Modular forms and SL(2, ℤ)-covariance of type IIB superstring theory

Abstract The local higher-derivative interactions that enter into the low-energy expansion of the effective action of type IIB superstring theory with constant complex modulus generally violate the U(1) R-symmetry of IIB supergravity by q U units. These interactions have coefficients that transform as non-holomorphic modular forms under SL(2, ℤ) transformations with holomorphic and anti-holomorphic weights (w, −w), where q U = −2w. In this paper SL(2, ℤ)-covariance and supersymmetry are used to determine first-order differential equations on moduli space that relate the modular form coefficients of classes of BPS-protected maximal U(1)-violating interactions that arise at low orders in the lowenergy expansion. These are the moduli-dependent coefficients of BPS interactions of the form d 2p $$\mathcal{P}$$ P n in linearised approximation, where $$\mathcal{P}$$ P n is the product of n fields that has dimension = 8 with q U = 8 − 2n, and p = 0, 2 or 3. These first-order equations imply that the coefficients satisfy SL(2, ℤ)-covariant Laplace eigenvalue equations on moduli space with solutions that contain information concerning perturbative and non-perturbative contributions to superstring amplitudes. For p = 3 and n ≥ 6 there are two independent modular forms, one of which has a vanishing tree-level contribution. The analysis of super-amplitudes for U(1)-violating processes involving arbitrary numbers of external fluctuations of the complex modulus leads to a diagrammatic derivation of the first-order differential relations and Laplace equations satisfied by the coefficient modular forms. Combining this with a SL(2, ℤ)-covariant soft axio-dilaton limit that relates amplitudes with different values of n determines most of the modular invariant coefficients, leaving a single undetermined constant.</jats:p

Superstring amplitudes, unitarily, and Hankel determinants of multiple zeta values

Abstract The interplay of unitarity and analyticity has long been known to impose strong constraints on scattering amplitudes in quantum field theory and string theory. This has been highlighted in recent times in a number of papers and lecture notes. Here we examine such conditions in the context of superstring tree-level scattering amplitudes, leading to positivity constraints on determinants of Hankel matrices involving polynomials of multiple zeta values. These generalise certain constraints on polynomials of single zeta values in the mathematics literature.</jats:p

Exact properties of an integrated correlator in N = 4 SU(N) SYM

Abstract We present a novel expression for an integrated correlation function of four superconformal primaries in SU(N) $$\mathcal{N}$$ N = 4 supersymmetric Yang-Mills ($$\mathcal{N}$$ N = 4 SYM) theory. This integrated correlator, which is based on supersymmetric localisation, has been the subject of several recent developments. In this paper the correlator is re-expressed as a sum over a two dimensional lattice that is valid for all N and all values of the complex Yang-Mills coupling $$\tau =\theta /2\pi +4\pi i/{g}_{\mathrm{YM}}^2$$ τ = θ / 2 π + 4 πi / g YM 2 . In this form it is manifestly invariant under SL(2, ℤ) Montonen-Olive duality. Furthermore, it satisfies a remarkable Laplace-difference equation that relates the SU(N) correlator to the SU(N + 1) and SU(N − 1) correlators. For any fixed value of N the correlator can be expressed as an infinite series of non-holomorphic Eisenstein series, $$E\left(s;\tau, \overline{\tau}\right)$$ E s τ τ ¯ with s ∈ ℤ, and rational coefficients that depend on the values of N and s. The perturbative expansion of the integrated correlator is an asymptotic but Borel summable series, in which the n-loop coefficient of order (gYM/π)2n is a rational multiple of ζ(2n + 1). The n = 1 and n = 2 terms agree precisely with results determined directly by integrating the expressions in one-loop and two-loop perturbative $$\mathcal{N}$$ N = 4 SYM field theory. Likewise, the charge-k instanton contributions (|k| = 1, 2, . . .) have an asymptotic, but Borel summable, series of perturbative corrections. The large-N expansion of the correlator with fixed τ is a series in powers of $${N}^{\frac{1}{2}-\mathrm{\ell}}$$ N 1 2 − ℓ (ℓ ∈ ℤ) with coefficients that are rational sums of $$E\left(s;\tau, \overline{\tau}\right)$$ E s τ τ ¯ with s ∈ ℤ + 1/2. This gives an all orders derivation of the form of the recently conjectured expansion. We further consider the ’t Hooft topological expansion of large-N Yang-Mills theory in which $$\lambda ={g}_{\mathrm{YM}}^2N$$ λ = g YM 2 N is fixed. The coefficient of each order in the 1/N expansion can be expanded as a series of powers of λ that converges for |λ| &lt; π2. For large λ this becomes an asymptotic series when expanded in powers of $$1/\sqrt{\lambda }$$ 1 / λ with coefficients that are again rational multiples of odd zeta values, in agreement with earlier results and providing new ones. We demonstrate that the large-λ series is not Borel summable, and determine its resurgent non-perturbative completion, which is $$O\left(\exp \left(-2\sqrt{\lambda}\right)\right)$$ O exp − 2 λ .</jats:p

