5 research outputs found
On the Non-renormalization of the AdS Radius
We show that the relation between the 't Hooft coupling and the radius of AdS
is not renormalized at one-loop in the sigma model perturbation theory. We
prove this by computing the quantum effective action for the superstring on
AdS_5 x S^5 and showing that it does not receive any finite alpha' corrections.
We also show that the central charge of the interacting worldsheet conformal
field theory vanishes at one-loop.Comment: 13 pages, harvmac. v2: refs added, version to be published on JHE
Holography, Fractionalization and Magnetic Fields
Four dimensional gravity with a U(1) gauge field, coupled to various fields
in asymptotically anti-de Sitter spacetime, provides a rich arena for the
holographic study of the strongly coupled (2+1)-dimensional dynamics of finite
density matter charged under a global U(1). As a first step in furthering the
study of the properties of fractionalized and partially fractionalized degrees
of freedom in the strongly coupled theory, we construct electron star solutions
at zero temperature in the presence of a background magnetic field. We work in
Einstein-Maxwell-dilaton theory. In all cases we construct, the magnetic source
is cloaked by an event horizon. A key ingredient of our solutions is our
observation that starting with the standard Landau level structure for the
density of states, the electron star limits reduce the charge density and
energy density to that of the free fermion result. Using this result we
construct three types of solution: One has a star in the infra-red with an
electrically neutral horizon, another has a star that begins at an electrically
charged event horizon, and another has the star begin a finite distance from an
electrically charged horizon.Comment: 18 pages, 2 figures. Submitted to Springer Lecture Notes: Strongly
interacting matter in magnetic fields. v2: Updated references and adjusted
some phrasing in the introductio
Review of AdS/CFT Integrability, Chapter II.3: Sigma Model, Gauge Fixing
This review is devoted to the classical integrability of the AdS5xS5
superstring theory. It starts with a reminder of the corresponding action as a
coset model. The symmetries of this action are then reviewed. The classical
integrability is then considered from the lagrangian and hamiltonian points of
view. The second part of this review deals with the gauge fixing of this
theory. Finally, some aspects of the pure spinor formulation are also briefly
reviewed.Comment: 18 pages, see also overview article arXiv:1012.3982, v2: references
to other chapters updated; v3: minor correction
UV finiteness of Pohlmeyer-reduced form of the AdS_5xS^5 superstring theory
We consider the Pohlmeyer-type reduced theory found by explicitly solving the
Virasoro constraints in the formulation of AdS_5xS^5 superstring in terms of
supercoset currents. The resulting set of classically equivalent, integrable
Lagrangian equations of motion has the advantage of involving only a physical
number of degrees of freedom and yet being 2d Lorentz invariant. The
corresponding reduced theory action may be written as a gauged WZW model
coupled to fermions with further bosonic and fermionic potential terms. Since
the AdS_5xS^5 superstring sigma model is conformally invariant, its classical
relation to the reduced theory may extend to the quantum level only if the
latter is, in fact, UV finite. This theory is power counting renormalizable
with the only possible divergences being of potential type. We explicitly
verify its 1-loop finiteness and show that the 2-loop divergences are, in
general, scheme dependent and vanish in dimensional reduction scheme. We expect
that the reduced theory is finite to all orders in the loop expansion.Comment: 40 pages, Latex; v2: typos corrected, minor clarifying remarks adde
Finite-size corrections for quantum strings on AdS<sub>4</sub> x CP<sup>3</sup>
We revisit the calculation of curvature corrections to the pp-wave energy of
type IIA string states on AdS_4 x CP^3 initiated in arXiv:0807.1527. Using the
near pp-wave Hamiltonian found in arXiv:0912.2257, we compute the first
non-vanishing correction to the energy of a set of bosonic string states at
order 1/R^2, where R is the curvature radius of the background. The leading
curvature corrections give rise to cubic, order 1/R, and quartic, order 1/R^2,
terms in the Hamiltonian, for which we implement the appropriate normal
ordering prescription. Including the contributions from all possible fermionic
and bosonic string states, we find that there exist logarithmic divergences in
the sums over mode numbers which cancel between the cubic and quartic
Hamiltonian. We show that the cubic Hamiltonian naturally requires that the
cutoff for summing over heavy modes must be twice the one for light modes. With
this prescription the strong-weak coupling interpolating function h(\lambda),
entering the magnon dispersion relation, does not receive a one-loop
correction, in agreement with the algebraic curve spectrum. However, the single
magnon dispersion relation exhibits finite-size exponential corrections.Comment: Published version, references added. A discussion on single
oscillator states include