The webpage of the a.y. 2022/23 is:

https://sites.google.com/view/trinity-theory-colloquia-22-23/home

The recorded colloquia can be found in our Youtube page: https://www.youtube.com/channel/UCh1QXrSmsPuxgdB_cJfAKbw/featured

Organizers: Marius de Leeuw, Fabrizio Nieri and Ana L. Retore

PAST:

Colloquium: 6th of October, 4 pm (Dublin time)

Pedro Vieira (Perimeter I. and ICTP/SAIFR)

Title: Where is string theory?

Abstract: Can we use the S-matrix bootstrap to explore the space of consistent UV completion of gravity? I will review recent progress in this direction.

Seminar: 11th of October, 2 pm (Dublin time)

Simon Ekhammar (Uppsala U.)

Title: SU(2|2) Quantum Spectral Curves from Monodromy Bootstrap

Abstract: I will talk about recent progress in formulating new Quantum Spectral Curves to describe integrable systems of AdS/CFT type. We develop the procedure of Monodromy Bootstrap that postulates a relation between analytic continuation and symmetry transformations of the underlying Q-system. Excitingly several new curves are obtained, among them is a natural candidate for AdS3*S3*T4.

Seminar: 18th of October, 2 pm (Dublin time)

Nicolò Piazzalunga (Uppsala U.)

Title: Towards the index of M-theory

Abstract: I will present the U(n) K-theoretic Donaldson-Thomas theory for toric Calabi-Yau three-folds X. Physically, this is the gauge theory that lives on a stack of D6-branes wrapping X, in the limit of large radius and B-field. I will focus on the case when X has compact four-cycles, so the BPS state counting includes D4-branes wrapping these. In this case, geometric engineering associates to X a gauge theory on the n-centered Taub-NUT space. I will discuss this 5d-7d correspondence for partition functions, some related conjectures, and explain how it fits within M-theory. Based on 2103.10271 and some upcoming work with Nekrasov and Zabzine.

Seminar: 1st of November, 2 pm (Dublin time)

Norton Lee (IBS)

Title: Spins, gauge theory, and KZ-equations

Abstract: We propose an interesting BPS/CFT correspondence playground: the correlation function of two intersecting half-BPS surface defects in four-dimensional N=2 supersymmetric SU(N) gauge theory with 2N fundamental hypermultiplets. We show it satisfies a difference equation, the fractional quantum T-Q relation. Its Fourier transform is the 5-point conformal block of the sl_N current algebra with one of the vertex operators corresponding to the N-dimensional sl_N representation, which we demonstrate with the help of the Knizhnik-Zamolodchikov equation.

We also identify the correlator with a state of the XXX sl_2 spin chain of N Heisenberg-Weyl modules over Y(sl_2). We discuss the associated quantum Lax operators, and connections to isomonodromic deformations.

Seminar: 8th of November, 2 pm (Dublin time)

Adam Chalabi (Southampton)

Title: Defect Central Charges

Abstract: Conformal defects can be characterised by their contributions to the Weyl anomaly. The coefficients of these terms, often called defect central charges, depend on the particular defect insertion in a given conformal field theory. I will review what is currently known about defect central charges across dimensions, and present novel results. I will discuss many examples where they can be computed exactly without requiring any approximations or limits. These include defects in free theories, and recently developed tools for defects in superconformal field theories.

Seminar: 15th of November, 2pm (Dublin time)

Fiona Seibold (Imperial College)

Title: S-matrices and Bethe equations for quantum-deformed strings.

Abstract: Two distinct eta-deformations of strings on AdS5×S5 can be defined: both amount to integrable quantum deformations of the string non-linear sigma model, but only one is itself a superstring background. In this talk I will compare their conjectured all-loop worldsheet S matrices and corresponding Bethe equations. While the S matrices are apparently different, they lead to the same Bethe equations, indicating that the integrable structure underlying the two constructions is essentially the same. Based on joint work with Alessandro Sfondrini.

Seminar: 22th of November, 2pm (Dublin time)

Benoit Vicedo (York)

Title: Non-ultralocality, affine Gaudin models and ODE/IM

Abstract: The spectrum of the Gaudin model associated with a finite-dimensional semisimple Lie algebra is well known to be described in terms of certain ordinary differential operators, known as opers, associated with the Langlands dual Lie algebra. In this talk I will review attempts at understanding the ODE/IM correspondence as a generalisation of this Gaudin/oper correspondence to the setting of affine Kac-Moody algebras and explain the connection to the problem of quantisation of non-ultralocal classical integrable field theories.

