Machine learning for lattice QFT and string theory
Machine learning has revolutionized most fields it has penetrated, and
the range of its applications is growing rapidly. The last years has
seen efforts towards bringing the tools of machine learning to lattice
QFT and, more recently, to string theory. After reviewing the general
ideas behind machine learning, I will discuss several applications: 1)
predicting the critical temperature of the confinement phase transition
in 2+1 QED, 2) computing the Casimir energy for a 3d QFT, 3) predicting
the Hodge numbers of Calabi-Yau 3-folds. I will conclude by giving some
general thoughts on the use of ML for mapping effective QFT and building
a string field theory.
Tuesday, 1st of October 2019, 14:30, sala Fubini
Canonical quantization of the Szekeres spacetime
In this talk, I will discuss the canonical quantisation of an inhomogeneous spacetime by the use of the symmetries on the configuration space. I focus on the Szekeres spacetime with or without a cosmological constant. The physical interest on this system is that it can describe early inhomogeneous discrepancies from the homogeneous spacetime in the early universe. I will explain the general procedure, usually performed in the context of the minisuperspace approximation. Then, I will discuss the solution of the quantum equations, which is a wave functional to be interpreted. We derive a probability density and discuss the transition to the classical limit and the implications for the current state of the universe.
Thursday, 26th September 2019, 14:30, sala Watachin
Holographic RG flows, on flat and curved manifolds and F-theorems
We carefully analyze the structure of holographic RG Flows dual to QFTs on Minkowski spacetime, and find several exotic possibilities beyond the known vanilla cases. We then proceed and study the holographic RG flows dual to QFTs on curved manifolds (spheres , de Sitter and AdS).
We analyze the general structure, and control fully the UV and IR asymptotic expansions. We also analyze the exotic flows found in flat space.
The de Sitter case provides an interesting interpretation of the on-shell action as a finite temperature free energy of the QFT.
We also study F-functions in the context of field theories on $S^3$, with the radius of $S^3$ playing the role of RG scale. We show that the on-shell action, evaluated over a set of holographic RG flow solutions, can be used to define good F-functions, which decrease monotonically along the RG flow from the UV to the IR for a wide range of examples. We check that these observations hold beyond holography for the case of a free fermion on $S^3$ ($\Delta=2$) and the free boson on $S^3$ ($\Delta=1$), resolving a long-standing problem regarding the non-monotonicity of the free energy for the free massive scalar. We also show that for a particular choice of entangling surface, we can define good F-functions from an entanglement entropy, which coincide with certain F-functions obtained from the on-shell action.
Tuesday, 11th of June 2019, 14:30, sala Castagnoli
N=2 to N=1 with one hypermultiplet
A clear picture, and a classification, of N=2 theories with a single hypermultiplet
and a ground state breaking only one supersymmetry has only recently emerged.
I will discuss these results in global supersymmetry and (Minkowski) supergravity
theories. Establishing them required to lift some controversies and
escape some strong statements in mathematical papers.
Tuesday, 21st of May 2019, 14:00, sala Wataghin
The large charge expansion
The large-charge approach consists in studying conformal field theories in sectors of fixed and large global charge. This allows performing a perturbative expansion of a generically strongly-coupled theory with the inverse charge acting as a controlling parameter. In this talk, I will present the basic idea of the large quantum number expansion using the simplest example of the 3D O(2) model at the Wilson-Fisher fixed point at large global charge and then extend its treatment to the O(2N) vector model. New lattice results confirm our predictions to high accuracy.
I will further show that the large-charge expansion can also be successfully applied to non-relativistic CFTs.
Tuesday, 7th of May 2019, 14:30, sala Wataghin
In a remarkable recent work by Arkani-Hamed et al, the amplituhedron program was extended to the realm of non-supersymmetric scattering amplitudes. In particular it was shown that for tree-level planar diagrams in massless $\phi^3$ theory (and its close cousin, bi-adjoint $\phi^3$ theory) a polytope known as the associahedron sits inside the kinematic space and is the amplituhedron for the theory. Precisely as in the case of amplituhedron, it was shown that scattering amplitude is nothing but residue of the canonical form associated to the associahedron. Combinatorial and geometric properties of associahedron naturally encode properties like locality and unitarity of (tree level) scattering amplitudes.
