Past Mathematical Physics Journal Club

Two different, almost orthogonal approaches to QFT are: (1) the study of von Neumann algebras of local observables in flat space, and (2) the study of extended and topological defects in general spacetime manifolds. While naively the two focus on different aspects, it has been recently pointed out that some of the axioms of approach (1) clash with certain expectations from approach (2). In this JC talk, I’ll give a brief introduction to both approaches and review the recent discussion in [2008.11748], [2503.20863], and [2509.03589], explaining (i) what the tensions are, (ii) a recent proposal to solve them, and (iii) why it can be useful.

In this talk we will construct a basis of quantum gravity states by cutting the Euclidean path integral. These states are made by inserting heavy dust shell operators on the asymptotic boundary. We will use this basis to resolve two puzzles : 

(1) The two boundary gravity Hilbert space seemingly does not factorise, which is in tension with holography. 

(2) Gibbons and Hawking proposed the gravity thermal partition function is computed by the euclidean path integral with a periodic time boundary condition. Why is does this perform a trace over gravity states?

To resolve these puzzles we will introduce some tricks that simply the evaluation of the gravity path integral in the saddle point approximation. 

Abstract: This talk introduces the ZX-calculus, a powerful graphical language for reasoning about quantum computations. I will start with an overview of process theories, a general framework for describing how processes act upon different types of information. I then focus on the process theory of quantum circuits, where each function (or gate) is a unitary linear transformation acting upon qubits. The ZX-calculus simplifies the set of available gates in terms of two atomic operations: Z and X spiders, which generalize rotations around the Z and X axes of the Bloch sphere. I demonstrate how to translate quantum circuits into ZX-diagrams and how to simplify ZX diagrams using a set of seven equivalences. Through examples and illustrations, I hope to convey that the ZX-calculus provides an intuitive and powerful tool for reasoning about quantum computations, allowing for the derivation of equivalences between circuits. By the end of the talk listeners should be able to understand equations written in the ZX-calculus and potentially use them in their own work.

The rise to fame of supersymmetry since the 1970s shook the world. It held much promise—from explaining naturalness, unifying fundamental forces, to being the ideal candidate for dark matter. But since the LHC (arguably even a bit before that), many of these dreams have been shattered by experiments. Today, the pursuit of supersymmetric theories by the physics community is a mere shadow of its former self.

This symposium is not to discuss whether supersymmetry is useful in the fields of physics and mathematics—it clearly is. Rather, this is a debate about whether its death is natural. We’ve had a crack at it for half a century. Is this the limit of what we can do? Are we any closer to achieving the original goals we set out? Is the death premature, accelerated by a negative campaign from SUSY critics? Or is it the other way around—has it been at death’s door for decades, kept alive only because authoritative figures cannot let go?

Twenty years ago, this wouldn’t even be a debate. Twenty years from now, there may not be any young people working on SUSY at all. This seems like the right time to talk.

String-inspired methods have revealed deep connections between seemingly unrelated field theories. A striking example is the double copy structure, rooted in the string theory Kawai–Lewellen–Tye (KLT) relations. In this talk, we will explore how a variety of theories—including colored scalars, pions, and gluons—emerge from a single, unifying object: the KLT kernel. We will argue that this kernel is not only a powerful computational tool, but also a conceptually rich structure worthy of independent study.

Based mainly on https://arxiv.org/abs/1610.04230 and the recent work https://arxiv.org/abs/2505.01501.

In recent meetings of the journal club, two constructions that have been
discussed are Mellin transforms and chord diagrams. In my talk, I will
continue that thread and review  how a Mellin transform describes the
insertion of subgraphs into Feynman integrals. This operation comes up
in various contexts, as a concrete example, I will show how to compute
the infinite sum of rainbow diagrams in phi^3 theory in 6 dimensions. On
a combinatorial level, the procedure can be encoded by chord diagrams,
or by tubings of rooted trees, which I will mention in passing.
The talk is loosely based on doi 10.1112/jlms.70006 .
 

