106 research outputs found
Anomalous dimensions of finite size field strength operators in N=4 SYM
In the N=4 super Yang-Mills theory, we consider the higher order anomalous
dimensions gamma_L(g) of purely gluonic operators Tr(F^L) where F is a
component of the self-dual field strength. We propose compact closed
expressions depending parametrically on L that reproduce the prediction of
Bethe Ansatz equations up to five loop order, including transcendental dressing
corrections. The size dependence follows a simple pattern as the perturbative
order is increased and suggests hidden relations for these special operators.Comment: 26 pages, 3 eps figures. v2: published version, minor changes,
references adde
Rational three-spin string duals and non-anomalous finite size effects
We determine by a one line computation the one-loop conformal dimension and
the associated non-anomalous finite size correction for all operators dual to
spinning strings of rational type having three angular momenta (J_1,J_2,J_3) on
S^5. Finite size corrections are conjectured to encode information about string
sigma model loop corrections to the spectrum of type IIB superstrings on
AdS_5xS^5. We compare our result to the zero-mode contribution to the leading
quantum string correction derived for the stable three-spin string with two out
of the three spin labels identical and observe agreement. As a side result we
clarify the relation between the Bethe root description of three-spin strings
of the type (J,J',J') with respectively J>J' and J<J'.Comment: 15 pages, v2: comparison to string theory changed, references added,
v3: textual modifications and title change
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
Ghost Condensates and Dynamical Breaking of SL(2,R) in Yang-Mills in the Maximal Abelian Gauge
Ghost condensates of dimension two in SU(N) Yang-Mills theory quantized in
the Maximal Abelian Gauge are discussed. These condensates turn out to be
related to the dynamical breaking of the SL(2,R) symmetry present in this gaugeComment: 16 pages, LaTeX2e, final version to appear in J. Phys.
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
TBA-like equations and Casimir effect in (non-)perturbative AdS/CFT
We consider high spin, , long twist, , planar operators (asymptotic
Bethe Ansatz) of strong SYM. Precisely, we compute the minimal
anomalous dimensions for large 't Hooft coupling to the lowest order
of the (string) scaling variable with GKP string size . At the leading order ,
we can confirm the O(6) non-linear sigma model description for this bulk term,
without boundary term . Going further, we derive,
extending the O(6) regime, the exact effect of the size finiteness. In
particular, we compute, at all loops, the first Casimir correction (in terms of the infinite size O(6) NLSM), which reveals only one
massless mode (out of five), as predictable once the O(6) description has been
extended. Consequently, upon comparing with string theory expansion, at one
loop our findings agree for large twist, while reveal for negligible twist,
already at this order, the appearance of wrapping. At two loops, as well as for
next loops and orders, we can produce predictions, which may guide future
string computations.Comment: Version 2 with: new exact expression for the Casimir energy derived
(beyond the first two loops of the previous version); UV theory formulated
and analysed extensively in the Appendix C; origin of the O(6) NLSM
scattering clarified; typos correct and references adde
Maximum expected accuracy structural neighbors of an RNA secondary structure
International audienceBACKGROUND: Since RNA molecules regulate genes and control alternative splicing by allostery, it is important to develop algorithms to predict RNA conformational switches. Some tools, such as paRNAss, RNAshapes and RNAbor, can be used to predict potential conformational switches; nevertheless, no existent tool can detect general (i.e., not family specific) entire riboswitches (both aptamer and expression platform) with accuracy. Thus, the development of additional algorithms to detect conformational switches seems important, especially since the difference in free energy between the two metastable secondary structures may be as large as 15-20 kcal/mol. It has recently emerged that RNA secondary structure can be more accurately predicted by computing the maximum expected accuracy (MEA) structure, rather than the minimum free energy (MFE) structure. RESULTS: Given an arbitrary RNA secondary structure Sâ for an RNA nucleotide sequence a = aâ,..., a(n), we say that another secondary structure S of a is a k-neighbor of Sâ, if the base pair distance between Sâ and S is k. In this paper, we prove that the Boltzmann probability of all k-neighbors of the minimum free energy structure Sâ can be approximated with accuracy Δ and confidence 1 - p, simultaneously for all 0 †k N(Δ,p,K)=Ίâ»Âč(p/2K)ÂČ/4ΔÂČ, where Ί(z) is the cumulative distribution function (CDF) for the standard normal distribution. We go on to describe the algorithm RNAborMEA, which for an arbitrary initial structure Sâ and for all values 0 †k < K, computes the secondary structure MEA(k), having maximum expected accuracy over all k-neighbors of Sâ. Computation time is O(nÂł * KÂČ), and memory requirements are O(nÂČ * K). We analyze a sample TPP riboswitch, and apply our algorithm to the class of purine riboswitches. CONCLUSIONS: The approximation of RNAbor by sampling, with rigorous bound on accuracy, together with the computation of maximum expected accuracy k-neighbors by RNAborMEA, provide additional tools toward conformational switch detection. Results from RNAborMEA are quite distinct from other tools, such as RNAbor, RNAshapes and paRNAss, hence may provide orthogonal information when looking for suboptimal structures or conformational switches. Source code for RNAborMEA can be downloaded from http://sourceforge.net/projects/rnabormea/ or http://bioinformatics.bc.edu/clotelab/RNAborMEA/
Spiky strings and giant magnons on S5
Recently, classical solutions for strings moving in AdS5 x S5 have played an
important role in understanding the AdS/CFT correspondence. A large set of them
were shown to follow from an ansatz that reduces the solution of the string
equations of motion to the study of a well-known integrable 1-d system known as
the Neumann-Rosochatius (NR) system. However, other simple solutions such as
spiky strings or giant magnons in S5 were not included in the NR ansatz. We
show that, when considered in the conformal gauge, these solutions can be also
accomodated by a version of the NR-system. This allows us to describe in detail
a giant magnon solution with two additional angular momenta and show that it
can be interpreted as a superposition of two magnons moving with the same
speed. In addition, we consider the spin chain side and describe the
corresponding state as that of two bound states in the infinite SU(3) spin
chain. We construct the Bethe ansatz wave function for such bound state.Comment: 33 pages, LaTeX, 2 figures. v2: minor corrections, v3: minor
corrections, figures enlarge
The generalised scaling function: a systematic study
We describe a procedure for determining the generalised scaling functions
at all the values of the coupling constant. These functions describe
the high spin contribution to the anomalous dimension of large twist operators
(in the sector) of SYM. At fixed , can be
obtained by solving a linear integral equation (or, equivalently, a linear
system with an infinite number of equations), whose inhomogeneous term only
depends on the solutions at smaller . In other words, the solution can be
written in a recursive form and then explicitly worked out in the strong
coupling regime. In this regime, we also emphasise the peculiar convergence of
different quantities ('masses', related to the ) to the unique mass gap
of the nonlinear sigma model and analyse the first next-to-leading order
corrections.Comment: Latex version, journal version (with explanatory appendices and more
references
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