Mills multiplets yields an array of D = 3 supergravity with N = 2, 3, 4, 5, 6, 8, 9, 10, 12, 16. For N> 8 the multiplets are those of pure supergravity, while for N<9 they are coupled to matter. In both cases the field content is such that the U-dualities exactly match the magic square! We conclude by generalising to D=4,6 and 10 introducing a magic pyramid of Lie algebras, which depends on 3 division algebras, one fixed by spacetime the other two inherited from left/right Yang-Mills theories. Craig Lawrie (KCL) Box Graphs and Singular Fibers We study crepant resolutions of singular elliptically fibered Calabi-Yau fourfolds by analysing the phases of the Coulomb branch of the 3d N=2 gauge theories arising from the compactification of M-theory on the Calabi-Yau. Each phase corresponds to a particular resolution of the singular fourfold and has a description in terms of a 'decorated box graph', or a path on such a graph. The phases are related by deformations of this path, called flops, which correspond to geometric flop transitions between the resolved geometries. Using these techniques we can determine all the resolved geometries and the transitions between them, and we can enumerate the fiber types in codimensions 2 and 3, including new, non-Kodaira, fiber types. Abera Muhamed (Canterbury) Moduli spaces of lumps on the projective plane RP^3 The $$CP^2$$ sigma model is a non-linear field theory possessing topological solitons, called lumps. The energy E and topological degree N satisfying the Bogomolny bound $$E \geq \pi |N|$$, The $$CP^2$$ sigma model can be defined on a Riemann surface. Here we will discuss lumps on the projective plane $$RP^2$$. Then the module space of solutions is given by a subset of rational maps. We first discuss the geometry and topology of rational maps as well as an explicit description. We also discuss the moduli psace of charge three lumps with symmetry in detail. Surprisingly, only three types of symmetry occur, namely axial, dihderal and the non-symmetric Vidas Regelskis (Surrey) In this talk I will present the a class of quantized enveloping algebras, called twisted Yangians, associated with the symmetric pairs of types B, C, D in terms of the Cartan classification of compact Riemannian symmetric spaces. These algebras play an important role in quantum integrable systems with open boundary conditions. They are regarded as coideal subalgebras of the extended Yangian for orthogonal or symplectic Lie algebras, whose defining relations are written in an R-matrix form. On the other hand, these algebras can be presented as quotients of the reflection equation algebra by additional symmetry relations. Paul Sutcliffe (Durham) Magnetic Vortex Rings

## Practical Information

### Room

The meeting is in room K2.31, on the second floor of the King's building. Here is a map of the campus [the King's building is in red] and a map of the second floor of the King's building

#### Travel

Local travel information including maps may be found here.

London transport information is available here. The nearest The station is Temple; other stations in walking distance are Embankment, Charing Cross, Covent Garden and Holborn.

Train information may be obtained from here. The nearest national rail stations are Charing Cross, Waterloo & Waterloo East, Blackfriars and City Thameslink.

#### Funds

Limited funds are available to help with travel expenses of participants with no other source of funding. We hope that this will encourage postgraduate students and postdocs to attend the meeting. Please email Clare Dunning (tcd at kent.ac.uk) in advance if you would like to apply for support.