Integrative analysis of next generation sequencing for small non-coding RNAs and transcriptional regulation in Myelodysplastic Syndromes

Abstract. Background: Myelodysplastic Syndromes (MDSS) are pre-leukemic disorders with increasing incident rates worldwide, but very limited treatment options. Little is known about small regulatory RNAs and how they contribute to pathogenesis, progression and transcriptome changes in MDS. Methods. Patients' primary marrow cells were screened for short RNAs (RNA-seq) using next generation sequencing. Exon arrays from the same cells were used to profile gene expression and additional measures on 98 patients obtained. Integrative bioinformatics algorithms were proposed, and pathway and ontology analysis performed. Results: In low-grade MDS, observations implied extensive post-transcriptional regulation via microRNAs (miRNA) and the recently discovered Piwi interacting RNAs (piRNA). Large expression differences were found for MDS-associated and novel miRNAs, including 48 sequences matching to miRNA star (miRNA*) motifs. The detected species were predicted to regulate disease stage specific molecular functions and pathways, including apoptosis and response to DNA damage. In high-grade MDS, results suggested extensive post-translation editing via transfer RNAs (tRNAs), providing a potential link for reduced apoptosis, a hallmark for this disease stage. Bioinformatics analysis confirmed important regulatory roles for MDS linked miRNAs and TFs, and strengthened the biological significance of miRNA*. The "RNA polymerase II promoters" were identified as the tightest controlled biological function. We suggest their control by a miRNA dominated feedback loop, which might be linked to the dramatically different miRNA amounts seen between low and high-grade MDS. Discussion. The presented results provide novel findings that build a basis of further investigations of diagnostic biomarkers, targeted therapies and studies on MDS pathogenesis. © 2011 Beck et al; licensee BioMed Central Ltd

Big bang simulation in superfluid 3He-B -- Vortex nucleation in neutron-irradiated superflow

We report the observation of vortex formation upon the absorption of a thermal neutron in a rotating container of superfluid $^3$He-B. The nuclear reaction n + $^3$He = p + $^3$H + 0.76MeV heats a cigar shaped region of the superfluid into the normal phase. The subsequent cooling of this region back through the superfluid transition results in the nucleation of quantized vortices. Depending on the superflow velocity, sufficiently large vortex rings grow under the influence of the Magnus force and escape into the container volume where they are detected individually with nuclear magnetic resonance. The larger the superflow velocity the smaller the rings which can expand. Thus it is possible to obtain information about the morphology of the initial defect network. We suggest that the nucleation of vortices during the rapid cool-down into the superfluid phase is similar to the formation of defects during cosmological phase transitions in the early universe.Comment: 4 pages, LaTeX file, 4 figures are available at ftp://boojum.hut.fi/pub/publications/lowtemp/LTL-95009.p

Simplifying instanton corrections to N=4 SYM correlators

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Direct observation of incommensurate magnetism in Hubbard chains

The interplay between magnetism and doping is at the origin of exotic strongly correlated electronic phases and can lead to novel forms of magnetic ordering. One example is the emergence of incommensurate spin-density waves with a wave vector that does not match the reciprocal lattice. In one dimension this effect is a hallmark of Luttinger liquid theory, which also describes the low energy physics of the Hubbard model. Here we use a quantum simulator based on ultracold fermions in an optical lattice to directly observe such incommensurate spin correlations in doped and spin-imbalanced Hubbard chains using fully spin and density resolved quantum gas microscopy. Doping is found to induce a linear change of the spin-density wave vector in excellent agreement with Luttinger theory predictions. For non-zero polarization we observe a decrease of the wave vector with magnetization as expected from the Heisenberg model in a magnetic field. We trace the microscopic origin of these incommensurate correlations to holes, doublons and excess spins which act as delocalized domain walls for the antiferromagnetic order. Finally, when inducing interchain coupling we observe fundamentally different spin correlations around doublons indicating the formation of a magnetic polaron

Note on Bonus Relations for N=8 Supergravity Tree Amplitudes

We study the application of non-trivial relations between gravity tree amplitudes, the bonus relations, to all tree-level amplitudes in N=8 supergravity. We show that the relations can be used to simplify explicit formulae of supergravity tree amplitudes, by reducing the known form as a sum of (n-2)! permutations obtained by solving on-shell recursion relations, to a new form as a (n-3)!-permutation sum. We demonstrate the simplification by explicit calculations of the next-to-maximally helicity violating (NMHV) and next-to-next-to-maximally helicity violating (N^2MHV) amplitudes, and provide a general pattern of bonus coefficients for all tree-level amplitudes.Comment: 21 pages, 9 figures; v2, minor changes, references adde