Academic Year 2018/2019

In the semiclassical quantization of 4D N=2 super-Yang-Mills, (framed) BPS states are represented by zeromode wavefunctions of certain Dirac-like operators on the moduli space of (singular) monopoles. A direct analysis of these Dirac operators utilizing the asymptotic metric on monopole moduli space leads to a physically intuitive derivation of the primitive wall-crossing formula for BPS states. The derivation holds modulo a technical assumption about the Fredholm properties of these operators. Proving this assumption and showing how it must be modified in the non-primitive case is an open problem that makes contact with recent developments in the mathematics literature on compactifications of monopole moduli spaces on manifolds with corners. Additionally, the physics derivation leads to a surprising prediction: the existence of completely stable non-BPS boundstates. This talk is based on work done in collaboration with Greg Moore and Daniel Brennan.

The algebraic Bethe ansatz provides a method for constructing eigenvectors for integrable transfer matrices, facilitating the solution of a variety of systems, including lattice models and spin chains. In this seminar, I study the spectral problem for the open spin chain with 'soliton non-preserving boundary conditions', a boundary type which interchanges particles and anti-particles. I will describe the underlying twisted Yangian algebra of the spin chain, and explain how, upon performing the nesting process, the problem of diagonalisation of its transfer matrix reduces to that of a periodic spin chain.

The study of dynamics and relaxation in quantum many-body systems is one of the main challenges of modern theoretical physics. While a large amount of intuition has been drawn from weakly interacting systems, linear response theory or semiclassical approximations, the dynamics of strongly interacting systems remains largely unexplored. We study the far-from-equilibrium dynamics of an interacting Quantum Field Theory, the sine-Gordon model. Using a combination of numerical and analytical techniques, we demonstrate some unexpected effects in the dynamics of correlations that can be explained by the topological nature of sine-Gordon excitations.

The linchpin of nAdS2/nCFT1 is the non-linear realization of symmetries, where the conformal symmetry of AdS2 is spontaneously broken and also broken by an anomaly. In this talk I'll discuss 3 new corners of this correspondence that are relevant for the holographic description of near-extremal black holes. The first corner is related to rotating black holes; the second corner relates to role of gravitational anomalies in nAdS2 holography; and finally, how the logarithmic corrections to black hole entropy reveal interesting features.

The compactified Ruijsenaars-Schneider (RS) models are obtained from the standard RS (aka relativistic Calogero-Sutherland) systems by Wick rotation. Models with trigonometric potentials describe particles moving along a circle with a pairwise interaction that depends on the chord distance. Moreover, the compactified Hamiltonians are periodic not only in the position variables, but also in the momenta. A surprising fact is that there are two dramatically different types of dynamics, distinguished by the value of the coupling parameter. For certain couplings (which we call type 1), particle distances have lower (and upper) bounds, while other (type 2) couplings allow particle collisions to happen resulting in a more complicated dynamics. We will present the global phase space and quantization of models with type 1 couplings. Based on joint work with László Fehér and Martin Hallnäs.

In this talk, I will define conformal and supersymmetric quantum mechanics, giving geometric interpretations for both. In order for these symmetries to give a superconformal quantum mechanics (with N=(4,4) supersymmetry), it is necessary that the target space is a hyperKähler cone. This leads to problems due to singularities that appear on all non-trivial such cones. I will show how to deal with these singularities and compute a protected part of the spectrum using a superconformal index. This index has limits that compute the homology, the coordinate ring and the index of fixed point manifolds of the space. Issues about the dependence on the choice of regularisation and wall crossing will be discussed.

I will describe some recent work illustrating the relation between hydrodynamic and chaotic properties of quantum field theories with holographic duals. Retarded Green's functions capture the causal response of quantum field theories to small external sources, and I will firstly show how a simple analysis of perturbations near black hole horizons can be used to provide interesting constraints on the forms of these Green's functions in holographic theories. I will use this analysis to prove that the chaotic properties of holographic systems are imprinted in a characteristic way on the retarded Green's function of energy density, and that as a consequence these chaotic properties govern the thermal diffusivity of holographic systems at low temperatures.

