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
Integrable sigma-models, 4d Chern-Simons and RG flow
I will show that the 1-loop divergences of integrable 2d sigma-models take a "universal" form in terms of the classical integrable data: the Lax connection. Using this observation, I will prove two non-trivial facts about these theories. First, a large class of these theories are known to be engineered, classically, on surface defects in 4d Chern-Simons theory. I will show that this engineering extends to the quantum theory at 1-loop order. Second, I will show that the class of theories engineered from 4d Chern-Simons is 1-loop renormalisable -- proving an old conjecture in this setting.
14th May 2024, 14:30
Microscopic Bounds on Macroscopic Theories
I will discuss Effective Field Theories that can originate from microscopic unitary theories, and their relation to moment theory. I will show that massive gravity, theories with isolated massive higher-spin particles, and theories with very irrelevant interactions, don’t possess healthy UV completions.
24th April 2024, 14:30
Regge spectroscopy of higher twist states in N=4 supersymmetric Yang-Mills theory.
We study a family of higher-twist Regge trajectories in N=4 supersymmetric Yang-Mills theory using the Quantum Spectral Curve. We explore the many-sheeted Riemann surface and show the interplay between the higher-twist trajectories and the several degenerate non-local operators, called (near-)horizontal trajectories, that have a strong connection to light ray operators, objects omnipresent in 4-dimensional Minkowskian CFTs.
We resolve the encountered degeneracy analytically by computing the first non-trivial order of the Regge intercept at weak coupling, which exhibits new behaviour: it depends linearly on the coupling. This is consistent with our numerics, which interpolate all the way to strong coupling.
16th April 2024, 14:30
Massive Feynman Integrals from String Loop Amplitudes.
For 1-loop closed or open string amplitudes on T^4/Z_N, we perform the worldsheet moduli integrals in the low-energy limit by constructing a systematic map to known massive Feynman integrals that are all finite, where the mass thresholds emerge from soft/collinear kinematic invariants.
09th April 2024, 14:30
I will discuss free higher derivative theories of scalars and Dirac fermions in the presence of a boundary in general dimension. We established a method for finding consistent conformal boundary conditions in these theories by removing certain boundary primaries from the spectrum. In particular, a rich set of renormalization group flows between various conformal boundary conditions is revealed, triggered by deformations quadratic in the boundary primaries. I will also discuss some quantities which characterize the boundary theory such as the hemisphere free energy and the two-point function of the displacement operator.
19th March 2024, 14:30