Spinning superstrings at two loops: strong-coupling corrections to dimensions of large-twist SYM operators

We consider folded spinning strings in AdS_5xS^5 (with one spin component S in AdS_5 and J in S^5) corresponding to the Tr(D^S Z^J) operators in the sl(2) sector of the N=4 SYM theory in the special scaling limit in which both the string mass M ~ \sqrt \lambda \ln S and J are sent to infinity with their ratio fixed. Expanding in the parameter \el= J/M we compute the 2-loop string sigma model correction to the string energy and show that it agrees with the expression proposed by Alday and Maldacena in arxiv:0708.0672. We suggest that a resummation of the logarithmic \el^2 \ln^n \el terms is necessary in order to establish an interpolation to the weakly coupled gauge theory results. In the process, we set up a general framework for the calculation of higher loop corrections to the energy of multi-spin string configurations. In particular, we find that in addition to the direct 2-loop term in the string energy there is a contribution from lower loop order due to a finite ``renormalization'' of the relation between the parameters of the classical solution and the fixed spins, i.e. the charges of the SO(2,4) x SO(6) symmetry.Comment: 31 pages, Latex. v2:minor corrections; few comments and references added v3: typos correcte

Stratigraphy and chronology of the Stent tephra, a c. 4000 year old distal silicic tephra from Taupo Volcanic Centre, New Zealand.

Tephrostratigraphic and chronologic studies in two areas of the North Island have identified a previously unrecorded, thin, distal silicic tephra derived from the Taupo Volcanic Centre. In Taranaki, three radiocarbon ages of the uncorrelated tephra are consistent with the independent radiocarbon chronology obtained from enveloping Egmontsourced tephras. In western Bay of Plenty, where the uncorrelated tephra is also directly dated, it is overlain by Whakaipo Tephra (c. 2.7 ka) and underlain by Hinemaiaia Tephra (c. 4.5 ka). From these sites in Taranaki and western Bay of Plenty, seven radiocarbon dates obtained on the uncorrelated silicic tephra yield an error-weighted mean age of 3970 ±31 conventional radiocarbon years B.P. The ages on the uncorrelated tephra (informally referred to as Stent tephra) from both areas are statistically identical but significantly different from those on both Waimihia and Hinemaiaia Tephras. occurrence of Stent tephra in Taranaki, c. 160 km upwind from the postulated source area, and in western Bay of Plenty, suggests that it represents the product of a moderately large plinian eruption. Until recently, its validity as a discrete eruptive event had been problematical, because a near-source equivalent deposit between Waimihia and Hinemaiaia Tephras was not recognised in the Taupo area. However, a revised stratigraphy proposed by C. J. N. Wilson in 1993 for eastern sectors of the Taupo area shows that multiple tephra layers were erupted from Taupo volcano between c. 3.9 and 5.2 ka. Of these newly recognised layers, unit-g--the product of a moderately large eruption (>0.15 km3) at c. 4.0 ka--is tentatively correlated with Stent tephra. Other eruptive units recognised by Wilson are either too old or too small in volume to be considered as likely correlatives

Lessons from All Logs Summation in Yukawa Theories

Some features of old results in the total summation of all logarithmic contributions of all diagrams in Yukawa theory are presented. We discuss some lessons from this picture for the description of Pomeron, odderon, etc. in QCD.Comment: 6 pages, 2 figure

Transcendentality and Crossing

We discuss possible phase factors for the S-matrix of planar N=4 gauge theory, leading to modifications at four-loop order as compared to an earlier proposal. While these result in a four-loop breakdown of perturbative BMN-scaling, Kotikov-Lipatov transcendentality in the universal scaling function for large spin twist operators may be preserved. One particularly natural choice, unique up to one constant, modifies the overall contribution of all terms containing odd zeta functions in the earlier proposed scaling function based on a trivial phase. Excitingly, we present evidence that this choice is non-perturbatively related to a recently conjectured crossing-symmetric phase factor for perturbative string theory on AdS_5xS^5 once the constant is fixed to a particular value. Our proposal, if true, might therefore resolve the long-standing AdS/CFT discrepancies between gauge and string theory

