Mathematical Physics Group

Seminars 2023-24

Oct 19th: Lucrezia Ravera (Torino P.)

Title: Geometric Approach to Supergravity in Superspace and Some Applications

Abstract: In 1978, Y. Ne’eman and T. Regge proposed a new approach to (super)gravity in which the theory is constructed on the (super)group manifold defining the Lie algebra valued gauge fields in the coadjoint representation of the (super)group. I will discuss key aspects, developments and applications of this approach in the context of supergravity, where it provides a geometric formulation of the theory in superspace and a geometric interpretation of supersymmetry transformations as superdiffeomorphisms. In particular, I will focus on the hidden gauge structure underlying Free Differential Algebras, which describe the vacuum of supergravity theories, and on the boundary problem in supergravity under a geometric perspective.

Nov 8th: Lorenzo Fatibene (UniTo & INFN)

Title: Exact Methods for Relativistic Positioning

Abstract: We shall discuss a model for exact, purely relativistic positioning in a Schwarzschild spacetime. It will make no assumptions about weak field or PN approximations, with no ground section, no particular synchronization at a distance, with the extra ability to autonomously detect deviations from the assumptions and restore operation when assumptions are restored. We shall consider positioning problem as 'geodesy on spacetime', in particular discussing how to extract information about intrinsic geometry of spacetime, a.k.a. the gravitational field. A different, though equivalent, way of describing a relativistic positioning system is that it provides a series of well defined observables for a gravitational theory.

Nov 16th: Alessia Segati (Milano S.)

Title: General Aspects of 5d Supergravity on the Spindle

Abstract: New superconformal field theories can be obtained compactifying higher-dimensional theories on curved spaces. The extremization procedure performed in field theory to derive the central charge of the (even) lower-dimensional theory is related by the AdS/CFT correspondence to an extremization problem in supergravity that resemble the attractor mechanism. When the original theory is compactified on a spindle, topologically a two-sphere with conical singularities at the poles, this mechanism exhibits new peculiar features. Complications arise in presence of hypermultiplets, because the boundary conditions for the scalars at the poles of the spindle are subtle. However, by an opportune ansatz, it is possible to extract the central charge from the pole analysis. Furthermore, numerical solutions can be still found in some cases. As a concrete example, I will present some examples of compactifications on the spindle of different AdS_5 consistent truncations that exhibit such behavior.

Nov 23rd: Antonio Gallerati (Torino P.)

Title: A Geometric Approach to Graphene

Abstract: The study of graphene-like materials opens up new connections between condensed matter, high-energy physics and curved space geometry. Graphene and other 2D materials realize the physics of spinorial fields, whose Dirac properties emerge thanks to the structure of the lattice with which the charge carriers interact, giving the possibility to observe quasi-relativistic particle behavior at sub-light speed regime. It is possible to argue that the geometric curvature of a 2D sample, combined with the aforementioned special relativistic-like behavior, naturally leads to a general relativistic-like description for the charge carriers, behaving as Dirac quantum fields in a laboratory 1+2 dimensional curved background. We will see how the emergence of intrinsic and extrinsic curvature in graphene-like materials can be used to investigate Dirac quantum dynamics in curved spacetime, as well as to probe certain quantum gravity scenarios. This formulation follows a bottom-up approach, where a condensed matter system (the 2D lattice) provides analogs of gravitational effects, so that the propagation of quantum fields is dictated by an effective metric, taking then advantage of mathematical tools from Einstein gravity. Finally, we will mention new theoretical results that conjecture the use of graphene and other 2D materials to have alternative (unconventional) realizations of some special symmetries, exploiting a holographic top-down approach. In the latter formulation, the substrate description originates from a well-defined geometric definition of a suitable, higher-dimensional gravity model.

Dec 7th: Riccardo Adami (Torino P.) 

Title: Ground States for the Nonlinear Schroedinger Equation on Hybrids

Abstract: Motivated by the recent technological developments in ultracold gases and atomtronic, the study of the Nonlinear Schroedinger Equation on exotic domains is nowadays a well-established topic in Mathematical Physics. Here we focus on the problem of the existence of Ground States on the so-called hybrid plane, made of a plane attached to the origin of a halfline. By Ground States we mean minimizers of the energy among the states with the same mass. We show that Ground States exist for small and large mass, while in the intermediate region there are intervals of nonexistence. The first half of the talk is devoted to the linear  part and focuses on the preliminary problem of what actually means to attach a plane to a halfline. Specifically, we start from the problem of constructing the Fermi pseudopotential, also called Dirac’s delta potential, for a spinless particle in dimension one and three. The second half of the talk deals with hybrids, and the nonlinearity is introduced. Then we give some results on the problem of the existence of Ground States.

Dec 14th: Luca Cassia (Melbourne U.) 

Title: An Equivariant Approach to Local Mirror Symmetry

Abstract: In this talk I will introduce the notion of equivariant quantum volumes for toric Calabi-Yau threefolds and I will discuss their relation to both open and closed string invariants in genus zero. I will argue that equivariance is the fundamental tool that allows to regularize the divergencies due to the non-compactness and I will elaborate on its meaning in the mirror geometry.

Jan 18th: Sante Carloni (UniGe) 

Title: Junction conditions for general LRS spacetimes in the 1+1+2 covariant formalism

Abstract: In this talk, I will show how distribution formalism can be used to derive the complete set of junction conditions for general Local Rotational Symmetric (LRS) spacetimes in the 1+1+2 covariant formalism.  Then, I will employ these conditions to deduce some very general prescriptions for the junction of two different spacetimes, highlighting the role of the observer in determining the junction.  I will then use the 1+1+2 junction conditions to analyze the Martinez thin shell, the Schwarzschild interior solution and the Oppenheimer-Snyder collapse.