Recently, work has been done to understand higher-form symmetries in linear gravity. Just like Maxwell theory, which has both electric and magnetic U(1) higher form symmetries, linearised gravity exhibits analogous structure. The authors of
[https://arxiv.org/pdf/2409.00178] investigate electric and magnetic higher form symmetries in linearised gravity, which correspond to shift symmetries of the graviton and the dual graviton respectively. By attempting to gauge the two symmetries, the authors investigate the mixed ’t Hooft anomalies anomaly structure of linearised gravity. Furthermore, if a specific shift symmetry is considered, the corresponding charges are related to Roger Penrose's quasi-local charge construction.

Based on: [https://arxiv.org/pdf/2410.08720][https://arxiv.org/pdf/2409.00178][https://arxiv.org/pdf/2401.17361]

This brief pedagogical talk introduces key concepts of Carroll geometries, which arise as the limit of relativistic spacetimes in the vanishing speed of light regime. In this limit, light cones collapse along a timelike direction, resulting in a manifold equipped with a degenerate metric. Consequently, physics in such spacetimes exhibits peculiar properties. Despite this, the Carroll contraction is relevant to a wide range of applications, from flat-space holography to condensed matter physics. To complement this introduction, and depending on the audience’s interests, I can discuss Carroll affine connections, symmetry groups, conservation laws, and Carroll-invariant field theories.

The time evolution of quantum matter systems toward their thermal equilibria, characterized by their entanglement entropy (EE), is a question that permeates many areas of modern physics. The dynamic of EE in generic chaotic many-body systems has an effective description in terms of a minimal membrane described by its membrane tension function. For strongly coupled systems with a gravity dual, the membrane tension can be obtained by projecting the bulk Hubeny-Rangamani-Ryu-Takayanagi (HRT) surfaces to the boundary along constant infalling time. In this talk, I will introduce the membrane theory of entanglement dynamics, its generalization to 2d CFT, as well as several applications. Based on arXiv: 1803.10244 and arXiv: 2411.16542.

It was recently argued that topological operators (at least those associated with continuous symmetries) need regularization. However, such regularization seems to be ill-defined when the underlying QFT is coupled to gravity. If both of these claims are correct, it means that charges cannot be meaningfully measured in the presence of gravity. I will review the evidence supporting these claims as discussed in [arXiv:2411.08858]. Given the audience's high level of expertise, I hope this will spark discussion about whether this is a promising approach to understanding the fate of global symmetries in quantum gravity.

Black holes play a central role in our understanding of quantum gravity, but identifying their precise counterparts in a dual QFT remains a tricky business. These states are heavy, chaotic, and encode various universal aspects — but are also notoriously hard to characterise. In this talk, we’ll explore how supersymmetric field theories provide a controlled setting to study black hole states. In particular, we’ll introduce the idea of fortuitous states as a useful criterion for identifying BPS black hole states. We’ll then illustrate this concept with concrete examples, including the (supersymmetric) SYK model and the D1-D5 CFT.

The discussion will be based on the following recent papers:
arXiv:2402.10129, arXiv:2412.06902, and arXiv:2501.05448.

 While extremal black hole microstates are reproduced by index calculations, the study of near-BPS black holes requires special care to account for quantum fluctuations. A semiclassical analysis indicates that the spectrum of such black holes has a large extremal degeneracy followed by a mass gap up to a continuum of non-BPS states. The inclusion of a theta angle term alters the properties of the spectrum (Witten effect shifting the mass gap and mixed 't Hooft anomaly). This journal club will study two papers by Toldo and Heydeman, [2412.03695] and [2412.03697] where they study 4d near-BPS black holes. As we shall see, a key point of their derivation is the reduction to 2d JT gravity. The dual CFTs are ABJM and some class R (non lagrangian) theories. Since these theories are strongly coupled, the gravity analysis offers a powerful tool to describe their specturm at finite temperature.

