Supergravity in a pencil: From AdS to Graphene
I - Fisica nucleare e subnucleare
Aula Palazzo dell'Emiciclo - Sala B. Croce - Martedì 24 h 17:30 - 19:30
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The AdS/CFT correspondence between a gravity model on a curved anti-de Sitter space in $D+1$ dimensions and a quantum field theory in $D$ dimensions allows to study a strongly interacting system starting from a weakly coupled classical supergravity in one dimension higher. An important application is in the framework of condensed matter, where it is well known that the properties of graphene are well described using the formalism of general relativity, since the equations of motion of the collective modes (quasiparticles) in graphene at the Dirac points have formally the same expression as the Dirac equation of a relativistic spin particle, provided the speed of light is substituted with the Fermi velocity in the material. We apply this gauge/gravity correspondence to a layer of graphene in $D=2+1$, first of all by identifying a $N=2$ supergravity theory in $D=3+1$, which correctly reproduces a model by Alvarez, Valenzuela and Zanelli, suitable to describe graphene. This top-down approach is more predictive than the conventional bottom-up one, because it is heavily constrained by the properties of the higher-dimensional supergravity theory, such as supersymmetry. Then we study the properties of the corresponding Chern-Simons supergravity in $D=2+1$, e.g. performing a BRST quantization and finding a generalization of this model to $N>2$.