Electronic state spectroscopy of C₂Cl₄

The VUV spectrum of C2Cl4 is reported in the energy range 3.8-10.8 eV (325-115 nm). Several photoabsorption features are observed for the first time, including a very weak low-lying band which is provisionally attributed to a π → π* triplet transition. Recent ab initio calculations of the molecule’s electronic transitions [Arulmozhiraja et al. J. Chem. Phys. 129 (2008) 174506] provide the basis for the present assignments below 8.5 eV. An extended ndπ series is proposed to account for several higher-energy Rydberg bands. The identification of vibrational structure, dominated by symmetric C=C and CCl2 stretching in excitations from the HOMO, largely agrees with previous spectroscopic studies. The present absolute photoabsorption cross sections cover a wider energy range than the previous measurements and are used to calculate UV photolysis lifetimes of this aeronomic molecule at altitudes between 20 and 50 km

Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops

We present an ansatz for the planar five-loop four-point amplitude in maximally supersymmetric Yang-Mills theory in terms of loop integrals. This ansatz exploits the recently observed correspondence between integrals with simple conformal properties and those found in the four-point amplitudes of the theory through four loops. We explain how to identify all such integrals systematically. We make use of generalized unitarity in both four and D dimensions to determine the coefficients of each of these integrals in the amplitude. Maximal cuts, in which we cut all propagators of a given integral, are an especially effective means for determining these coefficients. The set of integrals and coefficients determined here will be useful for computing the five-loop cusp anomalous dimension of the theory which is of interest for non-trivial checks of the AdS/CFT duality conjecture. It will also be useful for checking a conjecture that the amplitudes have an iterative structure allowing for their all-loop resummation, whose link to a recent string-side computation by Alday and Maldacena opens a new venue for quantitative AdS/CFT comparisons.Comment: 52 pages, 20 figures, revte

Four-Loop Cusp Anomalous Dimension From Obstructions

We introduce a method for extracting the cusp anomalous dimension at L loops from four-gluon amplitudes in N=4 Yang-Mills without evaluating any integrals that depend on the kinematical invariants. We show that the anomalous dimension only receives contributions from the obstructions introduced in hep-th/0601031. We illustrate this method by extracting the two- and three-loop anomalous dimensions analytically and the four-loop one numerically. The four-loop result was recently guessed to be f^4 = - (4\zeta^3_2+24\zeta_2\zeta_4+50\zeta_6- 4(1+r)\zeta_3^2) with r=-2 using integrability and string theory arguments in hep-th/0610251. Simultaneously, f^4 was computed numerically in hep-th/0610248 from the four-loop amplitude obtaining, with best precision at the symmetric point s=t, r=-2.028(36). Our computation is manifestly s/t independent and improves the precision to r=-2.00002(3), providing strong evidence in favor of the conjecture. The improvement is possible due to a large reduction in the number of contributing terms, as well as a reduction in the number of integration variables in each term.Comment: 23 pages, revtex; v2,v3: minor typos fixed and references adde

Anomalous Dimensions from a Spinning D5-Brane

We consider the anomalous dimension of a certain twist two operator in N=4 super Yang-Mills theory. At strong coupling and large-N it is captured by the classical dynamics of a spinning D5-brane. The present calculation generalizes the result of Gubser, Klebanov and Polyakov (hep-th/0204051): in order to calculate the anomalous dimension of a bound state of k coincident strings, the spinning closed string is replaced by a spinning D5 brane that wraps an S4 inside the S5 part of the AdS5 times S5 metric.Comment: 8 pages, LaTex. v2: figure added. minor changes. To appear in JHE

Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory at strong coupling

We construct an exact analytical solution to the integral equation which is believed to describe logarithmic growth of the anomalous dimensions of high spin operators in planar N=4 super Yang-Mills theory and use it to determine the strong coupling expansion of the cusp anomalous dimension.Comment: 5 pages. v3: minor corrections, references and important note adde

The gravitational S-matrix

We investigate the hypothesized existence of an S-matrix for gravity, and some of its expected general properties. We first discuss basic questions regarding existence of such a matrix, including those of infrared divergences and description of asymptotic states. Distinct scattering behavior occurs in the Born, eikonal, and strong gravity regimes, and we describe aspects of both the partial wave and momentum space amplitudes, and their analytic properties, from these regimes. Classically the strong gravity region would be dominated by formation of black holes, and we assume its unitary quantum dynamics is described by corresponding resonances. Masslessness limits some powerful methods and results that apply to massive theories, though a continuation path implying crossing symmetry plausibly still exists. Physical properties of gravity suggest nonpolynomial amplitudes, although crossing and causality constrain (with modest assumptions) this nonpolynomial behavior, particularly requiring a polynomial bound in complex s at fixed physical momentum transfer. We explore the hypothesis that such behavior corresponds to a nonlocality intrinsic to gravity, but consistent with unitarity, analyticity, crossing, and causality.Comment: 46 pages, 10 figure