We investigate all warped AdS_4 x M^{D-4} and AdS_3 x M^{D-3} backgrounds with the most general allowed fluxes that preserve more than 16 supersymmetries in D=10- and 11-dimensional supergravities. Assuming either that the internal manifold is compact without boundary or that the isometry algebra of the background decomposes into that of AdS4/AdS3 and that of the transverse space, we find that there are no AdS4 backgrounds in IIB supergravity. Similarly, in IIA supergravity, we find a unique such background with 24 supersymmetries, locally isometric to AdS4 x CP^3, and in D=11 all such backgrounds are locally isometric to the maximally supersymmetric AdS4 x S^7 solution. Finally, we establish a non-existence theorem for AdS3 solutions preserving strictly more than 16 supersymmetries.

In this talk I will show that multiplicative lambda-brackets provide a convenient framework to study differential-difference equations. The main application is to the theory of q-deformations of W-algebras.

Newton-Cartan (NC) geometry was introduced more than 90 years ago in order to find a geometric formulation of Newtonian gravity. This geometry (including a novel generalisation that includes torsion) has in recent years gained renewed interest as it appears in a variety of settings in modern theory involving gravity, string theory and holography. After a brief introduction, I will talk about recent work on an action principle for non-relativistic gravity, including its Newtonian limit. This requires a new notion of NC geometry, which naturally arises in a covariant 1/c expansion of general relativity, with c being the speed of light. By truncating this expansion at subleading order, we obtain the field content and transformation rules of the fields that appear in the action of Newtonian gravity. The equations of motion generalize Newtonian gravity by allowing for the effect of gravitational time dilation due to strong gravitational field. I will also discuss the relevance of non-relativistic geometry in connection to non-relativistric string theory and holography. In particular, I will show that non-relativistic strings and geometry appear in certain limits of the the AdS/CFT correspondence.

In this talk, we will consider 2d field theories invariant under the BMS algebra, putatively dual to 3d Minkowski spacetimes and discuss the notion of a version of modular invariance in these theories. We will revisit the derivation of the BMS-Cardy formula and its reproduction of the entropy of cosmological horizons in flat space. We would then discuss in detail the construction of highest weight characters for these 2d field theories.

Moduli space of doubly periodic monopoles, also called Monowalls, are hyperkaehler spaces of ALH-type. In the first part of the talk we describe the work of Rebekah Cross, who computed their asymptotic metric, via effective electromagnetic interaction, and expressed its Kaehler potential in therms of a single function given by the volume cut out by an associated plane arrangement. In the second part of the talk we discuss the compactification of this moduli space and the use of hyperfields for this purpose.

Motivated by the problem of defining the entanglement entropy of the graviton, we study the division of the phase space of general relativity across subregions. Our key requirement is demanding that the separation into subregions is imaginary---i.e., that entangling surfaces are not physical. This translates into a certain condition on the symplectic form. We find that gravitational subregions that satisfy this condition are bounded by surfaces of extremal area. We characterise the 'centre variables' of the phase space of the graviton in such subsystems, which can be taken to be the conformal class of the induced metric in the boundary, subject to a constraint involving the traceless part of the extrinsic curvature. We argue that this condition works to discard local deformations of the boundary surface to infinitesimally nearby extremal surfaces, that are otherwise available for generic codimension-2 extremal surfaces of dimension ≥ 2.

I'll describe how the BV-formalism maps classical field theories to strong homotopy Lie algebras and how quasi-isomorphisms between these capture field theory equivalence. This map explains in particular the recent renewed interest in strong homotopy Lie algebras. I point out the connection to higher Chern-Simons theory and finish by talking about some applications.

Magnetic skyrmions are topological solitons which occur in a large class of ferromagnetic materials and which are currently attracting much attention in the condensed matter community. The talk is about an integrable model for magnetic skyrmions, introduced in a recent paper with Bruno Barton-Singer and Calum Ross. Solutions can be written in terms of a fixed anti-holomorphic and an arbitrary holomorphic function. I will explain the model and the geometry behind, and exhibit some of the solutions.

