78 research outputs found
Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence
We introduce a new quantum mechanical theory called Spin Matrix theory (SMT).
The theory is interacting with a single coupling constant g and is based on a
Hilbert space of harmonic oscillators with a spin index taking values in a Lie
(super)algebra representation as well as matrix indices for the adjoint
representation of U(N). We show that SMT describes N=4 super-Yang-Mills theory
(SYM) near zero-temperature critical points in the grand canonical phase
diagram. Equivalently, SMT arises from non-relativistic limits of N=4 SYM. Even
though SMT is a non-relativistic quantum mechanical theory it contains a
variety of phases mimicking the AdS/CFT correspondence. Moreover, the infinite
g limit of SMT can be mapped to the supersymmetric sector of string theory on
AdS_5 x S^5. We study SU(2) SMT in detail. At large N and low temperatures it
is a theory of spin chains that for small g resembles planar gauge theory and
for large g a non-relativistic string theory. When raising the temperature a
partial deconfinement transition occurs due to finite-N effects. For
sufficiently high temperatures the partially deconfined phase has a classical
regime. We find a matrix model description of this regime at any coupling g.
Setting g=0 it is a theory of N^2+1 harmonic oscillators while for large g it
becomes 2N harmonic oscillators.Comment: 36 pages, 3 figures. v2: Refs. adde
The Hagedorn temperature in a decoupled sector of AdS/CFT
We match the Hagedorn/deconfinement temperature of planar N=4 super
Yang-Mills (SYM) on R x S^3 to the Hagedorn temperature of string theory on
AdS_5 x S^5. The match is done in a near-critical region where both gauge
theory and string theory are weakly coupled. On the gauge theory side we are
taking a decoupling limit found in hep-th/0605234 in which the physics of
planar N=4 SYM is given exactly by the ferromagnetic XXX_{1/2} Heisenberg spin
chain. We find moreover a general relation between the Hagedorn/deconfinement
temperature and the thermodynamics of the Heisenberg spin chain. On the string
theory side, we identify the dual limit which is taken of string theory on a
maximally symmetric pp-wave background with a flat direction, obtained from a
Penrose limit of AdS_5 x S^5. We compute the Hagedorn temperature of the string
theory and find agreement with the Hagedorn/deconfinement temperature computed
on the gauge theory side. Finally, we discuss a modified decoupling limit in
which planar N=4 SYM reduces to the XXX_{1/2} Heisenberg spin chain with an
external magnetic field.Comment: 7 pages. Talk presented by MO at the RTN workshop, Napoli, Oct. 9-13,
200
Thermal DBI action for the D3-brane at weak and strong coupling
We study the effective action for finite-temperature D3-branes with an
electromagnetic field at weak and strong coupling. We call this action the
thermal DBI action. Comparing at low temperature the leading correction
for the thermal DBI action at weak and strong coupling we find that the
factor well-known from the AdS/CFT correspondence extends to the case of
arbitrary electric and magnetic fields on the D3-brane. We investigate the
reason for this by taking the decoupling limit in both the open and the closed
string descriptions thus showing that the AdS/CFT correspondence extends to the
case of arbitrary constant electric and magnetic fields on the D3-brane.Comment: 30 pages, no figure
On Three-point Functions in the AdS_4/CFT_3 Correspondence
We calculate planar, tree-level, non-extremal three-point functions of
operators belonging to the SU(2) x SU(2) sector of ABJM theory. First, we
generalize the determinant representation, found by Foda for the three-point
functions of the SU(2) sector of N=4 SYM, to the present case and find that the
ABJM result up to normalization factors factorizes into a product of two N=4
SYM correlation functions. Secondly, we treat the case where two operators are
heavy and one is light and BPS, using a coherent state description of the heavy
ones. We show that when normalized by the three-point function of three BPS
operators the heavy-heavy-light correlation function agrees, in the
Frolov-Tseytlin limit, with its string theory counterpart which we calculate
holographically.Comment: 24 pages. v2: typos corrected, references added, published versio
Finite-size corrections to the rotating string and the winding state
We compute higher order finite size corrections to the energies of the
circular rotating string on AdS_5 x S^5, of its orbifolded generalization on
AdS_5 x S^5/Z_M and of the winding state which is obtained as the limit of the
orbifolded circular string solution when J -> infinity and J/M^2 is kept fixed.
