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
Integrable Structure of Higher Spin CFT and the ODE/IM Correspondence
We study two dimensional systems with extended conformal symmetry generated by the W_3-algebra. These are expected to have an infinite number of commuting conserved charges, which we refer to as the quantum Boussinesq charges. We show that it is possible to derive the current densities, whose integrals are the quantum Boussinesq charges in a systematic manner using two ingredients: (i) the eigenvalues of the quantum Boussinesq charges in both the vacuum and excited states of the higher spin module through the ODE/IM correspondence, and (ii) the thermal correlators involving the energy-momentum tensor and the spin-3 current by making use of the Zhu recursion relations. We also evaluate the thermal expectation values of the conserved charges, and show that these are quasi-modular differential operators acting on the character of the higher spin module.
9th July 2024, 14:30
Covariant properties of holographic entanglement
For any state of a quantum field theory, the entanglement entropy (EE) of subsystems satisfies two inequalities known as subadditivity (SA) and strong subadditivity (SSA). In holography, states with a smooth classical geometric dual are constrained further. For static states, the EE is given by the Ryu-Takayanagi (RT) formula, which has been shown to obey both SA and SSA, as well as an infinite family of higher inequalities. We address the question of whether holographic entropy inequalities obeyed in static states (by the RT formula) are obeyed in time-dependent states (by the HRT formula). Working in the context of 2+1 dimensional AdS3 quotient spacetimes, we numerically test all known inequalities for the HRT formula founding no counterexamples. We also introduce a new formulation of the HRT formula (known as minimax), and use it to explore the above question in full generality. The minimax formulation will imply a new decomposition of the bulk spacetime which may be helpful in covariantizing both the holographic entropy cone and tensor network models of holography.
2nd July 2024, 14:30
Tilings, tessellations, and quantum codes
Error correction is the hallmark of computation. Error correcting codes developed for classical computation are based on ideas from discrete mathematics, tessellations, geometry, and number theory. Based on models in condensed matter physics, topological codes have been designed. We construct surface codes corresponding to genus greater than one in the context of quantum error correction which surpass the encoding rate of topological codes hitherto known. The architecture is inspired by the topology of invariant integral surfaces of certain non-integrable classical billiards. Corresponding to the fundamental domains of rhombus and square torus billiard, surface codes of genus two and five are presented here. These new codes pave the way to gauge theories with novel particles, which would be the subject for another day. An attempt will be made to summarize the connections between classical nonlinear science and quantum information and coding, and quantum computation.
18th June 2024, 14:30
End of The World brane networks for infinite distance limits in CY moduli space.
Dynamical Cobordism provides a powerful method to probe infinite distance limits in moduli/field spaces parameterized by scalars constrained by generic potentials, employing configurations of codimension-1 end of the world (ETW) branes. These branes, characterized in terms of critical exponents, mark codimension-1 boundaries in the spacetime in correspondence of finite spacetime distance singularities at which the scalars diverge. Using these tools, I will explore the network of infinite distance singularities in the complex structure moduli space of Calabi-Yau fourfolds compactifications in M-theory with a four-form flux turned on, which is described in terms of normal intersecting divisors classified by asymptotic Hodge theory. I will provide spacetime realizations for these loci in terms of networks of intersecting codimension-1 ETW branes classified by specific critical exponents which encapsulate the relevant information of the asymptotic Hodge structure characterizing the corresponding divisors.
11th June 2024, 14:30
Duality defects of D_n type Niemeier Lattice CFTs.
In this talk, we will construct topological duality defects in 2-dimensional c=24 meromorphic conformal field theories (CFTs) with a D_n-type current algebra. In particular we will demonstrate how to extend the group of usual invertible symmetries of the 2d CFTs to the fusion category of symmetries with a unique non-invertible duality defect.
29th May 2024, 13:00
Exact integrated correlators in N=4 super Yang-Mills theory beyond localization
Certain four-point half BPS correlators in N=4 super Yang-Mills theory (SYM) can be computed exactly using supersymmetric localization when integrating over their space-time dependence. In this talk, I will consider general four-point half BPS correlators in N=4 SYM in the planar limit, which currently are not accessible from the localization method. Nevertheless, I will propose an exact expression for these general integrated correlators, with non-trivial evidence at both weak and strong coupling. I will also discuss predictions from our proposal, including results of higher-loop Feynman integrals that are associated with the integrated correlators and the Mellin amplitudes of the holographic dual type IIB string theory in AdS5xS5.
28th May 2024, 15:30
Bootstrapping bulk locality: interacting functionals
Locality of bulk operators in AdS space implies constraints on their representation in terms of boundary CFT operators, which may be characterised by sets of functional sum rules. In this work, we clarify what it means for such sum rules to be "complete": it means the corresponding functionals form a complete set in the relevant functional space. We demonstrate how to construct complete sets of sum rules dual to certain sparse spectra, where "duality" means the sum rules are diagonalised when acting on that spectrum. An immediate output is explicit formulae for special "extremal" solutions containing these spectra. We are able to do this -- producing explicit, interacting solutions -- for a huge class of sparse spectra that approach Generalised Free Fields in the UV. Our method is to prove that these sparse sets of blocks are themselves complete in a certain space of "hyperfunctions", which automatically produces a dual basis of functionals.
15th May 2024, 14:30