Forthcoming events in this series


Fri, 10 May 2024

12:00 - 13:15
L3

Chiralization of cluster structures

Mikhail Bershstein
(University of Edinburgh)
Abstract

The chiralization in the title denotes a certain procedure which turns cluster X-varieties into q-W algebras. Many important notions from cluster and q-W worlds, such as mutations, global functions, screening operators, R-matrices, etc emerge naturally in this context. In particular, we discover new bosonizations of q-W algebras and establish connections between previously known bosonizations. If time permits, I will discuss potential applications of our approach to the study of 3d topological theories and local systems with affine gauge groups. This talk is based on a joint project with J. Shiraishi, J.E. Bourgine, B. Feigin, A. Shapiro, and G. Schrader.

Fri, 26 Apr 2024

12:00 - 13:15
L3

On Spectral Data for (2,2) Berry Connections, Difference Equations, and Equivariant Quantum Cohomology

Daniel Zhang
(St John's College)
Abstract

We study supersymmetric Berry connections of 2d N = (2,2) gauged linear sigma models (GLSMs) quantized on a circle, which are periodic monopoles, with the aim to provide a fruitful physical arena for recent mathematical constructions related to the latter. These are difference modules encoding monopole solutions via a Hitchin-Kobayashi correspondence established by Mochizuki. We demonstrate how the difference modules arises naturally by studying the ground states as the cohomology of a one-parameter family of supercharges. In particular, we show how they are related to one kind of monopole spectral data, a deformation of the Cherkis–Kapustin spectral curve, and relate them to the physics of the GLSM. By considering states generated by D-branes and leveraging the difference modules, we derive novel difference equations for brane amplitudes. We then show that in the conformal limit, these degenerate into novel difference equations for hemisphere partition functions, which are exactly calculable. When the GLSM flows to a nonlinear sigma model with Kähler target X, we show that the difference modules are related to deformations of the equivariant quantum cohomology of X.

Fri, 01 Dec 2023

12:00 - 13:15
L3

A compendium of logarithmic corrections in AdS/CFT

Nikolay Bobev
(KU Leuven)
Abstract

I will discuss logarithmic corrections to various CFT partition functions in the context of the AdS4/CFT3 correspondence for theories arising on the worldvolume of M2-branes. I will use four-dimensional gauged supergravity and heat kernel methods and present general expressions for the logarithmic corrections to the gravitational on-shell action or black hole entropy for a number of different supergravity backgrounds. I will outline several subtleties and puzzles in these calculations and contrast them with a similar analysis of logarithmic corrections performed directly in the eleven-dimensional uplift of a given four-dimensional supergravity background. This analysis suggests that four-dimensional supergravity consistent truncations are not the proper setting for studying logarithmic corrections in AdS/CFT. These results have important implications for the existence of scale-separated AdS vacua in string theory and for effective field theory in AdS more generally.

Fri, 17 Nov 2023

12:00 - 13:15
L3

BV formalism in perturbative algebraic quantum field theory

Kasia Rejzner
(York University)
Abstract

In this talk I will review how the BV formalism is used in quantizing theories with local gauge symmetries within the framework of perturbative algebraic quantum field theory. The latter is a mathematically rigorous approach to QFT that combines the locality idea going back to Haag and Kastler with Epstein-Glaser renormalization. In my talk I will also show how these methods can also lead to the construction of a factorization algebra.

Tue, 13 Jun 2023

12:00 - 13:15
L3

Uncovering the Structure of the ε Expansion

Andreas Stergiou
(Kings College London)
Abstract

The ε expansion was invented more than 50 years ago and has been used extensively ever since to study aspects of renormalization group flows and critical phenomena. Its most famous applications are found in theories involving scalar fields in 4−ε dimensions. In this talk, we will discuss the structure of the ε expansion and the fixed points that can be obtained within it. We will mostly focus on scalar theories, but we will also discuss theories with fermions as well as line defects. Our motivation is based on the goal of classifying conformal field theories in d=3 dimensions. We will describe recently discovered universal constraints obtained within the framework of the ε expansion and show that a “heavy handed" quest for fixed points yields a plethora of new ones. These fixed points reveal aspects of the structure of the ε expansion and suggest that a classification of conformal field theories in d=3 is likely to be highly non-trivial.