Seminar: 29th of November, 2pm (Dublin time)

Peter Koroteev (Berkeley)

Title: q-Opers, QQ-Systems and Bethe Ansatz

Abstract: Motivated by recent progress in understanding the connections between string/gauge theories and integrable systems I will describe the correspondence between (G,q)-opers and Bethe equations for simple simply connected Lie group G. The statement can be understood as classical (critical level) version of the q-Langlands correspondence. Our results have numerous applications for 3d mirror symmetry, the ODE/IM correspondence, cluster algebras, to name just a few.

Seminar: 6th of December, 2pm (Dublin time)

Saskia Demulder (Münich)

Title: Yang-Baxter sigma-models and integrable defects

Abstract: We will discuss how defects can be added to Yang-Baxter models whilst preserving the property of classical integrability. Yang-Baxter models form a rich family of integrable deformations of the well-known principal chiral model, which have the added property to admit generalised T-duals. After a brief introduction to this family of integrable models, we will introduce Bäcklund transformation and how these can be used to implement defect in conjunction with the properties of bialgebra structure of the YB-models. Finally, we will explain how the SU(2) Yang-Baxter model in its ultra-local avatar can admit defects by introducing a modified monodromy matrix. This talk is based on an ongoing project with Thomas Raml.

Seminar: 13th of December, 2pm (Dublin time)

Alessandro Torrielli (Surrey)

Title: Form factors in massless relativistic AdS3

Abstract: We present a study of form factors in the relativistic limit of massless scattering in AdS3 integrable string theory. After briefly summarising the relevant spectrum and S-matrix theory, we describe minimal solutions for the 2 and 3 point form factors, outline the proofs of the form factor axioms and discuss the general features, difficulties and complications with respect to standard cases such as the Sine-Gordon soliton-antisoliton case.

Seminar: 20th of December, 2pm (Dublin time)

Murat Kologlu (Oxford)

Title: Factorization in Quantum Gravity and Supersymmetry

Abstract: One of the lasting puzzles in quantum gravity is whether the holographic description of a gravitational system is a single quantum mechanical theory or the disorder average of many. In the latter case, multiple copies of boundary observables do not factorize into a product, but rather have higher moments. These correlations are interpreted in the bulk as due to geometries involving spacetime wormholes which connect disjoint boundaries.

I will talk about the question of factorization and the role of wormholes for supersymmetric observables, specifically the supersymmetric index. Working with the Euclidean gravitational path integral, I will start with a bulk prescription for computing the supersymmetric index, which agrees with the usual boundary definition. Concretely, I will focus on the setting of charged black holes in asymptotically flat four-dimensional N=2 ungauged supergravity. In this case, the gravitational index path integral has an infinite family of Kerr-Newman classical saddles with different angular velocities. However, fermionic zero-mode fluctuations annihilate the contribution of each saddle except for a single BPS one which yields the expected value of the index. I will then turn to non-perturbative corrections involving spacetime wormholes, and show that fermionic zero modes are present for all such geometries, making their contributions vanish. This mechanism works for both single- and multi-boundary path integrals. In particular, only disconnected geometries without wormholes contribute to the index path integral, and the factorization puzzle that plagues the black hole partition function is resolved for the supersymmetric index. I will also present all other single-centered geometries that yield non-perturbative contributions to the gravitational index of each boundary. Finally, I will discuss implications and expectations for factorization and the status of supersymmetric ensembles in AdS/CFT in further generality. Talk based on [2107.09062] with Luca Iliesiu and Joaquin Turiaci.

January 19th, 4 pm (Dublin time)

Marcos Marino (University of Geneva)

Title: Renormalons, integrable QFTs and resurgence

Abstract: Understanding the behavior of perturbative series in quantum field theory is an old and venerable problem. In the 1970s-1980s it was found that this behavior is closely connected to non-perturbative physics, and ’t Hooft and Parisi argued that the most important non-perturbative corrections in asymptotically free theories are due to so-called renormalons. In contrast to instantons, renormalons do not have a semi-classical description, they are very difficult to compute, and they are still poorly understood.

