The Higher Structure of Symmetries

Descripción del proyecto

Estudio de las simetrías generalizadas en campos cuánticos

La teoría cuántica de campos (TCC) tiene una gran importancia en la física moderna, pero muchos de sus comportamientos —sobre todo durante transiciones de fase o a través de distintas escalas de energía— aún no se comprenden del todo. Un nuevo planteamiento, basado en las «simetrías generalizadas», está ganando popularidad a la hora de patrones ocultos en la TCC. La información obtenida a través de este planteamiento podría ayudar a comprender mejor una gran variedad de fenómenos, desde la física de partículas hasta la ciencia de los materiales. En este contexto, el proyecto HIGH, financiado por el Consejo Europeo de Investigación, combinará herramientas de la teoría de campos topológicos, la geometría de cuerdas y las dualidades para estudiar simetrías generalizadas. El equipo busca dilucidar nuevas reglas de selección que rigen los campos cuánticos. El objetivo es abordar algunas de las preguntas abiertas más fundamentales de la TCC y redefinir el modo en que los físicos abordan la simetría.

Objetivo

Quantum field theories (QFTs) are among the most powerful tools of modern theoretical physics, with wide applications from condensed matter to elementary particle physics, phase transitions, and quantum gravity. Over the past decade, and with tremendous progress over the past two years, QFT is undergoing a revolution: a generalized notion of symmetries, capable of giving conserved quantum numbers to extended field configurations, has emerged. Generalized symmetries are radically changing many aspects of the formalism, with applications ranging from the stability of impurities and defects in condensed matter systems, to the physics of hadrons in the standard model, as well as to the structures of phases. The hallmark of generalized symmetries is their higher structure, which encodes much more refined and sophisticated information about the QFT than that of ordinary symmetries.

The goal of this reaserch proposal is to consolidate my research team, which will be devoted to develop and exploit the higher structure of symmetries to attack foundational open questions about QFT. In particular, in this project we will exploit the higher structures to obtain novel selection rules on QFT correlators, to constrain the behavior of quantum fields upon phase transitions and dualities, and most importantly to give new tools to study the behavior of QFTs across different energy scales along the flow of renormalization. To this end we are exploiting two different strategies. Firstly, we capitalize on the description of generalized symmetries as topological membranes, which allows the characterization of the higher structure via QFT correlators and topological field theory techniques. Secondly, we use a combination of tools ranging from dualities to higher dimensional QFT, and strings geometry, to probe regimes that are out of reach of more conventional methods. These strategies are complementary and intertwined.