Tue, 06 Jun 2023

11:00 - 12:00
L4

Renormalization of perturbative quantum gravity

David Prinz
(MPIM Bonn)
Abstract

General Relativity and Quantum Theory are the two main achievements of physics in the 20th century. Even though they have greatly enlarged the physical understanding of our universe, there are still situations which are completely inaccessible to us, most notably the Big Bang and the inside of black holes: These circumstances require a theory of Quantum Gravity — the unification of General Relativity with Quantum Theory. The most natural approach for that would be the application of the astonishingly successful methods of perturbative Quantum Field Theory to the graviton field, defined as the deviation of the metric with respect to a fixed background metric. Unfortunately, this approach seemed impossible due to the non-renormalizable nature of General Relativity. In this talk, I aim to give a pedagogical introduction to this topic, in particular to the Lagrange density, the Feynman graph expansion and the renormalization problem of their associated Feynman integrals. Finally, I will explain how this renormalization problem could be overcome by an infinite tower of gravitational Ward identities, as was established in my dissertation and the articles it is based upon, cf. arXiv:2210.17510 [hep-th].

Tue, 30 May 2023

12:00 - 13:15
L3

Bethe ansatz in 2d conformal field theory

Tomáš Prochazka
(Institute of Physics of the Czech Academy of Sciences)
Abstract

The usual approach to study 2d CFT relies on the Virasoro algebra and its representation theory. Moving away from the criticality, this infinite dimensional symmetry is lost so it is useful to have a look at 2d CFTs from the point of view of more general framework of quantum integrability. Every 2d conformal field theory has a natural infinite dimensional family of commuting higher spin conserved quantities that can be constructed out of Virasoro generators. Perhaps surprisingly two different sets of Bethe ansatz equations are known that diagonalise these. The first one is of Gaudin/Calogero type and was discovered by Bazhanov–Lukyanov–Zamolodchikov in the context of ODE/IM correspondence. The second set is a very natural generalisation of the Bethe ansatz for the Heisenberg XXX spin chain and was found more recently by Litvinov. I will discuss these constructions as well as their relation to W-algebras and the affine Yangian.

Tue, 23 May 2023

12:00 - 13:15
L3

Construction of quantum gauge theories via stochastic quantisation

Ilya Chevyrev
(Edinburgh University)
Abstract

Recent years have seen many new ideas appearing in the solution theories of singular stochastic partial differential equations. An exciting application of SPDEs that is beginning to emerge is to the construction and analysis of quantum field theories. In this talk, I will describe how stochastic quantisation of Parisi–Wu can be used to study QFTs, especially those arising from gauge theories, the rigorous construction of which, even in low dimensions, is largely open.

 

Tue, 16 May 2023

12:00 - 13:15
L3

Abelian Chern-Simons theory on the lattice

Tin Sulejmanpasic
(University of Durham)
Abstract

I will discuss a formulation of an Abelian Chern-Simons theory on the lattice employing the modified Villain formalism. The theory suffers from a well-known problem of having extra zero modes in the Gaussian operator. I will argue that these zero modes are associated with a kind of subsystem symmetry which projects out almost all naive Wilson loops. The operators which survive are framed Wilson loops. These turn out to be topological charges of the associated one-form symmetry, and it has the correct topological spin and correlation functions.

Tue, 09 May 2023

12:00 - 13:15
L3

Virtual fundamental classes and Batalin-Vilkovisky quantization from supersymmetric twists

Pavel Safronov
(Edinburgh University)
Abstract

Supersymmetric localization allows one to reduce the computation of the partition function of a supersymmetric theory to a finite-dimensional integral, but the space over which one integrates is often singular. In this talk I will explain how one can use shifted symplectic geometry to get rigorous definitions of partition functions and state spaces in theories with extended supersymmetry. For instance, this gives a field-theoretic origin of DT invariants of CY4 manifolds. This is a report on joint work with Brian Williams.

