Semiclassical quantization of rotating superstring in AdS_5 x S^5

Motivated by recent proposals in hep-th/0202021 and hep-th/0204051 we develop semiclassical quantization of superstring in $AdS_5 x S^5$. We start with a classical solution describing string rotating in $AdS_5$ and boosted along large circle of $S^5$. The energy of the classical solution $E$ is a function of the spin $S$ and the momentum $J$ (R-charge) which interpolates between the limiting cases S=0 and J=0 considered previously. We derive the corresponding quadratic fluctuation action for bosonic and fermionic fields from the GS string action and compute the string 1-loop (large \lambda= {R^4\over \a'^2}) correction to the classical energy spectrum in the $(S,J)$ sector. We find that the 1-loop correction to the ground-state energy does not cancel for non-zero $S$. For large $S$ it scales as $\ln S$, i.e. as the classical term, with no higher powers of $\ln S$ appearing. This supports the conjecture made in hep-th/0204051 that the classical $E-S = a \ln S$ scaling can be interpolated to weak coupling to reproduce the corresponding operator anomalous dimension behaviour in gauge theory.Comment: harvmac, 35p. v2,3: minor corrections; v4: added remarks about higher-loop corrections in section 4 and an argument suggesting the absence of higher than log S corrections to the energy to all orders in string tension in section 6.1; v5: factor 1/2 misprints corrected in eqs. (6.6) and (6.8) and thus in (6.5) and (6.9

Wilson loops from supergravity and string theory

We present a theorem that determines the value of the Wilson loop associated with a Nambu-Goto action which generalizes the action of the $AdS_5\times S_5$ model. In particular we derive sufficient conditions for confining behavior. We then apply this theorem to various string models. We go beyond the classical string picture by incorporating quadratic quantum fluctuations. We show that the bosonic determinant of $D_p$ branes with 16 supersymmetries yields a Luscher term. We confirm that the free energy associated with a BPS configuration of a single quark is free from divergences. We show that unlike for a string in flat space time in the case of $AdS_5\times S_5$ the fermionic determinant does not cancel the bosonic one. For a setup that corresponds to a confining gauge theory the correction to the potential is attractive. We determine the form of the Wilson loop for actions that include non trivial $B_{\mu\nu}$ field. The issue of an exact determination of the value of the stringy Wilson loop is discussed. Talk presented in string 99 Potsdam.Comment: 12 pages Late

The hierarchy problem, radion mass, localization of gravity and 4D effective Newtonian potential in string theory on S1/Z2S^{1}/Z_{2}

We present a systematical study of brane worlds in string theory on $S^{1}/Z_{2}$. Starting with the toroidal compactification of the NS/NS sector in (D+d) dimensions, we first obtain an effective $D$-dimensional action, and then compactify one of the $(D-1)$ spatial dimensions by introducing two orbifold branes as its boundaries. By combining the Gauss-Codacci and Lanczos equations, we write down explicitly the general gravitational field equations on each of the two branes, while using distribution theory we express the matter field equations on the branes in terms of the discontinuities of the first derivatives of the matter fields. Afterwards, we address three important issues: (i) the hierarchy problem; (ii) the radion mass; and (iii) the localization of gravity, the 4-dimensional Newtonian effective potential and the Yukawa corrections due to the gravitational high-order Kaluza-Klein (KK) modes. With a very conservative estimation, we find that the radion mass is of the order of $10^{-2} GeV$. The gravity is localized on the visible brane, and the spectrum of the gravitational KK modes is discrete and can be of the order of TeV. The corrections to the 4-dimensional Newtonian potential from the higher order of gravitational KK modes are exponentially suppressed and can be safely neglected in current experiments. In an appendix, we also present a systematical and pedagogical study of the Gauss-Codacci equations and Israel's junction conditions across a (D-1)-dimensional hypersurface, which can be either spacelike or timelike.Comment: Considerably extended, Revtex4, 19 pages, 5 figures, published in IJMPA, 25, 1661-1698 (2010

Spheres, Deficit Angles and the Cosmological Constant

We consider compactifications of six dimensional gravity in four dimensional Minkowski or de Sitter space times a two dimensional sphere, S^2. As has been recently pointed out, it is possible to introduce 3-branes in these backgrounds with arbitrary tension without affecting the effective four dimensional cosmological constant, since its only effect is to induce a deficit angle in the sphere. We show that if a monopole like configuration of a 6D U(1) gauge field is used to produce the spontaneous compactification of the two extra dimensions in a sphere a fine tuning between brane and bulk parameters is reintroduced once the quantization condition for the gauge field is taken into account, so the 4D cosmological constant depends on the brane tension. This problem is absent if instead of the monopole we consider a four form field strength in the bulk to obtain the required energy-momentum tensor. Also, making use of the four form field, we generalize the solution to an arbitrary number of dimensions (\ge 6), keeping always four noncompact dimensions and compactifying the rest in a n-dimensional sphere. We show that a (n+1)-brane with arbitrary tension can be introduced in this background without affecting the effective 4D cosmological constant.Comment: 14 pages, LaTe

