I will discuss recent progress at computing form factors of
local operators in planar N=4 SYM using the duality with null periodic
Wilson loops and integrability. I will first recall the original duality
for the form factors of the stress-energy tensor and motivate a
generalisation to the form factors of all single-trace half-BPS operators.
I will then explain how the dual Wilson loops may be studied exactly in
the collinear limit using the Operator Product Expansion and
integrability, and present applications to higher-loop calculations of the
three-point form factors. If time permits, I will discuss preliminary
results for constructing Wilson loops dual to form factors of
non-protected operators, and more specifically for operators in the
Konishi supermultiplet.
3rd December 2024, 14:30
Scattering amplitudes from null-cone geometry
In recent years it has become clear that particular geometric structures, called positive geometries, underlie various observables in quantum field theories. In this talk I will focus on scattering amplitudes. After a broad introduction, I will consider maximally supersymmetric Yang-Mills theory and discuss a positive geometry encoding scattering processes in this theory -- the momentum amplituhedron. In particular, I will show that using the null structure of the kinematic space, one finds a geometry whose canonical differential form produces loop-amplitude integrands. Finally, I will present some of the main goals and research directions for the future.
26th November 2024, 14:30
Strings from Feynman Diagrams
How are bulk strings related to boundary Feynman diagrams? I will give an overview of my work with Rajesh Gopakumar on deriving the closed string dual to the simplest possible gauge theory, a Hermitian matrix integral. Working in the conventional ‘t Hooft limit, we extract topological string theories which replace the minimal string away from the double-scaling limit. We show how to exactly reconstruct both the closed string worldsheet and its embedding into the emergent target space, purely from the matrix Feynman diagrams. I’ll close by embedding our results in the broader context of AdS/CFT.
19th November 2024, 14:30
Metric positivity and the Swampland
The formulation of abstract notions about physical theories to study their universal features is a typical strategy of modern high-energy physics. In this regard, a widely accepted belief is that geometrical notions, like metrics and distances between vacua configurations of physical theories, should always exist. However, defining a consistent metric and distance between vacua in gravitational theories is an important open problem. In my talk, I will examine this issue in relation to the 'AdS conjecture', a key development within the Swampland program. The main goal is to introduce a consistent procedure for defining and computing metrics on the space of gravity vacua, providing a clear way to measure distance. Starting with simple vacua in string theory, I will demonstrate how these new concepts can be constructed explicitly. The key idea underlying the procedure involves considering the off-shell quadratic variation of the string theory action and evaluating it over the space of on-shell solutions. Finally, I will discuss how this framework offers insights into the ongoing debate about the consistency of scale-separated vacua in string theory.
12th November 2024, 14:30
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