27 research outputs found
A Constraint on Defect and Boundary Renormalization Group Flows
A conformal field theory (CFT) in dimension coupled to a planar,
two-dimensional, conformal defect is characterized in part by a "central
charge" that multiplies the Euler density in the defect's Weyl anomaly. For
defect renormalization group flows, under which the bulk remains critical, we
use reflection positivity to show that must decrease or remain constant
from ultraviolet to infrared. Our result applies also to a CFT in flat
space with a planar boundary.Comment: 9 pages, ReVTeX, v2: references added and a minor correctio
Holographic Renormalization of Probe D-Branes in AdS/CFT
We perform holographic renormalization for probe branes in AdS_5 x S^5. We
show that for four known probe D-branes wrapping an AdS_m x S^n, the
counterterms needed to render the action finite are identical to those for the
free, massive scalar in AdS_m plus counterterms for the renormalization of the
volume of AdS_m. The four cases we consider are the probe D7, two different
probe D5's and a probe D3. In the D7 case there are scheme-dependent finite
counterterms that can be fixed by supersymmetry.Comment: 22 pages; minor corrections, 5 references added, added calculation of
boundary two-point functions from fluctuations in Ad
On Holographic Entanglement Density
We use holographic duality to study the entanglement entropy (EE) of
Conformal Field Theories (CFTs) in various spacetime dimensions , in the
presence of various deformations: a relevant Lorentz scalar operator with
constant source, a temperature , a chemical potential , a marginal
Lorentz scalar operator with source linear in a spatial coordinate, and a
circle-compactified spatial direction. We consider EE between a strip or sphere
sub-region and the rest of the system, and define the "entanglement density"
(ED) as the change in EE due to the deformation, divided by the sub-region's
volume. Using the deformed CFTs above, we show how the ED's dependence on the
strip width or sphere radius, , is useful for characterizing states of
matter. For example, the ED's small- behavior is determined either by the
dimension of the perturbing operator or by the first law of EE. For
Lorentz-invariant renormalization group (RG) flows between CFTs, the "area
theorem" states that the coefficient of the EE's area law term must be larger
in the UV than in the IR. In these cases the ED must therefore approach zero
from below as . However, when Lorentz symmetry is broken and the
IR fixed point has different scaling from the UV, we find that the ED often
approaches the thermal entropy density from above, indicating area theorem
violation.Comment: References clarified and updated compared to JHEP versio
Holographic Zero Sound from Spacetime-Filling Branes
We use holography to study sound modes of strongly-interacting conformal
field theories with non-zero temperature, , and chemical potential,
. Specifically, we consider charged black brane solutions of Einstein
gravity in -dimensional Anti-de Sitter space coupled to a gauge
field with Dirac-Born-Infeld action, representing a spacetime-filling brane.
The brane action has two free parameters: the tension and the non-linearity
parameter, which controls higher-order terms in the field strength. For all
values of the tension, non-linearity parameter, and , and at
sufficiently small momentum, we find sound modes with speed given by the
conformal value and attenuation constant of hydrodynamic form. In particular we
find sound at arbitrarily low , outside the usual hydrodynamic regime,
but in the regime where a Fermi liquid exhibits Landau's "zero" sound. In fact,
the sound attenuation constant as a function of qualitatively resembles
that of a Fermi liquid, including a maximum, which in a Fermi liquid signals
the collisionless to hydrodynamic crossover. We also explore regimes of the
tension and non-linearity parameter where two other proposed definitions of the
crossover are viable, via pole collisions in Green's functions or peak movement
in the charge density spectral function.Comment: v2: minor corrections and edits, no changes to results, version
published in JHE
Fermionic Operator Mixing in Holographic p-wave Superfluids
We use gauge-gravity duality to compute spectral functions of fermionic
operators in a strongly-coupled defect field theory in p-wave superfluid
states. The field theory is (3+1)-dimensional N=4 supersymmetric SU(Nc)
Yang-Mills theory, in the 't Hooft limit and with large coupling, coupled to
two massless flavors of (2+1)-dimensional N=4 supersymmetric matter. We show
that a sufficiently large chemical potential for a U(1) subgroup of the global
SU(2) isospin symmetry triggers a phase transition to a p-wave superfluid
state, and in that state we compute spectral functions for the fermionic
superpartners of mesons valued in the adjoint of SU(2) isospin. In the spectral
functions we see the breaking of rotational symmetry and the emergence of a
Fermi surface comprised of isolated points as we cool the system through the
superfluid phase transition. The dual gravitational description is two
coincident probe D5-branes in AdS5 x S5 with non-trivial worldvolume SU(2)
gauge fields. We extract spectral functions from solutions of the linearized
equations of motion for the D5-branes' worldvolume fermions, which couple to
one another through the worldvolume gauge field. We develop an efficient method
to compute retarded Green's functions from a system of coupled bulk fermions.
We also perform the holographic renormalization of free bulk fermions in any
asymptotically Euclidean AdS space.Comment: 68 pages, 25 eps files in 9 figures; v2 minor corrections, added two
references, version published in JHE