# Fundamental Interactions, Geometry and Topology.

Thursday, 25 October 2018
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(Europe/Rome)

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**Dipartimento di Fisica "Ettore Pancini" ( Aula Caianiello )**via Cintia, ed. 6
80126 Napoli

Description |
One-day workshop on the interface between the Theory of Fundamental Interactions and Mathematics. Program: 9.30 - 10.30 Dmitri SOROKIN (INFN - Padua section - Italy) "Geometry of surfaces and dynamics of branes" 10.30-11.00 coffee-break 11.00-12.00 Erik PLAUSCHINN (LMU - Munich - Germany) "Non-Geometric Backgrounds in String Theory" 12.00-13.00 Falk HASSLER (Oviedo University - Spain) "Poisson-Lie T-Duality in Double Field Theory" 13.00-14.30 Lunch break 14.30-15.30 Giulio BONELLI (SISSA - Trieste - Italy) "Spectral Geometry of Supersymmetric Gauge Theories" 15.30- 16.00 Coffee break 16.00-17.00 Camillo IMBIMBO (Genoa Univ. - Italy) "Emergent Topological Structures in Supergravity" 17.00-17.30 Discussion and conclusions ABSTRACTS: SOROKIN - We will overview how the dynamics of relativistic objects such as particles, strings and membranes is naturally described by the geometric theory of surfaces embedded into ambient spaces. A generalization of the surface theory to the description of supersymmetric surfaces in target superspaces governed by a universal superembedding condition will be shown (using a simple example) to unify different formulations of String Theory and describe the dynamics of all known super-branes. PLAUSCHINN - String theory is a theory with compelling physical and mathematical features. One of them is its rich structure of dualities, which connects different formulations of string theory among each other. Using dualities, one finds that a string can be well-defined on spaces which are ill-defined for point-particles. Such spaces are called non-geometric backgrounds, and they give rise to interesting structures both in physics and mathematics. In this talk I will give an introduction to non-geometric backgrounds in string theory as well as an overview of the main developments in this field. HASSLER - A formulation of Double Field Theory is presented which makes Poisson-Lie T-duality manifest. It allows to identify the doubled space with a Drinfeld double and provides a powerful tool to extract the transformation of the metric, B-field, dilaton and R/R potentials under Poisson-Lie T-duality. BONELLI - The moduli space of vacua of supersymmetric gauge theories and of its BPS saturated observables is described by associated integrable systems. We will discuss the geometric engineering of supersymmetric gauge theories via superstring theory and show that the extra dimensions naturally encode the spectral geometry of the associated integrable systems. Distinct dual embeddings point to different features of the QFT encoding diverse presentations of exact partition functions. We will exemplify this class of phenomena in the case of 4 and 5 dimensional gauge theories with eight supercharges. IMBIMBO - We describe two different topological structures sitting inside supergravity. The first one is universal and consists of topological gravity coupled to topological Yang-Mills. The second one appears for a certain class of "twistable" supergravities: it consists of several topological scalar multiplets coupled to topological gravity. The topological scalar multiplets transform in the vector representation of a non-compact duality group. Both these structures are ``emergent', in the sense that (part of) the topological fields are composites of the microscopic supergravity fields. On the space of supersymmetric vacua, the two topological structures are related by certain polynomial relations, which are equivalent to the integrability conditions of the equations for generalized covariantly constant spinors. This fact provides a powerful tool to analyze the space of classical supersymmetric vacua of supergravity. More details on https://agenda.infn.it/conferenceDisplay.py?confId=17317 |

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