In this talk I will first summarize the physics and mathematics of renormalons. I will then argue that integrable field theories in two dimensions provide an excellent laboratory to obtain analytic results on the structure or renormalons. Some of these exact results turn out to challenge the standard orthodoxy on the subject. I will also explain how renormalons provide "trans-series” representations for observables, i.e. extensions of perturbation theory which include exponentially small corrections, as expected from the theory of resurgence.

Seminar: January 17th, 2pm (Dublin time)

Sibylle Driezen (Santiago)

Title: An Algebraic Classification of Solution Generating Techniques

Abstract: In this talk, I will consider a classification of a family of worldsheet dualities and deformations which can (i) generate a (modified) supergravity solution from another supergravity solution, and (ii) preserve integrability. The classification is given in the framework of Double Field Theory, which provides a convenient rewriting of both the supergravity equations as well as the Poisson brackets of a worldsheet sigma model: they can be written completely in terms of so-called generalised fluxes, which are constructed from the background frame fields. By changing non-trivially the frame fields, but demanding invariance of these fluxes, one can obtain a class of the aforementioned Solution Generating Techniques (SGTs). Using an underlying algebraic formulation — the existence of a doubled Lie group with a maximally isotropic subgroup — we can find the most general expression of the frame and thus include the most generic flux components. This allows us to obtain a master equation depending only on the initial background which, given that the initial background is a supergravity or arises from an integrable sigma model, captures all its possible SGTs. I will discuss how this equation is accompanied by conditions for the SGTs to remain within usual supergravity. When those are violated, I will argue how the equation still captures canonical transformations of sigma models (and, therefore, integrable deformations) as well as maps to so-called modified supergravities. To end, I will briefly argue how our master equation is classified in terms of Lie algebra cohomologies.

Seminar: January 24th, 2pm (Dublin time)

Tudor Dimofte (Edinburgh)

Title: A QFT for non-semisimple TQFT

Abstract: Topological twists of 3d N=4 gauge theories naturally give rise to non-semisimple 3d TQFT's. In mathematics, prototypical examples of the latter were constructed in the 90's (by Lyubashenko and others) from representation categories of small quantum groups at roots of unity; they were recently generalized in work of Costantino-Geer-Patureau Mirand and collaborators. I will introduce a family of physical 3d quantum field theories that (conjecturally) reproduce these classic non-semisimple TQFT's. The physical theories combine Chern-Simons-like and 3d N=4-like sectors. They are also related to Feigin-Tipunin vertex algebras, much the same way that Chern-Simons theory is related to WZW vertex algebras. (Based on work with T. Creutzig, N. Garner, and N. Geer.)

Seminar: January 31st, 2pm (Dublin time)

Alessandro Tanzini (SISSA)

Title: Surface defects and BPS spectra

Abstract: We show that the partition functions of 4d supersymmetric gauge theories with 8 supercharges in presence of surface defects obey RG equations of affine Toda type and we comment on their M-theory origin. These equations provide new recursion relations for instanton counting for all simple groups from A to E. The uplift to 5d theory on a circle is a discrete flow generated by the automorphisms of the relevant BPS quiver. We show that upon a suitable 4d reduction, a class of discrete flows points to an intriguing new viewpoint on Argyres-Douglas SCFTs.

Seminar: February 7th, 2pm (Dublin time)

Marika Taylor (Southampton)

Title: Holography, cellulations and error correcting codes

Abstract: Quantum error correction codes associated with the hyperbolic plane have been explored extensively in the context of the AdS3/CFT2 correspondence. In this talk we initiate a systematic study of codes associated with holographic geometries in higher dimensions, relating cellulations of the spatial sections of the geometries to stabiliser codes. We construct analogues of the HaPPY code

for three-dimensional hyperbolic space (AdS4), using both absolutely maximally entangled (AME) and non-AME codes. We will also explain how our codes could be applied to interesting classes of holographic dualities based on gravity-scalar theories (such as JT gravity) through toroidal reductions of hyperbolic spaces. Based on 2112.12468 & work in progress.