In this talk after briefly reviewing their work we attempt to extend this program to planar amplitudes in massless $\phi^4$ theory. We show that tree-level planar amplitudes in this theory can be obtained from geometry of objects known as the Stokes polytope which sits naturally inside the kinematic space. As in the case of associahedron we show that residues of the canonical form on these Stokes polytopes can be used to compute scattering amplitudes for quartic interactions. However unlike associahedron, Stokes polytope of a given dimension is not unique and as we show, one must sum over all of them to obtain the complete scattering amplitude. We shall finally discuss some ongoing work about generalisation of the program to all $\phi^p$ ($p>4$) theories.
Wednesday, 10th of April 2019, 14:30, sala Wataghin
Noncommutative gauge theories on D-branes in non-geometric backgrounds
I will describe some new perspectives on non-geometric backgrounds of string theory from the open string perspective, by a detailed analysis of the low-energy effective gauge theory on D-branes in these backgrounds. This theory is a noncommutative Yang-Mills theory wherein the T-duality monodromies of the non-geometric background become Morita duality monodromies of the noncommutative gauge theory. We elaborate on this perspective in detail for T-folds arising via T-duality from twisted tori, and extend the considerations to backgrounds with R-flux where the noncommutative Yang-Mills theories have a dependence on the dual coordinates, and so have no formulation in a conventional spacetime.
Tuesday, 9th of April 2019, 14:30, sala Wataghin
We start by a review of numerical and analytical conformal bootstrap techniques at our disposal.
We then use these tool to approach the "simplest" Argyres-Douglas theory, a four-dimensional N=2 strongly coupled superconformal field theory. We "zoom in" to the theory by specifying Coulomb branch data, and obtain strong constraints on its operator spectrum and OPE coefficients. We conclude with an outlook for the prospects of approaching other strongly coupled N=2 conformal theories.
Tuesday, 12th of March 2019, 14:30, sala Wataghin
On the holographic origin of the Bekenstein-Hawking entropy of 1/16 BPS $AdS_5$ black holes
Providing a microscopic derivation of the entropy of supersymmetric asymptotically $AdS_5$ black holes has been an open problem for some time. In the talk I will present progress towards such a derivation. On the gravity side of the AdS/CFT correspondence, I will define a BPS limit of black hole thermodynamics by first focussing on a supersymmetric family of complexified solutions and then reaching extremality. I will show that in this limit the black hole entropy is the Legendre transform of the on-shell gravitational action with respect to a set of chemical potentials subject to a constraint. This constraint follows from supersymmetry and regularity in the Euclidean bulk geometry. The gravitational analysis instructs us that the dual N=1 superconformal field theory is defined on a twisted $S^1 \times S^3$ with complexified chemical potentials obeying the constraint, and localization allows to compute the corresponding partition function exactly. This computation defines a generalization of the supersymmetric Casimir energy, whose Legendre transform at large N precisely reproduces the Bekenstein-Hawking entropy of the black hole.
Tuesday, 5th of March 2019, 14:30, sala Wataghin
3d Abelian Gauge theories at the Boundary
A four-dimensional abelian gauge theory can be coupled to a 3d CFT with a U(1) symmetry living on a boundary. This coupling gives rise to a continuous family of boundary conformal field theories (BCFTs) parametrized by the gauge coupling \tau and by the choice of the CFT in the decoupling limit. Upon performing an Electric-Magnetic duality in the bulk and going to the decoupling limit in the new frame, one finds a different 3d CFT on the boundary, related to the original one by Witten's SL(2, Z) action. In particular the cusps on the real \tau axis correspond to the 3d gauging of the original CFT. We study general properties of this family of BCFTs. We show how to express bulk one and two-point functions, and the hemisphere free-energy, in terms of the two-point functions of the boundary electric and magnetic currents. Finally, upon assuming particle-vortex duality (and its fermionic version), we show how to turn this machinery into a powerful computational tool to study 3d gauge theories.
Tuesday, 26th of February 2019, 14:30, sala Wataghin