Brane Supersymmetry Breaking

We show how to construct chiral tachyon-free perturbative orientifold models, where supersymmetry is broken at the string scale on a collection of branes while, to lowest order, the bulk and the other branes are supersymmetric. In higher orders, supersymmetry breaking is mediated to the remaining sectors, but is suppressed by the size of the transverse space or by the distance from the brane where supersymmetry breaking primarily occurred. This setting is of interest for orbifold models with discrete torsion, and is of direct relevance for low-scale string models. It can guarantee the stability of the gauge hierarchy against gravitational radiative corrections, allowing an almost exact supergravity a millimeter away from a non-supersymmetric world.Comment: 15 pages, LaTe

Split Supersymmetry in String Theory

Type I string theory in the presence of internal magnetic fields provides a concrete realization of split supersymmetry. To lowest order, gauginos are massless while squarks and sleptons are superheavy. For weak magnetic fields, the correct Standard Model spectrum guarantees gauge coupling unification with \sin^2{\theta_W}=3/8 at the compactification scale of M_{\rm GUT}\simeq 2 \times 10^{16} GeV. I discuss mechanisms for generating gaugino and higgsino masses at the TeV scale, as well as generalizations to models with split extended supersymmetry in the gauge sector.Comment: 7 pages, 3 figures, prepared for the Proceedings of PASCOS-05 and of CORFU2005 Summer Institut

Topics on String Phenomenology

These lectures present some topics of string phenomenology and contain two parts. In the first part, I review the possibility of lowering the string scale in the TeV region, that provides a theoretical framework for solving the mass hierarchy problem and unifying all interactions. The apparent weakness of gravity can then be accounted by the existence of large internal dimensions, in the submillimeter region, and transverse to a braneworld where our universe must be confined. I review the main properties of this scenario and its implications for observations at both particle colliders, and in non-accelerator gravity experiments. In the second part, I discuss a simple framework of toroidal string models with magnetized branes, that offers an interesting self-consistent setup for string phenomenology. I will present an algorithm for fixing the geometric parameters of the compactification, build calculable particle physics models such as a supersymmetric SU(5) Grand Unified Theory with three generations of quarks and leptons, and implement low energy supersymmetry breaking with gauge mediation that can be studied directly at the string level.Comment: 42 pages, 15 figures, Lectures given at Les Houches 2007 Summer School, Added reference

The Physics of Extra Dimensions

Lowering the string scale in the TeV region provides a theoretical framework for solving the mass hierarchy problem and unifying all interactions. The apparent weakness of gravity can then be accounted by the existence of large internal dimensions, in the submillimeter region, and transverse to a braneworld where our universe must be confined. I review the main properties of this scenario and its implications for observations at both particle colliders, and in non-accelerator gravity experiments. Such effects are for instance the production of Kaluza-Klein resonances, graviton emission in the bulk of extra dimensions, and a radical change of gravitational forces in the submillimeter range. I also discuss the warped case and localization of gravity in the presence of infinite size extra dimensions.Comment: 29 pages, 11 figures. Lectures to appear in the proceedings of the Third Aegean Summer School, Karfas, Chios, Greece, 26 September-1 October 200

Mass scales in string and M-theory

I review the relations between mass scales in various string theories and in M-theory. I discuss physical motivations and possible consistent realizations of large volume compactifications and low string scale. Large longitudinal dimensions, seen by Standard Model particles, imply in general that string theory is strongly coupled unless its tension is close to the compactification scale. Weakly coupled, low-scale strings can in turn be realized only in the presence of extra large transverse dimensions, seen through gravitational interactions, or in the presence of infinitesimal string coupling. In the former case, quantum gravity scale is also low, while in the latter, gravitational and string interactions remain suppressed by the four-dimensional Planck mass. There is one exception in this general rule, allowing for large longitudinal dimensions without low string scale, when Standard Model is embedded in a six-dimensional fixed-point theory described by a tensionless string. Extra dimensions of size as large as TeV$^{-1}\simeq 10^{-16}$ cm are motivated from the problem of supersymmetry breaking in string theory, while TeV scale strings offer a solution to the gauge hierarchy problem, as an alternative to softly broken supersymmetry or technicolor. I discuss these problems in the context of the above mentioned string realizations, as well as the main physical implications both in particle accelerators and in experiments that measure gravity at sub-millimeter distances.Comment: 32 pages, LaTeX, 2 eps-figures, uses sprocl.sty Lectures given at the Trieste Spring Workshop, ICTP, Italy, 22-30 March 1999, and at the Advanced School on "Supersymmetry in the Theories of Fields, Strings and Branes", Sandiago de Compostela, Spain, 26-31 July 1999. A short version was given as an invited talk at Strings 99, Potsdam, Germany, 19-24 July 1999 and at the European Program meeting on "Quantum Aspects of Gauge Theories, Supersymmetry and Unification", Paris, France, 1-7 September 199