We solve, at the first order in lambda'=lambda/J^2, where lambda is the 't
Hooft coupling, the Bethe equations that describe the anomalous dimensions of
the corresponding gauge dual operators in an expansion in m/K, where m is the
winding number and K is the "magnon number", and to all orders in the angular
momentum J. The solution for the circular rotating string and for the winding
state can be matched to the energy computed from an effective quantum
Landau-Lifshitz model beyond the first order correction in 1/J. For the leading
1/J corrections to the circular rotating string in m^2 and m^4 and for the
subleading 1/J^2 corrections to the m^2 term, we find agreement. For the
winding state we match the energy completely up to, and including, the order
1/J^2 finite-size corrections. The solution of the Bethe equations
corresponding to the spinning closed string is also provided in an expansion in
m/K and to all orders in J.Comment: v2: 33 pages, misprints corrected, references added, version accepted
for publication in JHE
The Flowing BIon
In this paper we use the effective blackfold description of branes to extend
the study of the thermal BIon, a D-brane and parallel anti-D-brane connected by
a wormhole with F-string charge in hot flat space, by introducing a radial
boost along the brane. The boosted system behaves qualitatively differently
from both the extremal and the thermal BIon considered previously.
Interestingly, we are able to formulate a first law of thermodynamics for the
system as a whole, despite the fact that it is not a stationary blackfold. In
particular, the global temperature is given by the rest frame temperature times
the gamma factor of special relativity which is the inverse transformation
compared to the case of stationary blackfolds. In addition we define two new
kinds of thermodynamic conjugate variables, the energy flux and the
integrated velocity on the brane. We find that a phase transition occurs by
varying the energy flux . Below a critical value of the brane separation
changes only slightly with . Instead above the critical value
grows exponentially.Comment: 26 pages, 6 figures. v2: Introduction and conclusion improved,
references adde
AdS/CFT v.s. String Loops
The one string-loop correction to the energies of two impurity BMN states are
computed using IIB light-cone string field theory with an improved 3-string
vertex that has been proposed by Dobashi and Yoneya. As in previous published
computations, the string vertices are truncated to the 2-impurity channel. The
result is compared with the prediction from non-planar corrections in the BMN
limit of supersymmetric Yang-Mills theory. It is found to agree
at leading order -- one-loop in Yang-Mills theory -- and is close but not quite
in agreement at order two Yang-Mills loops. Furthermore, in addition to the
leading 1/2 power in the t'Hooft coupling, which is generic in string field
theory, and which we have previously argued cancels, we find that the 3/2 and
5/2 powers are also miraculously absent.Comment: 13 page
On the existence of the Blandford-Znajek monopole for a slowly rotating Kerr black hole
The Blandford-Znajek monopole is a conjectured solution of force-free
electrodynamics in the vicinity of a slowly rotating Kerr black hole,
supposedly defined as a perturbation in small angular momentum. It is used to
argue for the extraction of energy from rotating black holes by the
Blandford-Znajek process. We set up a careful analysis of the perturbative
definition of the Blandford-Znajek monopole, showing in particular that the
regime in which it is defined allows to use the technique of matched asymptotic
expansions. Our conclusion is that the Blandford-Znajek monopole, as it is
defined, is not consistent with demanding physically reasonable boundary
conditions far away from the event horizon. This puts into question the
existence of the Blandford-Znajek monopole, at least in the limit of slow
rotation of the Kerr black hole.Comment: 8 pages, pdflatex. v2: minor typos corrected, conclusion improved,
acknowledgments added. v3: published version, references added, MAE
explanation and conclusions slightly expande
Fixing the non-relativistic expansion of the 1PM potential
We obtain a first order post-Minkowskian two-body effective potential whose
post-Newtonian expansion directly reproduces the Einstein-Infeld-Hoffmann
potential. Post-Minkowskian potentials can be extracted from on-shell
scattering amplitudes in a quantum field theory of scalar matter coupled to
gravity. Previously, such potentials did not reproduce the
Einstein-Infeld-Hoffmann potential without employing a suitable canonical
transformation. In this work, we resolve this issue by obtaining a new
expression for the first-order post-Minkowskian potential. This is accomplished
by exploiting the reference frame dependence that arises in the scattering
amplitude computation. Finally, as a check on our result, we demonstrate that
our new potential gives the correct scattering angle.Comment: 20 page
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