Jan 25th: Marco Serone (SISSA) 

Pre-Seminar - Room S at 11.00: Resurgence and the Power of Perturbation Theory

Abstract: Perturbation theory is one of the most important analytical tool in quantum mechanics and quantum field theory, but it is known to give rise to divergent asymptotic series. How can we then make sense out of it? Resurgence seems to be a possible answer. After an historical detour on the study of the asymptotic behaviour of perturbation theory, we introduce basic notions of resurgence and show some application in quantum mechanics and quantum field theory.

Seminar - Aula Magna at 14.30: EWKB in Quantum Mechanics and How to Avoid Trans-Series

Abstract: Using path integral methods, certain quantum mechanical systems were shown to admit deformations giving rise to Borel resummable expansions, dubbed Exact Perturbation Theory (EPT). Another notable way to study quantum mechanical models is the so called exact WKB method. Within exact WKB, energy eigenvalues are determined by quantization conditions and generally give rise to transseries in ħ. We review how EPT and exact WKB are related and show how exact quantization conditions can be trivialized to lead to EPT Borel resummable series for all energy eigenvalues.

Feb 1st: Davide Cassani (Padova U.) 

Title: Corrections to AdS5 black hole saddles

Abstract: I will discuss subleading corrections to the action and entropy of supersymmetric AdS_5 black holes. These are predicted by the analysis of the dual superconformal field theory (SCFT) and consist of finite and logarithmically divergent terms in the large-N expansion. The finite terms are captured by including higher-derivative couplings in five-dimensional gauged supergravity. These provide a holographic effective action for the SCFT anomalies and (in a setup where the solution uplifts to type IIB supergravity) should arise from one-loop corrections in the tower of KK modes. The logarithmic term accounts for the degeneracy of black hole saddles and can be seen as the consequence of the SCFT to admit a one-form symmetry. On the gravity side, it is reproduced by enumerating the flat two-form field configurations allowed by the quantum theory on the black hole background.

Feb 15th: Valentin Reys (IPhT Saclay) 

Title: Logarithmic Corrections in AdS/CFT 

Abstract: In this talk, I will review the heat kernel formalism and explain how it can be used to compute logarithmic terms in the semi-classical expansion of supergravity observables due to one-loop effects. When applied to holographic Kaluza-Klein supergravity theories with a known spectrum, this method produces results that can be matched to the logarithmic terms in the large N expansion of the dual CFT observables. When available, our results are also compatible with one-loop computations in 11d supergravity and in supergravity localization. Reverting the logic, a mild assumption on the coefficient of log N terms in CFT observables yields strong constraints on the spectrum of arbitrary gravity theories in order for them to be compatible with AdS/CFT at the quantum level.

Apr 4th: Anna Ceresole (UniTo & INFN) 

Title: Bridging Between Classical and Quantum Black Hole Interactions Through the Double Copy

Abstract: We report on ongoing work to compare the classical analytic description of the 2-body problem in Relativity via the Effective One body framework -- a basic tool in the context of gravitational wave modelling -- and results from quantum field theory and supergravity,  where quantum black hole scattering has been studied in recent years by amplitude techniques. There are lessons to be learned by examining computations of the scattering angle in Post--Minkowskian approximation for gravity and EOB representation, considering electrodynamics, gravity and supergravity. The aim is to reach a better understanding of the underlying symmetries, such as the "double copy" relating Yang Mills and gravity amplitudes.

May 16th: Andrea Antinucci (SISSA) 

Title: Continuous Symmetries, non-compact TQFTs, and Holography

Abstract: The progress in our understanding of symmetries in QFT has led to the proposal that the complete information on a symmetry structure is encoded in a TQFT in one dimension higher, known as the Symmetry TFT. This picture is well understood for finite symmetries, and I will explain the extension to continuous symmetries in the first part of the talk, based on a paper with F. Benini. This extension requires studying new TQFTs with a non-compact spectrum of operators. Like for finite symmetries, these TQFTs capture anomalies and topological manipulations via their topological boundary conditions. The main new ingredient for continuous symmetries is dynamical gauging, which is described by maps between different TQFTs. I will use this to derive the Symmetry TFT for the non-invertible chiral symmetry of QED. Moreover, the various TQFTs related by dynamical gauging arise as different boundary conditions of a unique TQFT in two dimensions higher. In the second part of the talk, based on work in progress with F. Benini and G. Rizi, I will use these tools to derive some new connections between the Symmetry TFTs and the universal EFTs describing the spontaneous symmetry breaking of any (generalized) global symmetry.

Jul 4th: Davide Astesiano (University of Iceleand) - Aula S

Title: Supersymmetric Wormholes in String Theory

Abstract: We construct a large family of Euclidean supersymmetric wormhole solutions of type IIB supergravity which are asymptotically AdS5xS5. The solutions are constructed using consistent truncation to maximally gauged supergravity in five dimensions which is further truncated to a four scalar model. Within this model we perform a full analytic classification of supersymmetric domain wall solutions with flat Euclidean domain wall slices. On each side of the wormhole, the solution asymptotes to AdS5 dual to N=4 supersymmetric Yang-Mills deformed by a supersymmetric mass term.