3 research outputs found
A maximally supersymmetric Kondo model
We study the maximally supersymmetric Kondo model obtained by adding a
fermionic impurity to N=4 supersymmetric Yang-Mills theory. While the original
Kondo problem describes a defect interacting with a free Fermi liquid of
itinerant electrons, here the ambient theory is an interacting CFT, and this
introduces qualitatively new features into the system. The model arises in
string theory by considering the intersection of a stack of M D5-branes with a
stack of N D3-branes, at a point in the D3 worldvolume. We analyze the theory
holographically, and propose a dictionary between the Kondo problem and
antisymmetric Wilson loops in N=4 SYM. We perform an explicit calculation of
the D5 fluctuations in the D3 geometry and determine the spectrum of defect
operators. This establishes the stability of the Kondo fixed point together
with its basic thermodynamic properties. Known supergravity solutions for
Wilson loops allow us to go beyond the probe approximation: the D5s disappear
and are replaced by three-form flux piercing a new topologically non-trivial
three-sphere in the corrected geometry. This describes the Kondo model in terms
of a geometric transition. A dual matrix model reflects the basic properties of
the corrected gravity solution in its eigenvalue distribution.Comment: 46 pages, 2 figures. Minor typos correcte
Adventures in Holographic Dimer Models
We abstract the essential features of holographic dimer models, and develop
several new applications of these models. First, semi-holographically coupling
free band fermions to holographic dimers, we uncover novel phase transitions
between conventional Fermi liquids and non-Fermi liquids, accompanied by a
change in the structure of the Fermi surface. Second, we make dimer vibrations
propagate through the whole crystal by way of double trace deformations,
obtaining nontrivial band structure. In a simple toy model, the topology of the
band structure experiences an interesting reorganization as we vary the
strength of the double trace deformations. Finally, we develop tools that would
allow one to build, in a bottom-up fashion, a holographic avatar of the Hubbard
model.Comment: 22 pages, 8 figures; v2: brief description of case of pure D5 lattice
added in sec.3; v3: minor typo fixed; v4: minor change
Strange metals and the AdS/CFT correspondence
I begin with a review of quantum impurity models in condensed matter physics,
in which a localized spin degree of freedom is coupled to an interacting
conformal field theory in d = 2 spatial dimensions. Their properties are
similar to those of supersymmetric generalizations which can be solved by the
AdS/CFT correspondence; the low energy limit of the latter models is described
by a AdS2 geometry. Then I turn to Kondo lattice models, which can be described
by a mean- field theory obtained by a mapping to a quantum impurity coupled to
a self-consistent environment. Such a theory yields a 'fractionalized Fermi
liquid' phase of conduction electrons coupled to a critical spin liquid state,
and is an attractive mean-field theory of strange metals. The recent
holographic description of strange metals with a AdS2 x R2 geometry is argued
to be related to such mean-field solutions of Kondo lattice models.Comment: 19 pages, 4 figures; Plenary talk at Statphys24, Cairns, Australia,
July 2010; (v2) added refs; (v3) more ref