Linear perturbations of extremal black holes exhibit the Aretakis instability, in which higher derivatives of the fields grow polynomially with time along the event horizon. Near-extremal black holes display similar behavior for some time, and eventually decay exponentially through quasinormal modes. In the talk I will show that the above behaviors are dictated by the conformal symmetry of the near-horizon region of such black holes. I will then discuss the significance of backreaction in the problem, and show how it can be simply accounted for within the near-horizon picture.

What are the possible classical symmetries of space and time? I will discuss a partial answer to this question by explaining a classification of simply-connected homogeneous spatially isotropic spacetimes obtained recently in collaboration with Stefan Prohazka. The talk will focus on the main results and not so much on the details of how they were obtained. I will also comment on some BMS-like algebras of symmetries of some of these spacetimes. That is based on recent work with Stefan and Ross Grassie.

During the breathing-like behaviour of chiral skyrmions and antiskyrmions in ferromagnets the core of the spin structure periodically grows and shrinks in time. We present a Hamiltonian formulation for magnetization dynamics in collective coordinates and derive from it a single mode approximation for the breathing behaviour, where skyrmions and antiskyrmions obey the same dynamical equations. The analysis is supported by comparison to full micromagnetic simulations of the Landau-Lifshitz-Gilbert field equation. We identify two regimes with different kinds of breathing oscillations and derive the periods and amplitudes for both. The motion can be understood intuitively from the view of an effective energy landscape. In a high energy rotating regime the spin structure breathes along with a non-uniform precession of the skyrmion phase along with a linear energy dissipation on average. In comparison in the low energy oscillatory regime the skyrmion phase does not precess but oscillates around the stable equilibrium and we find an exponential energy decay associated with damped harmonic oscillations. This is loosely analogous to a damped pendulum that fully rotates around its suspension point until it eventually does not possess enough energy to fully rotate past the “upside-down” unstable fixed point and thereafter only oscillates back and forth.

Hydrodynamics is a powerful framework for describing the large-scale behaviours of many-body systems in inhomogeneous, non-stationary states. Until recently, however, it was restricted to non-integrable models, as the assumption of local thermodynamic equilibrium is broken by the large amount of conserved charges afforded by integrability. I will describe how to generalise hydrodynamics to integrable systems. The resulting theory has a rich structure, and applies to large families of quantum and classical field theories, chains and gases. It allows us to solve experimentally relevant setups such as the famous ``quantum Newton's cradle" in cold atomic gases, and to evaluate exact non-equilibrium currents, correlations, Drude weights and full counting statistics of fluctuations in non-equilibrium transport. If time permits, I will explain the latter, which is based on new very general developments showing how linear fluctuating hydrodynamics gives access to the exact large deviation theory of ballistic transport.

Just as ordinary global symmetries are associated with a conserved particle number, quantum field theories with generalized global symmetries have a conserved density of higher-dimensional objects (such as strings, branes, etc.). I will discuss the emergence of gapless Goldstone modes when such a symmetry is spontaneously broken and will review how such a generalized symmetry plays an important role in characterizing the long-distance physics of familiar Maxwell electrodynamics in four dimensions. Many structures of ordinary symmetries admit a higher-form generalization; I will discuss some of these, focusing on the 4d analogues of familiar 2d concepts such as bosonization and (Abelian) Kac-Moody algebras. If time permits I will discuss the holographic realizations of such higher-form symmetries for field theories with gravity duals.

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In this talk I will consider N=4 SYM in the presence of a codimension 1 defect. This defect CFT is dual to a certain probe D3-D5 brane set-up. I will introduce a framework for quantum computations in this non-trivial dCFT and use it to compute one- and two-point functions. I will discuss the tree-level and one-loop computations to the one-point function of the BPS vacuum state, finding perfect agreement with an earlier string-theory prediction. Second I will discuss two-point functions and their relation to the boundary conformal bootstrap equations and three-point functions in N=4 SYM.