A criterion for admissible singularities in brane world

When gravity couples to scalar fields in Anti-de Sitter space, the geometry becomes non-AdS and develops singularities generally. We propose a criterion that the singularity is physically admissible if the integral of the on-shell Lagrangian density over the finite range is finite everywhere. For all classes of the singularities studied here, the criterion suggested in this paper coincides with an independent proposal made by Gubser that the potential should be bounded from above in the solution. This gives a reason why Gubser's conjecture works.Comment: 14 pages, revtex, 1 table, references added, two other criteria include

Factors associated with cognitive achievement in late childhood and adolescence: the Young Lives cohort study of children in Ethiopia, India, Peru, and Vietnam

Background There is a well-established link between various measures of socioeconomic status and the schooling achievement and cognition of children. However, less is known about how cognitive development is impacted by childhood improvements in growth, a common indicator of child nutritional status. This study examines the relationship between socioeconomic status and child growth and changes in cognitive achievement scores in adolescents from resource-poor settings. Methods Using an observational cohort of more than 3000 children from four low- and middle-income countries, this study examines the association between cognitive achievement scores and household economic, educational, and nutritional resources to give a more accurate assessment of the influence of families on cognitive development. A composite measure of cognition when children were approximately 8, 12, and 15 years of age was constructed. Household factors included maternal schooling, wealth, and children’s growth. Results A positive and statistically significant relationship between household factors and child cognition was found for each country. If parents have more schooling, household wealth increases, or child growth improves, then children’s cognitive scores improve over time. Results for control variables are less consistent. Conclusion Our findings suggest there is a consistent and strong association between parental schooling, wealth, and child growth with child cognitive achievement. Further, these findings demonstrate that a household’s ability to provide adequate nutrition is as important as economic and education resources even into late childhood and adolescence. Hence, efforts to improve household resources, both early in a child’s life and into adolescence, and to continue to promote child growth beyond the first few years of life have the potential to help children over the life course by improving cognition

Cosmological Constant of the (p+1)(p+1)-Dimensional World, Embedded in the dd-Dimensional Bulk Space

In this manuscript we study the cosmological constant of a $(p+1)$-dimensional world, which lives in the higher dimensional bulk space. We assume the extra dimensions are compact on tori. We consider two cases: positive and negative bulk cosmological constant. It is pointed out that the tiny cosmological constant of our world can be obtained by the dynamics of a scalar field and adjusting the parameters of the model. The cosmological constant of the dual world also will be discussed. We obtain the Dirac quantization of these cosmological constants.Comment: 11 pages, Latex, No figure. In the revised version, major changes have been introduced and also references have been adde

Meta-Stable Supersymmetry Breaking in a Cooling Universe

We look at the recently proposed idea that susy breaking can be accomplished in a meta-stable vacuum. In the context of one of the simplest models (the Seiberg-dual of super-QCD), we address the following question: if we look at this theory as it cools from high temperature, is it at all possible that we can end up in a susy-breaking meta-stable vacuum? To get an idea about the answer, we look at the free energy of the system at high temperature. We conclude that the phase-structure of the free-energy as the temperature drops, is indeed such that there is a second order phase transition in the direction of the non-susy vacuum at a finite $T=T_c^Q$. On the other hand, the potential barrier in the direction of the susy vacuum is there all the way till $T \sim 0$.Comment: writing full author name

Localized gravity and mass hierarchy in D=6 with the Gauss-Bonnet term

We obtain the localized gravity on the intersection of two orthogonal non-solitonic or solitonic 4-branes in D=6 in the presence of the Gauss-Bonnet term. The tension of the intersection is allowed to exist unlike the case without the Gauss-Bonnet term. We show that gravity could be confined to the solitonic 4-branes for a particular choice of the Gauss-Bonnet coupling. If the extra dimensions are compactified with the $T^2/(Z_2\times Z_2)$ orbifold symmetry, the mass hierarchy between the Planck scale and the weak scale can be explained by putting our universe at the TeV intersection of positive tension located at the orbifold fixed point.Comment: Latex file of 12 page

Superparticle and superstring in AdS_3 x S^3 Ramond-Ramond background in light-cone gauge

We discuss superparticle and superstring dynamics in AdS_3 x S^3 supported by R-R 3-form background using light-cone gauge approach. Starting with the superalgebra psu(1,1|2) + psu(1,1|2) representing the basic symmetry of this background we find the light-cone superparticle Hamiltonian. We determine the harmonic decomposition of light-cone superfield describing fluctuations of type IIB supergravity fields expanded near AdS_3 x S^3 background and compute the corresponding Kaluza-Klein spectrum. We fix the fermionic and bosonic light-cone gauges in the covariant Green-Schwarz AdS_3 x S^3 superstring action and find the light-cone string Hamiltonian. We also obtain a realization of the generators of psu(1,1|2) + psu(1,1|2) in terms of the superstring 2-d fields in the light-cone gauge.Comment: 32 pages, late