33 research outputs found
Star product and the general Leigh-Strassler deformation
We extend the definition of the star product introduced by Lunin and
Maldacena to study marginal deformations of N=4 SYM. The essential difference
from the latter is that instead of considering U(1)xU(1) non-R-symmetry, with
charges in a corresponding diagonal matrix, we consider two Z_3-symmetries
followed by an SU(3) transformation, with resulting off-diagonal elements. From
this procedure we obtain a more general Leigh-Strassler deformation, including
cubic terms with the same index, for specific values of the coupling constants.
We argue that the conformal property of N=4 SYM is preserved, in both beta-
(one-parameter) and gamma_{i}-deformed (three-parameters) theories, since the
deformation for each amplitude can be extracted in a prefactor. We also
conclude that the obtained amplitudes should follow the iterative structure of
MHV amplitudes found by Bern, Dixon and Smirnov.Comment: 21 pages, no figures, JHEP3, v2: references added, v3: appendix A
added, v4: clarification in section 3.
Typicality versus thermality: An analytic distinction
In systems with a large degeneracy of states such as black holes, one expects
that the average value of probe correlation functions will be well approximated
by the thermal ensemble. To understand how correlation functions in individual
microstates differ from the canonical ensemble average and from each other, we
study the variances in correlators. Using general statistical considerations,
we show that the variance between microstates will be exponentially suppressed
in the entropy. However, by exploiting the analytic properties of correlation
functions we argue that these variances are amplified in imaginary time,
thereby distinguishing pure states from the thermal density matrix. We
demonstrate our general results in specific examples and argue that our results
apply to the microstates of black holes.Comment: 22 pages + appendices, 3 eps figure
On the existence of supergravity duals to D1--D5 CFT states
We define a metric operator in the 1/2-BPS sector of the D1-D5 CFT, the
eigenstates of which have a good semi-classical supergravity dual; the
non-eigenstates cannot be mapped to semi-classical gravity duals. We also
analyse how the data defining a CFT state manifests itself in the gravity side,
and show that it is arranged into a set of multipoles. Interestingly, we find
that quantum mechanical interference in the CFT can have observable
manifestations in the semi-classical gravity dual. We also point out that the
multipoles associated to the normal statistical ensemble fluctuate wildly,
indicating that the mixed thermal state should not be associated to a
semi-classical geometry.Comment: 22 pages, 2 figures. v2 : references added, typos correcte
Integrable Spin Chains with U(1)^3 symmetry and generalized Lunin-Maldacena backgrounds
We consider the most general three-state spin chain with U(1)^3 symmetry and
nearest neighbour interaction. Our model contains as a special case the spin
chain describing the holomorphic three scalar sector of the three parameter
complex deformation of N=4 SYM, dual to type IIB string theory in the
generalized Lunin-Maldacena backgrounds discovered by Frolov. We formulate the
coordinate space Bethe ansatz, calculate the S-matrix and determine for which
choices of parameters the S-matrix fulfills the Yang-Baxter equations. For
these choices of parameters we furthermore write down the R-matrix. We find in
total four classes of integrable models. In particular, each already known
model of the above type is nothing but one in a family of such models.Comment: 16 pages, 3 figures, references correcte
Supersymmetric Wilson loops on S^3
This paper studies in great detail a family of supersymmetric Wilson loop
operators in N=4 supersymmetric Yang-Mills theory we have recently found. For a
generic curve on an S^3 in space-time the loops preserve two supercharges but
we will also study special cases which preserve 4, 8 and 16 supercharges. For
certain loops we find the string theory dual explicitly and for the general
case we show that string solutions satisfy a first order differential equation.
