Lectures on string theory and cosmology

In these lectures I review recent attempts to apply string theory to cosmology, including string cosmology and various models of brane cosmology. In addition, the review includes an introduction to inflation as well as a discussion of transplanckian signatures. I also provide a critical discussion of the possible role of holography. The material is based on lectures given in January 2004 at the RTN String School in Barcelona, but also contain some additional material.Comment: Lectures given in January 2004 at the RTN Barcelona String School, 50 pages, 9 figure

Noncommutative Field Theory and Spontaneous Symmetry Breaking

We investigate the noncommutative analogue of the spontaneously broken linear sigma model at the one-loop quantum level. In the commutative case, renormalization of a theory with a spontaneously broken continuous global symmetry depends on cancellations that enable the limited set of counterterms consistent with that symmetry to remove the divergences even after its spontaneous breaking, while preserving the masslessness of the associated Goldstone modes. In the noncommutative case, we find that these cancellations are violated, and the renormalized one-loop correction to the inverse pion propagator explicitly yields a mass shift which depends on the ultraviolet cutoff. Thus, we cannot naively take the ultraviolet cutoff to infinity first, and then take the external momentum to zero to verify Nambu-Goldstone symmetry realization. However, from the Wilsonian perspective where the cutoff is fixed and physical, the zero external momentum limit of the inverse pion propagator still vanishes, and implies the masslessness of the pion fields at one-loop. This is another demonstration of the failure of ultraviolet and infrared limits to commute in noncommutative field theories, and signals the incompatibility of Nambu-Goldstone symmetry realization with the continuum renormalization of these theories.Comment: 17 pages, LaTeX, uses feynmp package; analyzes general case using all orderings of star product in quartic vertices; uses symmetrized Feynman vertex rules; revised combinatorics; reference added; conclusions unaltered; diagrams now appear correctl

Critical Constraints on Chiral Hierarchies

We consider the constraints that critical dynamics places on models with a top quark condensate or strong extended technicolor (ETC). These models require that chiral-symmetry-breaking dynamics at a high energy scale plays a significant role in electroweak symmetry breaking. In order for there to be a large hierarchy between the scale of the high energy dynamics and the weak scale, the high energy theory must have a second order chiral phase transition. If the transition is second order, then close to the transition the theory may be described in terms of a low-energy effective Lagrangian with composite ``Higgs'' scalars. However, scalar theories in which there are more than one $\Phi^4$ coupling can have a {\it first order} phase transition instead, due to the Coleman-Weinberg instability. Therefore, top-condensate or strong ETC theories in which the composite scalars have more than one $\Phi^4$ coupling cannot always support a large hierarchy. In particular, if the Nambu--Jona-Lasinio model solved in the large-$N_c$ limit is a good approximation to the high-energy dynamics, then these models will not produce acceptable electroweak symmetry breaking.Comment: 10 pages, 1 postscript figure (appended), BUHEP-92-35, HUTP-92/A05

The heavy quark decomposition of the S-matrix and its relation to the pinch technique

We propose a decomposition of the S-matrix into individually gauge invariant sub-amplitudes, which are kinematically akin to propagators, vertices, boxes, etc. This decompsition is obtained by considering limits of the S-matrix when some or all of the external particles have masses larger than any other physical scale. We show at the one-loop level that the effective gluon self-energy so defined is physically equivalent to the corresponding gauge independent self-energy obtained in the framework of the pinch technique. The generalization of this procedure to arbitrary gluonic $n$-point functions is briefly discussed.Comment: 11 uuencoded pages, NYU-TH-94/10/0

High-Temperature Effective Potential of Noncommutative Scalar Field Theory: Reduction of Degree of Freedom by Noncommutativity

The renormalization of effective potentials for the noncommutative scalar field theory at high temperature are investigated to the two-loop approximation. The Feynman diagrams in evaluating the effective potential may be classified into two types: the planar diagrams and nonplanar diagrams. The nonplanar diagrams, which depend on the parameter of noncommutativity, do not appear in the one-loop potential. Despite their appearance in the two-loop level, they do not have an inclination to restore the symmetry breaking in the tree level, in contrast to the planar diagrams. This phenomenon is explained as a consequence of the drastic reduction of the degrees of freedom in the nonplanar diagrams when the thermal wavelength is smaller than the noncommutativity scale. Our results show that the nonplanar two-loop contribution to the effective potential can be neglected in comparsion with that from the planar diagrams.Comment: Latex, 17 pages, change the conclusion, improve the Englis

