Past Mathematical Physics Journal Club

Quantum field theory is hard for several reasons, for example one can rarely compute perturbation series (=Feynman integrals) at large loop order, and even if you can, the series diverges. Conversely, intrinsically non-perturbative approaches like the functional renormalization group require approximations that are often not easy to control, or have unclear relations to perturbative computations.
Tropical field theory is a new approach for solving these issues for a generic theory without restricting to unphysical boundary cases. It keeps almost all qualitative and combinatorial features of perturbative QFT (in particular all non-planar diagrams, renormalization, relative numerical importance of Feynman integrals, and divergence of perturbation series), while at the same time reducing the analytic complexity, and establishing a rigorous connection to non-perturbative functional/path integral methods of QFT. Based on 2512.21091 with Erik.

Negative-form symmetries arise when one extends the usual p-form dictionary below ordinary zero-form symmetries. Conceptually, however, they are different: the action of (-n)-form symmetries on a QFT modifies the parameters or background data that defines the QFT, as opposed to acting on the extended operators of the theory. For example, (-1)-form symmetries are implemented by spacetime-filling topological operators that act on a theory by shifting its theta-angle. I will review recent work arxiv:2606.05543 that has begun to develop the machinery of (-2)-form symmetries, which act of a QFT by modifying the anomaly inflow data – equivalently the SymTFT action – thereby relating QFTs whose ordinary global symmetries differ by anomaly data.

Global symmetries have been generalized to non-invertible ones. For finite symmetries in $(1+1)$d, these are known as unitary fusion category symmetries. One natural question is: which fusion categories can arise as symmetries on a lattice? 
Progress has been made including the anyon chains, which realizes any fusion category symmetries. However, their Hilbert spaces do not admit the usual tensor product structure (tensor product of local Hilbert spaces over each site).
In [arxiv:2507.05185], Evans and Jones introduced an operator-algebraic framework and showed that a fusion category symmetry can be realized on a tensor product quasi-local algebra if and only if it is "integral". After reviewing this result, I will discuss a recent extension by Bunner and Jones [arxiv:2605.21327], who showed that this constraint disappears after stabilization with infinite-dimensional ancilla spaces on anyon chains. As a consequence, every unitary fusion category can be realized on tensor product Hilbert spaces.

Quantum magic quantifies the computational resources needed for quantum operations that cannot be easily performed classically. This requires unitaries, known as "Non-Clifford gates", that map Pauli operators to outside the Pauli group. I will first provide a pedagogical introduction to these concepts following [arXiv:quant-ph/9807006] and then summarise the recent results of [arXiv:2604.14271] constructing non-Clifford gates from path integrals in Chern-Simons theories, whose magic-generating properties are determined by the algebraic data of the topological field theory.

It is in general nontrivial to construct a 2d worldsheet model whose correlators evaluate to the amplitudes of a target theory. In this talk I will go through a neat, self contained (and to my knowledge, isolated) example in which the matter content and vertex operators of the dual 2d theory can be straightforwardly read off from the action of a 4d theory. Specifically, we will see that a genus 0 worldsheet model whose correlators compute all the tree amplitudes for pure 4d N=4 super Yang-Mills can be essentially derived from the twistor action in elementary steps. We will then discuss the limitations of this approach. There are no twistorial prerequisites assumed.

The period matrix of a smooth complex projective variety encodes the isomorphism between its singular homology and its algebraic De Rham cohomology. Numerical approximations with high precision of the entries of the period matrix allow to recover some algebraic invariants of the variety, such as the Néron-Severi group in the case of surfaces. In this talk, we will see a method relying on the computation of an effective description of the homology for obtaining such numerical approximations of periods of algebraic varieties, and showcase implementations and applications, in particular to computation of the Picard rank of certain K3 surfaces related to Feynman diagrams.

In an AdS compactification the no-scale-separation conjecture states that the AdS scale cannot be parametrically separated from the KK scale of the internal manifold. This calls into question the validity of the effective lower-dimensional theory whilst also making holographic duals more complicated: obtaining a dense spectrum of low-dimension operators which are strongly mixed. This also poses problems for constructing de-Sitter vacua. 
I will discuss the papers Holography vs Scale Separation, Holographic Constraints on the String Landscape and A Holographic Constraint on Scale Separation which use holography to find constraints on scale separation, with the latter two papers focussing DGKT. 

Flat space holography, if there really is such a thing, is intimately related to Carrollian geometry. I will give an introduction to Carrollian geometry, and discuss how many Carrollian spaces of interest arise as homogeneous spaces of the Poincaré group. Finally, I will discuss the construction of Cartan geometries modelled on these spaces.

