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

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

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, $s$, long twist, $L$, planar operators (asymptotic Bethe Ansatz) of strong ${\cal N}=4$ SYM. Precisely, we compute the minimal anomalous dimensions for large 't Hooft coupling $\lambda$ to the lowest order of the (string) scaling variable $\ell \sim L/ (\ln \mathcal{S} \sqrt{\lambda})$ with GKP string size $\sim\ln \mathcal{S}\equiv 2 \ln (s/\sqrt{\lambda})$. At the leading order $(\ln \mathcal{S}) \cdot \ell ^2$, we can confirm the O(6) non-linear sigma model description for this bulk term, without boundary term $(\ln \mathcal{S})^0$. 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 $\ell ^0/\ln \mathcal{S}$ (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 S₀ for an RNA nucleotide sequence a = a₁,..., a(n), we say that another secondary structure S of a is a k-neighbor of S₀, if the base pair distance between S₀ and S is k. In this paper, we prove that the Boltzmann probability of all k-neighbors of the minimum free energy structure S₀ can be approximated with accuracy ε and confidence 1 - p, simultaneously for all 0 ≤ k N(ε,p,K)=Φ⁻¹(p/2K)²/4ε², where Φ(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 S₀ and for all values 0 ≤ k < K, computes the secondary structure MEA(k), having maximum expected accuracy over all k-neighbors of S₀. Computation time is O(n³ * K²), and memory requirements are O(n² * 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 $f_n(g)$ 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 $sl(2)$ sector) of ${\cal N}=4$ SYM. At fixed $n$, $f_n(g)$ 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 $n$. 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 $f_n(g)$) to the unique mass gap of the $O(6)$ nonlinear sigma model and analyse the first next-to-leading order corrections.Comment: Latex version, journal version (with explanatory appendices and more references