String and D-brane Physics at Low Energy

1. Preliminaries. 2. Heterotic string and motivations for large volume compactifications; 2.1 Gauge coupling unification; 2.2 Supersymmetry breaking by compactification. 3. M-theory on S^1/Z_2 \times Calabi-Yau. 4. Type I/I' string theory and D-branes; 4.1 Low-scale strings and extra-large transverse dimensions; 4.2 Relation type I/I' -- heterotic. 5. Type II theories; 5.1 Low-scale IIA strings and tiny coupling; 5.2 Large dimensions in type IIB; 5.3 Relation type II -- heterotic. 6. Theoretical implications; 6.1 U.V./I.R. correspondence; 6.2 Unification ; 6.3 Supersymmetry breaking and scales hierarchy ; 6.4 Electroweak symmetry breaking in TeV-scale strings. 7. Scenarios for studies of experimental constraints. 8. Extra-dimensions along the world brane: KK excitations of gauge bosons; 8.1 Production at hadron colliders; 8.2 High precision data low-energy bounds; 8.3 One extra dimension for other cases; 8.4 More than one extra dimension. 9. Extra-dimensions transverse to the brane world: KK excitations of gravitons; 9.1 Signals from missing energy experiments; 9.2 Gravity modification and sub-millimeter forces. 10. Dimension-eight operators and limits on the string scale. 11. D-brane Standard Model; 11.1 Hypercharge embedding and the weak angle; 11.2 The fate of U(1)'s and proton stability. 12. Appendix: Supersymmetry breaking in type I strings; 12.1 Scherk-Schwarz deformations; 12.2 Brane supersymmetry breaking.Comment: 53 pages, Latex, 7 eps-figures, references and acknowledgments added. Based on lectures given at Centre Emile Borel during the semester "Supergravity, Superstrings and M-theory", at the "LNF-INFN Spring School in Nuclear, Subnuclear and Astropartcle Physics", Frascati, at the Glasgow "Workshop on Phenomenology of Extra Dimensions", at the "NATO ASI school on Recent Developments in Particle Physics and Cosmology", Portugal, at the "38th Course on Theory and Experiment Heading for New Physics", Erice, and at the "RTN Workshop on the Quantum Structure of Spacetime", Berli

Direct collider signatures of large extra dimensions

The realization of low (TeV) scale strings usually requires the existence of large (TeV) extra dimensions where gauge bosons live. The direct production of Kaluza-Klein excitations of the photon and Z-boson at present and future colliders is studied in this work. At the LEPII, NLC and Tevatron colliders, these Kaluza-Klein modes lead to deviations from the standard model cross-sections, which provide lower bounds on their mass. At the LHC the corresponding resonances can be produced and decay on-shell, triggering a characteristic pattern in the distribution of the dilepton invariant mass.Comment: 14 pages, LateX, 5 figure

A closer look at string resonances in dijet events at the LHC

The first string excited state can be observed as a resonance in dijet invariant mass distributions at the LHC, if the scenario of low-scale string with large extra dimensions is realized. A distinguished property of the dijet resonance by string excited states from that the other "new physics" is that many almost degenerate states with various spin compose a single resonance structure. It is examined that how we can obtain evidences of low-scale string models through the analysis of angular distributions of dijet events at the LHC. Some string resonance states of color singlet can obtain large mass shifts through the open string one-loop effect, or through the mixing with closed string states, and the shape of resonance structure can be distorted. Although the distortion is not very large (10% for the mass squared), it might be able to observe the effect at the LHC, if gluon jets and quark jets could be distinguished in a certain level of efficiency.Comment: 12 pages, 8 figure

Open string topological amplitudes and gaugino masses

We discuss the moduli-dependent couplings of the higher derivative F-terms (\Tr W^2)^{h-1}, where $W$ is the gauge N=1 chiral superfield. They are determined by the genus zero topological partition function $F^{(0,h)}$, on a world-sheet with $h$ boundaries. By string duality, these terms are also related to heterotic topological amplitudes studied in the past, with the topological twist applied only in the left-moving supersymmetric sector of the internal $N=(2,0)$ superconformal field theory. The holomorphic anomaly of these couplings relates them to terms of the form $\Pi^n({\rm Tr}W^2)^{h-2}$, where $\Pi$'s represent chiral projections of non-holomorphic functions of chiral superfields. An important property of these couplings is that they violate R-symmetry for $h\ge 3$. As a result, once supersymmetry is broken by D-term expectation values, (\Tr W^2)^2 generates gaugino masses that can be hierarchically smaller than the scalar masses, behaving as $m_{1/2}\sim m_0^4$ in string units. Similarly, $\Pi{\rm Tr}W^2$ generates Dirac masses for non-chiral brane fermions, of the same order of magnitude. This mechanism can be used for instance to obtain fermion masses at the TeV scale for scalar masses as high as $m_0\sim{\cal O}(10^{13})$ GeV. We present explicit examples in toroidal string compactifications with intersecting D-branes.Comment: 57 pages, 6 figures; Abstract and references correcte