In 2005, Wolfgang Rump discovered some connections between noncommutative ring theory and set theoretic solutions of the quantum Yang-Baxter equation. In particular, he showed that every nilpotent ring gives a highly non-trivial solution to the Yang-Baxter equation. In the first part of this talk we will present the introduction to this research area and explain how to obtain set-theoretic solutions from nilpotent rings, using Rump's theorems. In the second part we will present new solutions of the Reflection Equation. Our solutions work for both set-theoretic and parameter dependent solutions of the Reflection Equation and are obtained from nilpotent rings. This is a joint work with with Robert Weston and Leandro Vendramin.

The classical motion of a string in AdS_3 spacetime is governed by the generalized sinh-Gordon theory. This theory has singular soliton solutions which correspond to cusps on the string. In this talk, I examine string solutions where such cusps are classically pair-produced. For the calculations, I use an exact discretization of the equation of motion. If time permits, I will also discuss some recent results.

I will describe holographic duals to topologically twisted gauge theories on Riemannian four- and three-manifolds. Imposing boundary conditions for the supergravity fields corresponding to the topological twists, the renormalised supergravity action is independent of the choice of boundary metric. Under additional regularity assumptions, the on-shell action can be evaluated and shown to always vanish, which provides a prediction for the large N limit of topologically twisted theories.

Ambitwistor strings are chiral worldsheet theories that correspond to a field theory on their target space. On flat space, they provide the theoretical framework in which to understand the `scattering equations’ approach to amplitudes in massless field theories pioneered by Cachazo, He and Yuan. These strings are consistent whenever the background space-time obeys Einstein’s equations, so in principle can also be used to resum supergravity Witten diagrams in AdS. I report on progress in this direction, seeking an explicit form for the `AdS scattering equations’.

In the first part of the talk I will introduce the formalism of non-equilibrium EFT and show how it provides a unified field theory description of the low-energy behavior of systems in local thermal equilibrium. I will then describe recent progress showing consistency with unitarity and causality at (perturbative) quantum level. In the second part of the talk I will discuss effective theory for Floquet systems, which do not possess any strict notion of equilibrium. I will show how one can adapt the general approach of non-equilibrium EFT to describe topological response of such systems.

TBA

Conformal field theories with higher spin currents have been known to govern type II string dynamics in exceptional holonomy manifolds since the work of Shatashvili and Vafa. From a nonlinear sigma-model viewpoint, the reduction of holonomy yields chiral symmetries extending (1,1) supersymmetry. I will generalise this result to generic (1,0) models with Fermi superfields, appropriate in particular for heterotic compactifications. I will then comment on anomalies of these symmetries, as a first step to bridge the gap between target space geometry and abstract conformal field theory. Based on 1809.01138.

When M5 branes are placed in an A type ALE background there are tensionless strings which arise each time 2 or more M5 branes coincide. The system has no low energy Lagrangian description and new techniques need to be applied in order to figure out the relevant physics of such coincident M5 branes. The world volume theory on the M5 branes has (0,1) supersymmetry in 6 dimensions with massless vector, tensor and hyper multiplets. There are two branches on the moduli space of vacuum configurations where scalar fields in tensor and hyper multiplets receive VEVs, respectively. In this talk we will focus on the Higgs branch of the low energy theory and find new and fairly surprising results. Each time there is a new tensionless string, there is a new Higgs branch, thus the theory has a multitude of Higgs branches depending on the types of tensionless strings in the spectrum. There are two main effects: “discrete gauging” and “small instanton transitions” (when one extends beyond A type) and a need to efficiently describe the so many Higgs branches which arise. The main tool is the Coulomb branch of 3d N=4 gauge theories, which has been studied intensively by many of my collaborators.

Quantum integrability is typically underpinned by factorizability criteria (say, of a scattering process). Away from boundaries this is the Yang-Baxter equation, a cubic relation which is intimately connected to certain bialgebras known as affine quantum groups and their representations. In the presence of a boundary, a quartic relation known as the reflection equation is the natural analogue. It arises naturally in the representation theory of certain pairs (affine quantum group, coideal subalgebra). We will survey this and highlight some recent work: the classification of solutions in the case of quantum affine sl_N (joint work with V. Regelskis). We will also outline some work in progress about the axiomatic characterization and construction of so-called universal solutions (joint with R. Weston and A. Appel, respectively).