Abelian gauge theories in 2+1 dimensions are very interesting QFTs: they are strongly coupled and exhibit non-trivial dynamics. However, they are somewhat more tractable than non-Abelian theories in 3+1 dimensions. In this talk, I will first review the known properties of fermions in 2+1 dimensions and some conjectures about QED_3 with a single Dirac fermion. I will then present the recent proposal from [arXiv:2409.17913] regarding the phase diagram of QED_3 with two fermions. The findings reveal surprising (yet compelling) features: while semiclassical analysis would suggest two trivially gapped phases and a single phase transition, the actual dynamics indicate the presence of two distinct phase transitions separated by a "quantum phase." This intermediate phase exists over a finite range of parameters in the strong coupling regime and is not visible semiclassically. Moreover, these phase transitions are second-order and exhibit symmetry enhancement. The proposal is supported by several non-trivial checks and is consistent with results from numerical bootstrap, lattice simulations, and extrapolations from the large-Nf expansion.

Measurement-Based Quantum Computation (MBQC) is a model of quantum computation driven by measurements instead of unitary gates.   In 2D it is capable of supporting universal quantum computations.   Interestingly, while all measurements are local, the computational output involves non local observables.   We will use the simpler case of 1D MBQC to illustrate how these features can be captured by ideas from gauge theory and extended TQFT. We will also explain  MBQC from the perspective of the extended Hilbert space construction in gauge theories, in which the entanglement edge modes play the role of the logical qubit.

Since Hawking first discovered that black holes radiate, the evaporation of black holes has been a subject of great interest. In this talk, based on [2411.03447], we review some recent results about the evaporation of charged (Reissner-Nordström) black holes. We consider in particular the difference between neutral and charged particle emission, and explain how this drives the black hole near extremality, as well as how evaporation is then changed in that limit.

I will discuss the preprint arXiv:2409.18130 describing an interesting connection between 4d N=2 SCFTs and 2d chiral CFTs (alias: Vertex Operator Algebras) by way of 3d EFTs.

Celestial holography posits that the 4D S-matrix may be calculated holographically by a 2D conformal field theory. However, bulk translation invariance forces low-point massless celestial amplitudes to be distributional, which is an unusual property for a 2D CFT. In this talk, I show that translation-invariant MHV gluon amplitudes can be extracted from smooth 'leaf' amplitudes, where a bulk interaction vertex is integrated only over a hyperbolic slice of spacetime. After describing gluon leaf amplitudes' soft and collinear limits, I will show that MHV leaf amplitudes can be generated by a simple 2D system of free fermions and the semiclassical limit of Liouville theory, showing that translation-invariant, distributional amplitudes can be obtained from smooth correlation functions. An important step is showing that, in the semiclassical limit of Liouville theory, correlation functions of light operators are given by contact AdS Witten diagrams. This talk is based on a series of papers with Atul Sharma, Andrew Strominger, and Tianli Wang [2312.07820, 2402.04150,2403.18896]. 

Abstract: I will introduce and explain a new symmetry structure for type IIA string theory, called string^h. Using string^h I will explain  how some objects of stable homotopy theory relating to elliptic cohomology enter into type IIA string theory.

I will review recent progess on a topic of common interest to many
physicists https://www.arxiv.org/abs/2410.12043. Time permitting, I will
also comment about new sum rules for protected operators along RG flows:
https://arxiv.org/pdf/2409.09006. 

One recent(ish) development in classical black hole thermodynamics is the inclusion of vacuum energy (cosmological constant) in the form of thermodynamic pressure. New thermodynamic phase transitions emerge in this extended phase space, beyond the usual Hawking—Page transition. This allows us to understand black holes from the viewpoint of chemistry in terms of concepts such as Van Der Waals fluids, reentrant phase transitions and triple points. I will review these developments and discuss the dictionary between the bulk laws and those of the dual CFT.