Seminar: February 14th, 2pm (Dublin time)

Giulio Bonelli (SISSA)

Title: Spinning Black Holes, 2D CFTs, N = 2 supersymmetric gauge theories & Heun functions

Abstract: The study of perturbation theory around the Kerr black hole is a classical problem in General Relativity. Due to the high order of symmetry of the gravitational field and the consequent separation of variables at the linear order, the problem reduces to the study of linear ordinary second order differential equations. The resulting equations are of Fuchsian type and therefore, as already observed long ago by A.M.Polyakov, can be solved exactly in terms of classical irregular Virasoro conformal blocks. By making use of the specific exact expressions of the latter implied by the AGT dual perspective on the conformal field theory, it is possible to explicitly solve the connection problem of the resulting (confluent)Heun equation and give novel exact and explicit formulas for the grey body factor, quasi-normal modes and Love numbers of the Kerr black hole.

Seminar: February 21st, 2pm (Dublin time)

Fedor Levkovich-Maslyuk (IPhT Saclay & IITP Moscow)

Title: Separation of variables and correlation functions

Abstract: I will present new results in the separation of variables (SoV) program for integrable models. The SoV methods are expected to be very powerful but until recently have been barely developed beyond the simplest gl(2) models. I will describe how to realize the SoV for any gl(N) and demonstrate how to solve the longstanding problem of deriving the scalar product measure in SoV for gl(N) spin chains. Using these results I will compute a large class of correlation functions and overlaps in a simple determinant form. I will also present novel applications of SoV in 4d integrable CFT's. Based on arXiv:2103.15800, 2011.08229, 1910.13442, 1907.03788, 1610.08032.

Seminar: February 28th, 2pm (Dublin time)

Mathew Bullimore (Durham)

Title: Symmetries and 't Hooft anomalies of 3d N = 4 SCFTs

Abstract: I will discuss aspects of higher-form and higher-group symmetries and their 't Hooft anomalies in 3d N = 4 SCFTs. Time permitting, I will comment on how these symmetries are encoded in a generalisation of Higgs and Coulomb branch moduli spaces to moduli stacks.

Seminar: March 14th, 2pm (Dublin time)

Konstantin Zarembo (NORDITA)

Title: Domain walls and integrability in ABJM theory

Abstract: The ABJM model (supersymmetric matter-Chern-Simons theory) admits domain wall solutions holographically described as D-branes in the bulk. Vacuum condensates induced by the domain walls can be efficiently computed using integrability and admit a concise determinant representation through the Gaudin matrix of the underlying spin chain. Based on https://arxiv.org/pdf/2112.10438.pdf

Seminar: March 28th, 2pm (Dublin time)

Susanne Reffert (Bern U.)

Title: The Large Charge Expansion

Abstract: Over the last few years, it has become clear that working in sectors of large global charge leads to significant simplifications when studying strongly coupled CFTs, theories which are otherwise often inaccessible to analytic methods. It allows us in particular to calculate the CFT data as an expansion in inverse powers of the large charge. In this talk, I will introduce the large-charge expansion via the simple example of the O(2) model and will then apply it to a number of other systems which display a richer structure, such as those with non-Abelian global symmetry groups. Using large-N methods in conjunction with large charge gives us even more control over the dynamics and lets us study the system away from the conformal point.

Seminar: April 4th, 2pm (Dublin time)

Du Pei (Harvard U.)

Title: Holomorphic CFTs and topological modular forms

Abstract: The theory of topological modular forms leads to many interesting constraints and predictions for two-dimensional quantum field theories. In this talk, I will show that a conjecture by Segal, Stolz and Teichner requires the constant term of the partition function of a bosonic holomorphic CFTs to be divisible by specific integers determined by the central charge. We verify this constraint in large classes of physical examples, and rule out the existence of an infinite set of "extremal CFTs", including those with central charges c = 48, 72, 96 and 120.

Seminar: April 11th, 2pm (Dublin time)

Miranda Cheng (Amsterdam U.)

Title: Learning Quantum Field Theory with Equivariant Continuous Flows

Abstract: Machine learning has the potential of becoming, among other things, a major computational tools in physics, making possible what was not. Specifically, I will summarise my recent work which aims to use a continuous flow model to help ameliorate the numerical difficulties in sampling in lattice field theories, which for instance hampers high-precision computations in LQCD. I will focus on the case study of the phi^4 theory in 2 dimensions. The talk will be based on 2110.02673 and to appear with de Haan, Gerdes, Rainone, and Bondesan.