Quantum gravity, black holes and holography
The conundrums originating from the quantization of gravity, which manifest themselves most vividly in the black hole information paradox, are one of the main driving forces of the modern research in theoretical physics. We tackle these problems with the conceptual and technical tools provided by string theory. In particular, the holographic duality between gravity and field theories offers important clues on the degrees of freedom that encode the information that is inaccessible to the classical description of black holes. The elementary objects — strings and D-branes — that provide the building blocks of the string-theoretic construction of black holes, admit two different but equivalent descriptions, useful in opposite regimes: on one side, they are associated with gravitational configurations, on the other, with states in ordinary field theories. This latter picture implies, at least for some classes of black holes, that the gravitational backgrounds representing the microstates of black holes depart from the classical geometry already at the horizon scale, and it thus removes the very origin of the paradox. Turning things around, the equivalence of the two descriptions can also be usefully applied to extract information on the field theory from the dual gravity backgrounds.
Supersymmetric and Topological Quantum Field Theories and Strings
Topological (field and string) theories are close “cousins” of supersymmetric theories. They are defined by a distinctive form of “topological” supersymmetry, known as BRST symmetry. Topological theories exhibit simpler dynamics and are more manageable compared to their supersymmetric counterparts. Despite this simplicity, the BRST symmetry of topological theories is intimately connected, by means of a mechanism known as “twisting”, to the physical supersymmetries of the corresponding supersymmetric theories. As a result, the physical quantities computed in topological theories describe certain subsectors of supersymmetric theories, the so-called BPS sectors. For this reason, topological theories and methods have been essential in advancing our understanding of the non-perturbative dynamics of supersymmetric field theories and strings, as well as in establishing the holographic duality between gravity and gauge theories.
The specific topics of our research in this area include: supersymmetric indices, topological gravity and its coupling to topological gauge theories, matrix models and their applications to topological string theory, the holomorphic anomaly of topological strings, holographic conformal anomalies, the Wilson-Polchinski renormalization group equation and its large N limit, open string field theory and tachyon condensation, localization of supersymmetric gauge theories, topological structures in supergravity, topological and holographic formulations of superconformal anomalies.
Strongly coupled Quantum and Conformal Field Theories
Quantum Field Theories (QFTs) have a wide range of applications, and are incredibly effective in particle physics, where they describe behavior of elementary particles, as well as in condensed matter, where they can be used to study collective phenomena. However, studying them is notoriously hard, with only a small portion of them being under analytic control. A necessary step in order to improve our comprehension of QFTs is to understand what their general properties: what consitutes a consistent theory? What sort of symmetry can a theory have? At the same time, it’s important to develop methods (both analytic and numerical) to study specific examples of strongly coupled QFTs.
A special place in the space of QFTs is occupied by Conformal Field Theories (CFTs). Given their larger symmetry groups, these theories are more approachable, as shown by the results of the conformal bootstrap in the last fifteen years, and are the perfect setting to try to answer these questions. More in detail, the research topics include: conformal bootstrap, generalized symmetries, non-unitary theories, gauge theories, lattice approaches to gauge theory
Fractons
What are known as “fractons” represent new phases of quantum matter characterized by excitations that exhibit restricted mobility, being either immobile, or mobile only in certain directions. They constitute a new class of quantum state of matter, which does not wholly fit into any of the existing paradigms, but which connects to areas including glassy quantum dynamics, topological order, spin liquids, elasticity theory, quantum information theory, and gravity. Fractons can be connected to generalized gauge theories, and may be obtained from more familiar theories, like tensor gauge theory. The main properties of the fracton quasiparticles can be obtained from a generalized covariant Maxwell-like action.
The canonical momentum derived from the fracton Lagrangian coincides with the tensor electric field appearing in the fracton Literature, and the field equations of motion, which have the same form as the covariant Maxwell equations, can be written in terms of the generalized electric and magnetic fields and yield two of the four Maxwell equations (generalized electric Gauss and Ampère laws), while the other two (generalized magnetic Gauss and Faraday laws) are consequences of the “Bianchi identity” for a rank-three fracton strength tensor, as in Maxwell theory. The equations describing the fracton limited mobility, namely the charge and dipole conservation, in our formalism are not external constraints, but rather consequences of the field equations of motion, hence of the invariant action and, ultimately, of the fracton covariant symmetry. Finally, the known analogies between Linearized Gravity and fracton theory can be increased by noting that both satisfy the generalized Gauss constraint which underlies the limited mobility property, which one would not expect in LG.
Staff
Stefano Giusto
Camillo Imbimbo
Nicola Maggiore
Bernardo Zan
Postdocs
PhD Students
Daniel Sacco Shaikh