Tue, 25 Apr 2023

12:00 - 13:15
L3

Bootstrapping surface defects in the 6d N=(2,0) theories

Carlo Meneghelli
(Università di Parma)
Abstract

6d N=(2,0) superconformal field theories have natural surface operators similar in many ways to Wilson lines in gauge theories. In this talk, I will discuss how they can be studied using conformal bootstrap techniques, including connection to W-algebras and the so-called inversion formula, focusing on the limit of large central charge.

Tue, 07 Feb 2023

12:00 - 13:15
L3

The stochastic analysis of Euclidean QFTs

Massimiliano Gubinelli
(Mathematical Insitute, Oxford)
Abstract

I will report on a research program which uses ideas from stochastic analysis in the context of constructive Euclidean quantum field theory. Stochastic analysis is the study of measures on path spaces via push-forward from Gaussian measures. The foundational example is the map, introduced by Itô, which sends Brownian motion to a diffusion process solution to a stochastic differential equation. Parisi–Wu's stochastic quantisation is the stochastic analysis of an Euclidean quantum field, in the above sense. In this introductory talk, I will put these ideas in context and illustrate various stochastic quantisation procedures and some of the rigorous results one can obtain from them.

Tue, 08 Nov 2022
12:00
Virtual

Bi-twistors, G_2*, and Split-Octonions

Roger Penrose
((Oxford University))

Note: we would recommend to join the meeting using the Zoom client for best user experience.

Abstract

Standard twistor theory involves a complex projective
3-space PT which naturally divides into two halves PT+
and PT, joined by their common 5-real-dimensional
boundary PN. However, this splitting has two quite
different basic physical interpretations, namely
positive/negative helicity and positive/negative
frequency, which ought not to be confused in the
formalism, and the notion of “bi-twistors” is introduced
to resolve this issue. It is found that quantized bi-
twistors have a previously unnoticed G2* structure,
which enables the split-octonion algebra to be directly
formulated in terms of quantized bi-twistors, once the
appropriate complex structure is incorporated.

Tue, 11 Oct 2022
12:00
Virtual

Mathematical reflections on locality

Sylvie Paycha
(Institute of Mathematics University of Potsdam)

Note: we would recommend to join the meeting using the Zoom client for best user experience.

Abstract

Starting from the principle of locality in quantum field theory, which
states that an object is influenced directly only by its immediate

surroundings, I will first briefly review some features of the notion of
locality arising in physics and mathematics. These are then encoded
in  locality relations, given by symmetric binary relations whose graph
consists of pairs of "mutually independent elements".

I will mention challenging questions that arise from  enhancing algebraic
structures to their locality counterparts, such as i) when  is the quotient
of a locality vector space by a linear subspace, a locality vector space, if
equipped with the quotient locality relation,  ii) when does  the locality
tensor product of two locality vector spaces  define a locality vector
space. These are discussed in recent joint work  with Pierre Clavier, Loïc
Foissy and Diego López.

Locality morphisms, namely maps that factorise on   products of  pairs of
"mutually independent" elements, play a key role in the context of
renormalisation in
multiple variables. They include "locality evaluators", which we use to

consistently evaluate meromorphic germs in several variables at
their poles. I will  also report on recent joint work with Li Guo and Bin
Zhang. which gives a classification of locality evaluators on certain
classes of algebras of meromorphic germs.

 

Tue, 14 Jun 2022

12:00 - 13:15
Virtual

Quantum hair and black hole information

Xavier Calmet
(University of Sussex)
Abstract

In this talk, I review some recent results obtained for black holes using
effective field theory methods applied to quantum gravity, in particular the
unique effective action. Black holes are complex thermodynamical objects
that not only have a temperature but also have a pressure. Furthermore, they
have quantum hair which provides a solution to the black hole information
paradox.

