12 research outputs found
CFT description of three-dimensional Kerr-de Sitter spacetime
We describe three-dimensional Kerr-de Sitter space using similar methods as
recently applied to the BTZ black hole. A rigorous form of the classical
connection between gravity in three dimensions and two-dimensional conformal
field theory is employed, where the fundamental degrees of freedom are
described in terms of two dependent SL(2,C) currents. In contrast to the BTZ
case, however, quantization does not give the Bekenstein-Hawking entropy
connected to the cosmological horizon of Kerr-de Sitter space.Comment: 12 pages, v2: references added and some structural change
Another Leigh-Strassler deformation through the Matrix model
In here the matrix model approach, by Dijkgraaf and Vafa, is used in order to
obtain the effective superpotential for a certain deformation of N=4 SYM
discovered by Leigh and Strassler. An exact solution to the matrix model
Lagrangian is found and is expressed in terms of elliptic functions.Comment: 15 pages,2 figure
New symmetries of the chiral Potts model
In this paper a hithertho unknown symmetry of the three-state chiral Potts
model is found consisting of two coupled Temperley-Lieb algebras. From these we
can construct new superintegrable models. One realisation is in terms of a
staggered isotropic XY spin chain. Further we investigate the importance of the
algebra for the existence of mutually commuting charges. This leads us to a
natural generalisation of the boost-operator, which generates the charges.Comment: 19 pages, improved notation, made the text easier to read, corrected
some typo
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
The general Leigh-Strassler deformation and integrability
The success of the identification of the planar dilatation operator of N=4
SYM with an integrable spin chain Hamiltonian has raised the question if this
also is valid for a deformed theory. Several deformations of SYM have recently
been under investigation in this context. In this work we consider the general
Leigh-Strassler deformation. For the generic case the S-matrix techniques
cannot be used to prove integrability. Instead we use R-matrix techniques to
study integrability. Some new integrable points in the parameter space are
found.Comment: 22 pages, 8 figures, reference adde
Quantum Symmetries and Marginal Deformations
We study the symmetries of the N=1 exactly marginal deformations of N=4 Super
Yang-Mills theory. For generic values of the parameters, these deformations are
known to break the SU(3) part of the R-symmetry group down to a discrete
subgroup. However, a closer look from the perspective of quantum groups reveals
that the Lagrangian is in fact invariant under a certain Hopf algebra which is
a non-standard quantum deformation of the algebra of functions on SU(3). Our
discussion is motivated by the desire to better understand why these theories
have significant differences from N=4 SYM regarding the planar integrability
(or rather lack thereof) of the spin chains encoding their spectrum. However,
our construction works at the level of the classical Lagrangian, without
relying on the language of spin chains. Our approach might eventually provide a
better understanding of the finiteness properties of these theories as well as
help in the construction of their AdS/CFT duals.Comment: 1+40 pages. v2: minor clarifications and references added. v3: Added
an appendix, fixed minor typo
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
Is there a tower of charges to be discovered?
We investigate higher-loop integrability for a q-deformation of the -sector of SYM theory. First we construct a generalization of the long-range spin chain, which for the lowest orders describes the non-deformed dilatation operator. This generalized model is built up from TemperleyâLieb algebra generators and describes the deformed theory to at least two loops. When constructing the model we have demanded the existence of one commuting charge, which puts strong constraints on the parameters to three-loop orders. We also write the five first charges for this model at two-loops order. Our main goal is to obtain an explicit expression for an infinite number of commuting charges, all commuting with the dilatation operator. This would imply integrability. As a step towards this goal we present in this paper an expression for a generic local charge of the one-loop dilatation operator, which happens to be a generator of the TemperleyâLieb algebra.QC 2012021