Leptonic constants of heavy quarkonia in potential approach of NRQCD

We consider a general scheme for calculating the leptonic constant of heavy quarkonium QQ-bar in the framework of nonrelativistic quantum chromodynamics, NRQCD, operating as the effective theory of nonrelativistic heavy quarks. We explore the approach of static potential in QCD, which takes into account both the evolution of effective charge in the three-loop approximation and the linearly raising potential term, which provides the quark confinement. The leptonic constants of bb-bar and cc-bar systems are evaluated by making use of two-loop anomalous dimension for the current of nonrelativistic quarks, where the factor for the normalization of matrix element is introduced in order to preserve the renormalization group invariance of estimates.Comment: 18 pages, 6 eps-figures, discussion and references added, vNRQCD analysis considere

Direct Mediation and Metastable Supersymmetry Breaking for SO(10)

We examine a metastable $\mathcal{N}=1$ Macroscopic SO(N) SQCD model of Intriligator, Seiberg and Shih (ISS). We introduce various baryon and meson deformations, including multitrace operators and explore embedding an SO(10) parent of the standard model into two weakly gauged flavour sectors. Direct fundamental messengers and the symmetric pseudo-modulus messenger mediate SUSY breaking to the MSSM. Gaugino and sfermion masses are computed and compared for each deformation type. We also explore reducing the rank of the magnetic quark matrix of the ISS model and find an additional fundamental messenger.Comment: 43 pages, Latex. Version to appear in JHEP

Higgs boson couplings to quarks with supersymmetric CP and flavor violations

In minimal supersymmetric model (SUSY) with a light Higgs sector, explicit CP violation and most general flavor mixings in the sfermion sector, integration of the superpartners out of the spectrum induces potentially large contributions to the Yukawa couplings of light quarks via those of the heavier ones. These corrections can be sizeable even for moderate values of tan(beta), and remain nonvanishing even if all superpartners decouple. When the SUSY breaking scale is close to the electroweak scale, the Higgs exchange effects can compete with the gauge boson and box diagram contributions to rare processes, and their partial cancellations can lead to relaxation of the existing bounds on flavor violation sources. In this case there exist sizeable enhancements in flavor-changing Higgs decays. When the superpartners completely decouple, however, the Higgs mediation becomes the dominant SUSY contribution to rare processes the saturation of which, without a strong suppression of the flavor mixings, prefers large tan(beta) and certain ranges for the CP-odd phases. The decay rate of the lightest Higgs into light down quarks become comparable with that into the bottom quark. Moreover, the Higgs decay into the up quark is significantly enhanced. There are observable implications for rare processes, atomic electric dipole moments, and collider searches for Higgs bosons.Comment: 20 pp. Added references, improved the discussion of FCNC constraints;journal versio

Primeval Corrections to the CMB Anisotropies

We show that deviations of the quantum state of the inflaton from the thermal vacuum of inflation may leave an imprint in the CMB anisotropies. The quantum dynamics of the inflaton in such a state produces corrections to the inflationary fluctuations, which may be observable. Because these effects originate from IR physics below the Planck scale, they will dominate over any trans-Planckian imprints in any theory which obeys decoupling. Inflation sweeps away these initial deviations and forces its quantum state closer to the thermal vacuum. We view this as the quantum version of the cosmic no-hair theorem. Such imprints in the CMB may be a useful, independent test of the duration of inflation, or of significant features in the inflaton potential about 60 e-folds before inflation ended, instead of an unlikely discovery of the signatures of quantum gravity. The absence of any such substructure would suggest that inflation lasted uninterrupted much longer than ${\cal O}(100)$ e-folds.Comment: 17 pages, latex, no figures; v3: added references and comments, final version to appear in Phys. Rev.

General structure of the photon self-energy in non-commutative QED

We study the behavior of the photon two point function, in non-commutative QED, in a general covariant gauge and in arbitrary space-time dimensions. We show, to all orders, that the photon self-energy is transverse. Using an appropriate extension of the dimensional regularization method, we evaluate the one-loop corrections, which show that the theory is renormalizable. We also prove, to all orders, that the poles of the photon propagator are gauge independent and briefly discuss some other related aspects.Comment: 16 pages, revtex4. This is the final version to be published in Phys. Rev.