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
Non-invertible symmetries, anomalies and scattering amplitudes.
We show that crossing symmetry of S-matrices is modified in certain theories with non-invertible symmetries or anomalies. Focusing on integrable flows to gapped phases in two dimensions, we find that S-matrices derived previously from the bootstrap approach are incompatible with non-invertible symmetries along the flow. We present consistent alternatives, which however violate standard crossing symmetry and obey modified rules dictated by fusion categories. Based on work with Christian Copetti and Shota Komatsu.
12th March 2024, 14:30
Orientifold reductions with fluxes and dynamical open strings
I will explain in detail how a compactification of type II string theory with orientifold planes and parallel D-branes with dynamical open strings may be effectively described by a lower-dimensional half-maximal gauged supergravity coupled to a generic number of vector multiplets. In particular, I will illustrate it explicitly in the context of orientifold reductions of type IIB down to 6d. Then I’ll sketch how this machinery can be applied to massive IIA reductions to 4d, as well. I will also discuss some preliminary results concerning 6d & 4d vacua.
5th March 2024, 14:30
Non-supersymmetric heterotic strings on tori
In the absence of experimental evidence for supersymmetry, compactifications of the non-supersymmetric heterotic strings make their reappearance in the landscape of possibly phenomenologically-relevant backgrounds. Furthermore, they have been recently used to build non-supersymmetric AdS backgrounds, which according to one of the swampland conjectures, should not be part of the landscape. In this talk we will analyse compactifications on string-size tori, focusing on the phenomenon of gauge symmetry enhancement at special points in moduli space.Concentrating on the circle, we find all the points that have non-Abelian gauge symmetries of maximal rank, and analyze their matter spectrum. We show that all gauge symmetry enhancements, and where they are realised in moduli space, can actually be obtained from an extended Dynkin diagram. We will show the one-loop cosmological constant, as well as its Hessian at points of maximal enhancement, finding a surprising result. Finally, we will discuss their use in building non supersymmetric AdS backgrounds.
27th February 2024, 14:30