Fri, 03 Jun 2022

12:00 - 13:00
L5

Entanglement Measures in Quantum Field Theory: An Approach Based on Symmetry Fields

Olalla Castro Alvaredo
(City University London)
Further Information

Jointly with Relativity

Abstract

In this talk I will review some of the key ideas behind
the study of entanglement measures in 1+1D quantum field theories employing
the so-called branch point twist field approach. This method is based on the
existence of a one-to-one correspondence between different entanglement
measures and different multi-point functions of a particular type of
symmetry field. It is then possible to employ standard methods for the
evaluation of correlation functions to understand properties of entanglement
in bipartite systems. Time permitting, I will then present a recent
application of this approach to the study of a new entanglement measure: the
symmetry resolved entanglement entropy.

Tue, 31 May 2022

12:00 - 13:15
Virtual

Implementing Bogoliubov transformations beyond the Shale-Stinespring condition

Sascha Lill
(University of Tuebingen and BCAM Bilbao)
Abstract

Quantum many–body systems can be mathematically described by vectors in a certain Hilbert space, the so–called Fock space, whose Schroedinger dynamics are generated by a self–adjoint Hamiltonian operator H. Bogoliubov transformations are a convenient way to manipulate H while keeping the physical predictions in- variant. They have found widespread use for analyzing the dynamics of quantum many–body systems and justifying simplified models that have been heuristically derived by physicists.

In the 1960s, Shale and Stinespring derived a necessary and sufficient condition for when a Bogoliubov transformation is implementable on Fock space, i.e. for when there exists a unitary operator U such that the manipulated Hamiltonian takes the form U*HU. However, non–implementable Bogoliubov transformations appear frequently in the literature for systems of infinite size.

In this talk, we therefore construct two extensions of the Fock space on which certain Bogoliubov transformations become implementable, although they violate the Shale–Stinespring condition.

Tue, 10 May 2022

12:00 - 13:15
Virtual

From dS to AdS, and back

Charlotte Sleight
(Univeristy of Durham)
Abstract

In the search for a complete description of quantum mechanical and
gravitational phenomena, we are inevitably led to consider observables on
boundaries at infinity. This is the common mantra that there are no local
observables in quantum gravity and gives rise to the tantalising possibility
of a purely boundary--or holographic--description of physics in the
interior. The AdS/CFT correspondence provides an important working example
of these ideas, where the boundary description of quantum gravity in anti-de
Sitter (AdS) space is an ordinary quantum mechanical system-- in particular,
a Lorentzian Conformal Field Theory (CFT)--where the rules of the game are
well understood. It would be desirable to have a similar level of
understanding for the universe we actually live in. In this talk I will
explain some recent efforts that aim to understand the rules of the game for
observables on the future boundary of de Sitter (dS) space. Unlike in AdS,
the boundaries of dS space are purely spatial with no standard notion of
locality and time. This obscures how the boundary observables capture a
consistent picture of unitary time evolution in the interior of dS space. I

will explain how, despite this difference, the structural similarities
between dS and AdS spaces allow to forge relations between boundary
correlators in these two space-times. These can be used to import
techniques, results and understanding from AdS to dS.

 

 

Tue, 26 Apr 2022

12:00 - 13:00
L3

What is the iε for the S-matrix?

