On the Heterotic World-sheet Instanton Superpotential and its individual Contributions

For supersymmetric heterotic string compactifications on a Calabi-Yau threefold $X$ endowed with a vector bundle $V$ the world-sheet superpotential $W$ is a sum of contributions from isolated rational curves \C in $X$; the individual contribution is given by an exponential in the K\"ahler class of the curve times a prefactor given essentially by the Pfaffian which depends on the moduli of $V$ and the complex structure moduli of $X$. Solutions of $DW=0$ (or even of $DW=W=0$) can arise either by nontrivial cancellations between the individual terms in the summation over all contributing curves or because each of these terms is zero already individually. Concerning the latter case conditions on the moduli making a single Pfaffian vanish (for special moduli values) have been investigated. However, even if corresponding moduli - fulfilling these constraints - for the individual contribution of one curve are known it is not at all clear whether {\em one} choice of moduli exists which fulfills the corresponding constraints {\em for all contributing curves simultaneously}. Clearly this will in general happen only if the conditions on the 'individual zeroes' had already a conceptual origin which allows them to fit together consistently. We show that this happens for a class of cases. In the special case of spectral cover bundles we show that a relevant solution set has an interesting location in moduli space and is related to transitions which change the generation number.Comment: 47 page

Numerical Hermitian Yang-Mills Connections and Vector Bundle Stability in Heterotic Theories

A numerical algorithm is presented for explicitly computing the gauge connection on slope-stable holomorphic vector bundles on Calabi-Yau manifolds. To illustrate this algorithm, we calculate the connections on stable monad bundles defined on the K3 twofold and Quintic threefold. An error measure is introduced to determine how closely our algorithmic connection approximates a solution to the Hermitian Yang-Mills equations. We then extend our results by investigating the behavior of non slope-stable bundles. In a variety of examples, it is shown that the failure of these bundles to satisfy the Hermitian Yang-Mills equations, including field-strength singularities, can be accurately reproduced numerically. These results make it possible to numerically determine whether or not a vector bundle is slope-stable, thus providing an important new tool in the exploration of heterotic vacua.Comment: 52 pages, 15 figures. LaTex formatting of figures corrected in version 2

The Worldvolume Action of Kink Solitons in AdS Spacetime

A formalism is presented for computing the higher-order corrections to the worldvolume action of co-dimension one solitons. By modifying its potential, an explicit "kink" solution of a real scalar field in AdS spacetime is found. The formalism is then applied to explicitly compute the kink worldvolume action to quadratic order in two expansion parameters--associated with the hypersurface fluctuation length and the radius of AdS spacetime respectively. Two alternative methods are given for doing this. The results are expressed in terms of the trace of the extrinsic curvature and the intrinsic scalar curvature. In addition to conformal Galileon interactions, we find a non-Galileon term which is never sub-dominant. This method can be extended to any conformally flat bulk spacetime.Comment: 32 pages, 3 figures, typos corrected and additional comments adde

Flavor Structure in F-theory Compactifications

F-theory is one of frameworks in string theory where supersymmetric grand unification is accommodated, and all the Yukawa couplings and Majorana masses of right-handed neutrinos are generated. Yukawa couplings of charged fermions are generated at codimension-3 singularities, and a contribution from a given singularity point is known to be approximately rank 1. Thus, the approximate rank of Yukawa matrices in low-energy effective theory of generic F-theory compactifications are minimum of either the number of generations N_gen = 3 or the number of singularity points of certain types. If there is a geometry with only one E_6 type point and one D_6 type point over the entire 7-brane for SU(5) gauge fields, F-theory compactified on such a geometry would reproduce approximately rank-1 Yukawa matrices in the real world. We found, however, that there is no such geometry. Thus, it is a problem how to generate hierarchical Yukawa eigenvalues in F-theory compactifications. A solution in the literature so far is to take an appropriate factorization limit. In this article, we propose an alternative solution to the hierarchical structure problem (which requires to tune some parameters) by studying how zero mode wavefunctions depend on complex structure moduli. In this solution, the N_gen x N_gen CKM matrix is predicted to have only N_gen entries of order unity without an extra tuning of parameters, and the lepton flavor anarchy is predicted for the lepton mixing matrix. We also obtained a precise description of zero mode wavefunctions near the E_6 type singularity points, where the up-type Yukawa couplings are generated.Comment: 148 page

A New Class of Four-Dimensional N=1 Supergravity with Non-minimal Derivative Couplings

In the N=1 four-dimensional new-minimal supergravity framework, we supersymmetrise the coupling of the scalar kinetic term to the Einstein tensor. This coupling, although introduces a non-minimal derivative interaction of curvature to matter, it does not introduce harmful higher-derivatives. For this construction, we employ off-shell chiral and real linear multiplets. Physical scalars are accommodated in the chiral multiplet whereas curvature resides in a linear one.Comment: 18 pages, version published at JHE

Supermembrane interaction with dynamical D=4 N=1 supergravity. Superfield Lagrangian description and spacetime equations of motion

We obtain the complete set of equations of motion for the interacting system of supermembrane and dynamical D=4 N = 1 supergravity by varying its complete superfield action and writing the resulting superfield equations in the special gauge where the supermembrane Goldstone field is set to zero. We solve the equations for auxiliary fields and discuss the effect of dynamical generation of cosmological constant in the Einstein equation of interacting system and its renormalization due to some regular contributions from supermembrane. These two effects (discussed in late 70th and 80th, in the bosonic perspective and in the supergravity literature) result in that, generically, the cosmological constant has different values in the branches of the spacetime separated by the supermembrane worldvolume.Comment: 23 pages, no figures. V2 two references added, 24 page

General Gauge Mediation with Gauge Messengers

We generalize the General Gauge Mediation formalism to allow for the possibility of gauge messengers. Gauge messengers occur when charged matter fields of the susy-breaking sector have non-zero F-terms, which leads to tree-level, susy-breaking mass splittings in the gauge fields. A classic example is that SU(5) / SU(3) x SU(2) x U(1) gauge fields could be gauge messengers. We give a completely general, model independent, current-algebra based analysis of gauge messenger mediation of susy-breaking to the visible sector. Characteristic aspects of gauge messengers include enhanced contributions to gaugino masses, (tachyonic) sfermion mass-squareds generated already at one loop, and also at two loops, and significant one-loop A-terms, already at the messenger scale.Comment: 79 pages, 5 figure

Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory

This article is meant as a summary and introduction to the ideas of effective field theory as applied to gravitational systems. Contents: 1. Introduction 2. Effective Field Theories 3. Low-Energy Quantum Gravity 4. Explicit Quantum Calculations 5. ConclusionsComment: 56 pages, 2 figures, JHEP style, Invited review to appear in Living Reviews of Relativit

Supersymmetric Hidden Sectors for Heterotic Standard Models

Within the context of the weakly coupled E 8 × E 8 heterotic string, we study the hidden sector of heterotic standard model compactifications to four-dimensions. Specifically, we present a class of hidden sector vector bundles — composed of the direct sum of line bundles only — that, together with an effective bulk five-brane, renders the heterotic standard model entirely N = 1 supersymmetric. Two explicit hidden sectors are constructed and analyzed in this context; one with the gauge group E 7 × U(1) arising from a single line bundle and a second with an SO(12) × U(1) × U(1) gauge group constructed from the direct sum of two line bundles. Each hidden sector bundle is shown to satisfy all requisite physical constraints within a finite region of the Kähler cone. We also clarify that the first Chern class of the line bundles need not be even in our context, as has often been imposed in the model building literature