This equation expresses the fact that the strings are pseudo-holomorphic with
respect to a novel almost complex structure we construct on AdS_4 x S^2. We
then discuss loops restricted to S^2 and provide evidence that they can be
calculated in terms of similar observables in purely bosonic YM in two
dimensions on the sphere.Comment: Latex, 84 pages, 4 figures. v2: minor changes, references added; to
appear in JHE
Beauty and the Twist: The Bethe Ansatz for Twisted N=4 SYM
It was recently shown that the string theory duals of certain deformations of
the N=4 gauge theory can be obtained by a combination of T-duality
transformations and coordinate shifts. Here we work out the corresponding
procedure of twisting the dual integrable spin chain and its Bethe ansatz. We
derive the Bethe equations for the complete twisted N=4 gauge theory at one and
higher loops. These have a natural generalization which we identify as twists
involving the Cartan generators of the conformal algebra. The underlying model
appears to be a form of noncommutative deformation of N=4 SYM.Comment: 28 pages, v2: reference flip corrected, v3: some typos in
(4.10,4.20,5.5) correcte
A note on the universality of the Hagedorn behavior of pp-wave strings
Following on from recent studies of string theory on a one-parameter family
of integrable deformations of proposed by Lunin and
Maldacena, we carry out a systematic analysis of the high temperature
properties of type IIB strings on the associated pp-wave geometries. In
particular, through the computation of the thermal partition function and free
energy we find that not only does the theory exhibit a Hagedorn transition in
both the and class of pp-waves, but that the Hagedorn
temperature is insensitive to the deformation suggesting an interesting
universality in the high temperature behaviour of the pp-wave string theory. We
comment also on the implications of this universality on the
confinement/deconfinement transition in the dual
Leigh-Strassler deformation of Yang-Mills theory.Comment: 25 pages; fixed minor typo; added reference
Integrable twists in AdS/CFT
A class of marginal deformations of four-dimensional N=4 super Yang-Mills
theory has been found to correspond to a set of smooth, multiparameter
deformations of the S^5 target subspace in the holographic dual on AdS_5 x S^5.
We present here an analogous set of deformations that act on global toroidal
isometries in the AdS_5 subspace. Remarkably, certain sectors of the string
theory remain classically integrable in this larger class of so-called
gamma-deformed AdS_5 x S^5 backgrounds. Relying on studies of deformed
su(2)_gamma models, we formulate a local sl(2)_gamma Lax representation that
admits a classical, thermodynamic Bethe equation (based on the Riemann-Hilbert
interpretation of Bethe's ansatz) encoding the spectrum in the deformed AdS_5
geometry. This result is extended to a set of discretized, asymptotic Bethe
equations for the twisted string theory. Near-pp-wave energy spectra within
sl(2)_gamma and su(2)_gamma sectors provide a useful and stringent test of such
equations, demonstrating the reliability of this technology in a wider class of
string backgrounds. In addition, we study a twisted Hubbard model that yields
certain predictions of the dual beta-deformed gauge theory.Comment: v2: references and clarifications added, 46 page
Green-Schwarz Strings in TsT-transformed backgrounds
We consider classical strings propagating in a background generated by a
sequence of TsT transformations. We describe a general procedure to derive the
Green-Schwarz action for strings. We show that the U(1) isometry variables of
the TsT-transformed background are related to the isometry variables of the
initial background in a universal way independent of the details of the
background. This allows us to prove that strings in the TsT-transformed
background are described by the Green-Schwarz action for strings in the initial
background subject to twisted boundary conditions. Our construction implies
that a TsT transformation preserves integrability properties of the string
sigma model. We discuss in detail type IIB strings propagating in the
\g_i-deformed AdS_5 x S^5 space-time, find the twisted boundary conditions for
bosons and fermions, and use them to write down an explicit expression for the
monodromy matrix. We also discuss string zero modes whose dynamics is governed
by a fermionicgeneralization of the integrable Neumann model.Comment: 33 pages, latex, v2: typos correcte
Holographic anatomy of fuzzballs
We present a comprehensive analysis of 2-charge fuzzball solutions, that is,
horizon-free non-singular solutions of IIB supergravity characterized by a
curve on R^4. We propose a precise map that relates any given curve to a
specific superposition of R ground states of the D1-D5 system. To test this
proposal we compute the holographic 1-point functions associated with these
solutions, namely the conserved charges and the vacuum expectation values of
chiral primary operators of the boundary theory, and find perfect agreement
within the approximations used. In particular, all kinematical constraints are
satisfied and the proposal is compatible with dynamical constraints although
detailed quantitative tests would require going beyond the leading supergravity
approximation. We also discuss which geometries may be dual to a given R ground
state. We present the general asymptotic form that such solutions must have and
present exact solutions which have such asymptotics and therefore pass all
kinematical constraints. Dynamical constraints would again require going beyond
the leading supergravity approximation.Comment: 87 pages, begins with 10 page self contained summary of
results;v2:JHEP version; v3: typos corrected, see in particular formula D.1