Holmfridur S. Hannesdottir
(IAS Princeton)
Abstract

Can the S-matrix be complexified in a way consistent with causality? Since the 1960's, the affirmative answer to this question has been well-understood for 2→2 scattering of the lightest particle in theories with a mass gap at low momentum transfer, where the S-matrix is analytic everywhere except at normal-threshold branch cuts. We ask whether an analogous picture extends to realistic theories, such as the Standard Model, that include massless fields, UV/IR divergences, and unstable particles. Especially in the presence of light states running in the loops, the traditional iε prescription for approaching physical regions might break down, because causality requirements for the individual Feynman diagrams can be mutually incompatible. We demonstrate that such analyticity problems are not in contradiction with unitarity. Instead, they should be thought of as finite-width effects that disappear in the idealized 2→2 scattering amplitudes with no unstable particles, but might persist at higher multiplicity. To fix these issues, we propose an iε-like prescription for deforming branch cuts in the space of Mandelstam invariants without modifying the analytic properties. This procedure results in a complex strip around the real part of the kinematic space, where the S-matrix remains causal. To help with the investigation of related questions, we introduce holomorphic cutting rules, new approaches to dispersion relations, as well as formulae for local behavior of Feynman integrals near branch points, all of which are illustrated on explicit examples.

Tue, 22 Feb 2022
12:00
Virtual

Anomalous boundaries of topological matter

Guo Chuan Thiang
(University of Peking)
Abstract

A topological insulator has anomalous boundary spectrum which completely fills up gaps in the bulk spectrum. This ``topologically protected’’ spectral property is a physical manifestation of coarse geometry and index theory ideas. Special examples involve spectral flow and gerbes, related to Hamiltonian anomalies, and they arise experimentally in quantum Hall systems, time-reversal invariant mod-2 insulators, and shallow-water waves.

Tue, 15 Feb 2022
12:00
Virtual

Gravitational entropy and the flatness, homogeneity and isotropy puzzles

Neil Turok
(University of Edinburgh and Perimeter Institute)
Abstract

I’ll review a new, simpler explanation for the large-scale properties of the
cosmos, presented with L. Boyle in our recent preprint arXiv:2201.07279. The
basic ingredients are elementary and well-known, namely Einstein’s theory of
gravity and Hawking’s method of computing gravitational entropy. The new
twist is provided by the boundary conditions we proposed for big bang-type
singularities, allowing conformal zeros but imposing CPT symmetry and

analyticity at the bang. These boundary conditions, which have significant
overlap with Penrose’s Weyl curvature hypothesis, allow gravitational
instantons for universes with Lambda, massless radiation and space
curvature, of either sign, from which we are able to infer a gravitational
entropy. We find the gravitational entropy can exceed the de Sitter entropy
and that, to the extent that it does, the most probable large-scale geometry
for the universe is flat, homogeneous and isotropic. I will briefly
summarise our earlier work showing how the gauge-fermion Lagrangian of the
standard model may be reconciled with Weyl symmetry and a small cosmological
constant, at leading order, provided there are precisely three generations
of fermions. The same mechanism generates scale-invariant primordial
perturbations. The cosmic dark matter consists of a right-handed neutrino.
In summary, we have taken significant steps towards a new, highly principled
and testable theory of cosmology.

Tue, 18 Jan 2022
12:00
Virtual

Symmetry protected topological (SPT) phases of quasifree gapped ground states and coarse geometry

Chris Bourne
(Tohoku University and RIKEN)
Abstract

Symmetry protected topological (SPT) phases have recently attracted a lot of
attention from physicists and mathematicians as a topological classification
scheme for gapped ground states. In this talk I will briefly introduce the
operator algebraic approach to SPT phases in the infinite-volume limit. In
particular, I will focus on the quasifree (free-fermionic) setting, where we

can adapt tools from algebraic quantum field theory to describe phases of
gapped ground states using K-homology and the coarse index.

Tue, 23 Nov 2021
12:00
Virtual

Wick rotation and the axiomatisation of quantum field theory

Graeme Segal
Abstract

I shall present joint work with Maxim Kontsevich describing an interesting
domain of complex metrics on a smooth manifold. It is a complexification of
the space of ordinary Riemannian metrics, and has the Lorentzian metrics
(but not metrics of other signatures) on its boundary. Use of the domain
leads to a modified axiom system for QFT which illuminates not only the
special role of Lorentz signature, but also of features such as local
commutativity, unitarity, and global hyperbolicity.