Quantum groups as global symmetries
What is the most general internal symmetry a Quantum Field Theory can have? The answer to this question has significantly changed in the past decade, with the understanding of generalized symmetries such as non-invertible and p-form symmetries. An orthogonal direction, which so far has been unexplored, is that of quantum groups; these are some exotic symmetry algebras which are well known to play a role in lattice systems, some of which are critical, and should therefore play a role in two dimensional Conformal Field Theory. I will discuss this question in the case of the simplest quantum group Uq(sl2), giving both the general picture and studying a specific example arising from the continuum limit of a lattice model. I will discuss the consequences of this symmetry, and how this is related to ordinary theories (e.g. minimal models) where quantum groups are known to appear somehow indirectly.
5th November 2024, 14:30
AdS string amplitudes from single-valuedness
It has long been known that string theory amplitudes have intriguing single-valuedness properties. When considering string theories on curved backgrounds, which are still lacking a complete worldsheet description, these properties become even richer. For AdS/CFT, single-valuedness can be combined with the structure of the OPE in the dual CFT to fix AdS string amplitudes in a small curvature expansion. In this way we found curvature corrections to the AdS Virasoro-Shapiro amplitude for graviton scattering in type IIB on AdS5xS5 and the AdS Veneziano amplitude for gluon scattering in orientifolds of type IIB on AdS5xS5. The results have the form of worldsheet integrals involving single-valued multiple polylogarithms. Our answers determine the CFT data for unprotected operators in planar N=4 SYM theory and certain N=2 SCFTs at strong coupling, making contact with integrability, localization and conformal bootstrap. Furthermore, the high energy limit of the amplitudes agrees with classical scattering computations in AdS.
29th October 2024, 14:30
Sliver frame stubs in open string field theory
There are a couple of reasons why adding stubs to the 3-vertex of Witten's open string field theory is interesting. In this talk I will first explain the general construction and then apply it in the sliver frame, where the Witten star product takes a simple form. We will find some non-trivial constraints and singularities appearing which are analyzed in detail. Moreover, I will show how the stubbed theory can be recast in a cubic form using an auxiliary field and also show its consistency at the full quantum level.
22nd October 2024, 14:30
Exploring Replica-Potts CFTs in Two Dimensions
We initiate a numerical conformal bootstrap study of CFTs with Sn⋉(SQ)n global symmetry. These include CFTs that can be obtained as coupled replicas of two-dimensional critical Potts models. Particular attention is paid to the special case S3⋉(S3)3, which governs the critical behaviour of three coupled critical 3-state Potts models, a multi-scalar realisation of a (potentially) non-integrable CFT in two dimensions. The model has been studied in earlier works using perturbation theory, transfer matrices, and Monte Carlo simulations. This work represents an independent non-perturbative analysis. Our work sets the necessary groundwork for a future precision study of these theories in the conformal bootstrap.
15th October 2024, 14:30
Integration on higher-genus Riemann surfaces from and for string amplitudes
In this talk, multiloop string amplitudes are discussed as a rewarding laboratory to develop integration techniques on higher-genus Riemann surfaces. I will review a string-amplitude inspired generalization of the Brown-Levin elliptic polylogarithms and their Kronecker-Eisenstein integration kernels to arbitrary genus. The key ingredients are convolutions of Arakelov Green functions on genus-g surfaces which transform as tensors under the modular group Sp(2g, Z). Our higher-genus integration kernels simplify the spin-structure summations in the RNS formulation of multiloop string amplitudes and the low-energy expansion of moduli-space integrals. The recent Fay identities among the higher-genus kernels play a key role in the development of more general integration algorithms relevant to precision calculations for particle colliders or gravitational-wave experiments and to mathematical classifications of period integrals on higher-genus surfaces.
8th October 2024, 14:30
Heterotic asymmetric orbifolds revisited
In this talk I will first review the basics of toroidal asymmetric orbifolds. I will then discuss a class of 6-dimensional models with 8 supercharges. I will also consider models with 16 supercharges and reduced rank, describing a novel formalism that will be applied to construct “islands” without vector multiplets.
1st October 2024, 14:30
Finite Feynman Integrals
Classifying and organizing Feynman integrals according to their degree of divergence may be a useful tool in presenting scattering amplitudes. In this talk, I focus on the first step: systematically organizing and finding finite Feynman integrals. I will briefly discuss an approach based on Landau equations. I will then focus mostly on an approach based on Newton polytopes.
18th September 2024, 14:30
The perturbative bootstrap of the Wilson-line defect CFT
Conformal line defects play a crucial role as observables in
physics, with applications ranging from condensed-matter systems to
high-energy physics. They also provide a valuable platform for studying
new techniques in quantum field theory, as they break the conformal
symmetry of the bulk theory in a controlled manner. The defect conformal
field theory involving a Maldacena-Wilson line in $\mathcal{N}=4$
supersymmetric Yang-Mills (SYM) theory is particularly compelling, as it
preserves a significant portion of the supersymmetry and exhibits a
one-dimensional CFT formed by correlators of excitations localized on the
defect.
In this talk, I will introduce a perturbative bootstrap framework that
enables the computation of correlation functions in this theory at weak
coupling. This method integrates non-perturbative insights, such as
superconformal symmetry, with minimal perturbative input. I will present
new results for multipoint correlators of defect operators as well as
bulk-defect-defect correlators. These correlators contain in principle a
wealth of previously inaccessible CFT data and offer promising directions
for further developments in the defect bootstrap program.
11th September 2024, 14:30
Gauge theories on noncommutative spaces
We explore the notions of noncommutative principal bundles and of gauge fields and gauge transformations in this context. We use an Atiyah sequence of twisted derivations (vector fields) associated to the principal bundle. A gauge connection is a splittings of the sequence (a way to lift twisted derivations from the base space to the total space of the sequence). Vertical twisted derivations act as infinitesimal gauge transformations on connections. As an example we give families of instantons (anti-self dual connections) on a quantum 4-sphere via an action of a twisted conformal algebra. Also, on the principal bundle of orthonormal frames over the quantum 2n-sphere the splitting leads to the Levi-Civita connection on the module of twisted derivations.
10th September 2024, 14:30
In this talk, I will explain how to construct an infinite family
of classically integrable deformations of the principal chiral model (PCM)
using auxiliary fields. This class of theories includes deformations of
the PCM by functions of all of its spin-$s$ conserved currents, which for
$s = 2$, includes flows driven by functions of the stress tensor such as
$T \overline{T}$ and root-$T \overline{T}$. I will also describe the
non-Abelian T-duals of these models, all of which are related to their
pre-T-duality cousins by canonical transformations, and are thus also
classically integrable.
17th July 2024, 14:30