58 research outputs found
Twisted Bethe equations from a twisted S-matrix
All-loop asymptotic Bethe equations for a 3-parameter deformation of
AdS5/CFT4 have been proposed by Beisert and Roiban. We propose a Drinfeld twist
of the AdS5/CFT4 S-matrix, together with c-number diagonal twists of the
boundary conditions, from which we derive these Bethe equations. Although the
undeformed S-matrix factorizes into a product of two su(2|2) factors, the
deformed S-matrix cannot be so factored. Diagonalization of the corresponding
transfer matrix requires a generalization of the conventional algebraic Bethe
ansatz approach, which we first illustrate for the simpler case of the twisted
su(2) principal chiral model. We also demonstrate that the same twisted Bethe
equations can alternatively be derived using instead untwisted S-matrices and
boundary conditions with operatorial twists.Comment: 42 pages; v2: a new appendix on sl(2) grading, 2 additional
references, and some minor changes; v3: improved Appendix D, additional
references, and further minor changes, to appear in JHE
Pulsating Strings in Lunin-Maldacena Backgrounds
We consider pulsating strings in Lunin-Maldacena backgrounds, specifically in
deformed Minkowski spacetime and deformed AdS_5xS^5. We find the relation
between the energy and the oscillation number of the pulsating string when the
deformation is small. Since the oscillation number is an adiabatic invariant it
can be used to explore the regime of highly excited string states. We then
quantize the string and look for such a sector. For the deformed Minkowski
background we find a precise match with the classical results if the
oscillation number is quantized as an even number. For the deformed AdS_5xS^5
we find a contribution which depends on the deformation parameter.Comment: 16 pages, 2 figures, typos fixe
Spinning strings and integrable spin chains in the AdS/CFT correspondence
In this introductory review we discuss dynamical tests of the AdS_5 x S^5
string/N=4 super Yang-Mills duality. After a brief introduction to AdS/CFT we
argue that semiclassical string energies yield information on the quantum
spectrum of the string in the limit of large angular momenta on the S^5. The
energies of the folded and circular spinning string solutions rotating on a S^3
within the S^5 are derived, which yield all loop predictions for the dual gauge
theory scaling dimensions. These follow from the eigenvalues of the dilatation
operator of N=4 super Yang-Mills in a minimal SU(2) subsector and we display
its reformulation in terms of a Heisenberg s=1/2 spin chain along with the
coordinate Bethe ansatz for its explicit diagonalization. In order to make
contact to the spinning string energies we then study the thermodynamic limit
of the one-loop gauge theory Bethe equations and demonstrate the matching with
the folded and closed string result at this loop order. Finally the known gauge
theory results at higher-loop orders are reviewed and the associated long-range
spin chain Bethe ansatz is introduced, leading to an asymptotic all-loop
conjecture for the gauge theory Bethe equations. This uncovers discrepancies at
the three-loop order between gauge theory scaling dimensions and string theory
energies and the implications of this are discussed. Along the way we comment
on further developments and generalizations of the subject and point to the
relevant literature.Comment: 40 pages, invited contribution to Living Reviews in Relativity. v2:
improvements in the text and references adde
p-wave Holographic Superconductors and five-dimensional gauged Supergravity
We explore five-dimensional and
SO(6) gauged supergravities as frameworks for condensed matter applications.
These theories contain charged (dilatonic) black holes and 2-forms which have
non-trivial quantum numbers with respect to U(1) subgroups of SO(6). A question
of interest is whether they also contain black holes with two-form hair with
the required asymptotic to give rise to holographic superconductivity. We first
consider the case, which contains a complex two-form potential
which has U(1) charge . We find that a slight
generalization, where the two-form potential has an arbitrary charge , leads
to a five-dimensional model that exhibits second-order superconducting
transitions of p-wave type where the role of order parameter is played by
, provided . We identify the operator that condenses
in the dual CFT, which is closely related to Super Yang-Mills
theory with chemical potentials. Similar phase transitions between R-charged
black holes and black holes with 2-form hair are found in a generalized version
of the gauged supergravity Lagrangian where the two-forms have
charge .Comment: 35 pages, 14 figure
The dual string sigma-model of the SU_q(3) sector
In four-dimensional N=4 super Yang-Mills (SYM) the SU(3) sub-sector spanned
by purely holomorphic fields is isomorphic to the corresponding mixed one
spanned by both holomorphic and antiholomorphic fields. This is no longer the
case when one considers the marginally deformed N=4 SYM. The mixed SU(3) sector
marginally deformed by a complex parameter beta, i.e. SU_q(3) with q=e^{2
i\pi\beta}, has been shown to be integrable at one-loop hep-th/0703150, while
it is not the case for the corresponding purely holomorphic one. Moreover, the
marginally deformed N=4 SYM also has a gravity dual constructed by Lunin and
Maldacena in hep-th/0502086. However, the mixed SU_q(3) sector has not been
studied from the supergravity point of view. Hence in this note, for the case
of purely imaginary marginal -deformations, we compute the superstring
SU_q(3) \sigma-model in the fast spinning string limit and show that, for
rational spinning strings, it reproduces the energy computed via Bethe
equations.Comment: 20 page
Holographic Wilsonian flows and emergent fermions in extremal charged black holes
We study holographic Wilsonian RG in a general class of asymptotically AdS
backgrounds with a U(1) gauge field. We consider free charged Dirac fermions in
such a background, and integrate them up to an intermediate radial distance,
yielding an equivalent low energy dual field theory. The new ingredient,
compared to scalars, involves a `generalized' basis of coherent states which
labels a particular half of the fermion components as coordinates or momenta,
depending on the choice of quantization (standard or alternative). We apply
this technology to explicitly compute RG flows of charged fermionic operators
and their composites (double trace operators) in field theories dual to (a)
pure AdS and (b) extremal charged black hole geometries. The flow diagrams and
fixed points are determined explicitly. In the case of the extremal black hole,
the RG flows connect two fixed points at the UV AdS boundary to two fixed
points at the IR AdS_2 region. The double trace flow is shown, both numerically
and analytically, to develop a pole singularity in the AdS_2 region at low
frequency and near the Fermi momentum, which can be traced to the appearance of
massless fermion modes on the low energy cut-off surface. The low energy field
theory action we derive exactly agrees with the semi-holographic action
proposed by Faulkner and Polchinski in arXiv:1001.5049 [hep-th]. In terms of
field theory, the holographic version of Wilsonian RG leads to a quantum theory
with random sources. In the extremal black hole background the random sources
become `light' in the AdS_2 region near the Fermi surface and emerge as new
dynamical degrees of freedom.Comment: 37 pages (including 8 pages of appendix), 10 figures and 2 table
On the Rotating and Oscillating strings in
We study rigidly rotating strings in the -deformed background. We find out two classes of solutions corresponding to the
giant magnon and single spike solutions of the string rotating in two
subspace of rotations reduced along two different isometries.
We verify that the dispersion relations reduce to the well known relation in
the limit. We further study some oscillating string
solutions in the subspace.Comment: 20 pages, clarifications added, version to appear in JHE
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