The canonical example of AdS/CFT relates N=4 SYM in 4d to supergravity on AdS5 x S5 by considering a stack of D3-branes. A natural question then emerges: what about considering other Dp-branes? The worldvolume theory is again SYM but is not conformal anymore, while the supergravity dual is now only conformally AdS. Despite these differences, some control remains, and some inspiration from the p=3 case can be sought. In this talk, I will review this setup and discuss the recent results of [2503.18770] and [2503.14685] regarding the computation of correlation functions.

For this JC, I will review the recently much debated puzzles that arise in holographic systems with baby universes. After describing the original set-up of Antonini-Sasieta-Swingle, I will explain the paradox raised by Antonini-Rath, which suggests the existence of a single CFT state that can have two distinct holographic descriptions in the bulk: one with a closed baby universe and one without. I will discuss various proposed resolutions of this puzzle, which may (or may not) require us to rethink the holographic dictionary in AdS/CFT.

I will review an elegant, theory-independent argument that proves the existence of exactly marginal operators in the presence of a conformal manifold. The proof relies on a few technical assumptions, which I will discuss in detail. The rest of the discussion will be phrased in terms of conformal interfaces separating two CFTs on the conformal manifold, which we take as an opportunity to discuss the fundamentals of defect CFTs. The overarching topic into which this result fits is that of proving certain (AdS) swampland conjectures from CFT principles.

The ’t Hooft expansion is a powerful organizational framework for understanding QFTs as perturbations away from the large N limit and has deep connections to string theory and holography. In this talk, I will discuss categorical aspects of the ’t Hooft expansion, i.e. what one learns about topological defects from the ’t Hooft expansion and, correspondingly, topological strings and twisted holography. This talk is based off the paper arXiv:2411.00760 from last year as well as the more recent review paper arXiv:2511.19776.

Renormalization group (RG) flow is a central aspect of our modern understanding of QFT. We may wonder about the relationship of renormalization to some of the other properties of a QFT, and if we can reconstruct RG flow from these properties. It has recently been proposed by Chavda, McLoughlin, Mizera and Staunton in [2510.25822] and [2511.10613] that unitarity can give us at least a part of RG flow, which is known as the Unitarity Flow Conjecture. In this talk, I will summarize the central ideas of this conjecture, and provide some evidence for it.

I will discuss some of my work on thermal correlators in AdS/CFT. In particular, given a thermal correlator, how are the characteristic properties of bulk black holes encoded in such correlators? This includes exploring the spectrum of QNMs, the so-called thermal product formula, the photon ring, and geodesics bouncing off the black hole singularity. I will discuss how the latter might change when finite string effects are considered.

There will be no journal club this week to avoid conflicting with FPUK.

I will discuss a two-dimensional dilaton gravity theory with a sine potential. At the disk level, this theory admits a microscopic holographic realization as the double-scaled SYK model. Remarkably, in the open channel canonical quantization of the theory, the momentum conjugate to the length of two-sided Cauchy slices becomes periodic. As a result, the ERB length in sine dilaton gravity is discretized upon gauging this symmetry. For closed Cauchy slices, a similar discretization occurs in the physical Hilbert space, corresponding to a discrete spectrum for the length of the necks of trumpet geometries. By appropriately gluing two such trumpets together, one can then construct a wormhole geometry in sine dilaton gravity, whose amplitude matches the spectral correlation functions of a one-cut matrix integral. This correspondence suggests that the theory provides a path integral formulation of q-deformed JT gravity, where the matrix size is large but finite. Finally, I will describe how this theory of gravity can be regarded as a realization of q-deformed holography and propose a possible implementation of this framework to study the near-horizon dynamics of near-extremal de Sitter black holes.

The organisers asked me to give a brief talk on what I’ve been thinking about lately. So, I’ll tell you about Schwinger-Keldysh EFTs: an EFT framework for non-equilibrium dissipative systems such as hydrodynamics. These are built on a closed-time contour that runs forward and backward in time, allowing access to a variety of non-equilibrium observables. However, these EFTs fundamentally miss a wider class of observables, called out-of-time-ordered correlators (OTOCs), which are closely tied to quantum chaos. In this talk, I’ll share some thoughts on extending Schwinger-Keldysh EFTs to multifold contours that capture such observables. I’ll also touch on the discrete KMS symmetry of thermal systems, which generalises from Z_2 in the single-fold case to the dihedral group D_n in the n-fold case. With any luck, I’ll reach the point where I’m stuck and you can help me figure it out.

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.