Topics in String Theory and Quantum Gravity

These are the lecture notes for the Les Houches Summer School on Quantum Gravity held in July 1992. The notes present some general critical assessment of other (non-string) approaches to quantum gravity, and a selected set of topics concerning what we have learned so far about the subject from string theory. Since these lectures are long (133 A4 pages), we include in this abstract the table of contents, which should help the user of the bulletin board in deciding whether to latex and print the full file. 1-FIELD THEORETICAL APPROACH TO QUANTUM GRAVITY: Linearized gravity; Supergravity; Kaluza-Klein theories; Quantum field theory and classical gravity; Euclidean approach to Quantum Gravity; Canonical quantization of gravity; Gravitational Instantons. 2-CONSISTENCY CONDITIONS: ANOMALIES: Generalities about anomalies; Spinors in 2n dimensions; When can we expect to find anomalies?; The Atiyah-Singer Index Theorem and the computation of anomalies; Examples: Green-Schwarz cancellation mechanism and Witten's SU(2) global anomaly. 3-STRING THEORY I. BOSONIC STRING: Bosonic string; Conformal Field Theory; Quantization of the bosonic string; Interaction in string theory and the characterization of the moduli space; Bosonic strings with background fields. Stringy corrections to Einstein equations; Toroidal compactifications. $R$-duality; Operator formalism 4-STRING THEORY II. FERMIONIC STRINGS: Fermionic String; Heterotic String; Strings at finite temperature; Is string theory finite? 5-OTHER DEVELOPMENTS AND CONCLUSIONS: String ``Phenomenology''; Black Holes and Related SubjectsComment: 133 pages, 22 figures (not included, available upon request), LaTe

Comments on Noncommutative Field Theories

We discuss some aspects of noncommutative quantum field theories obtained from the Seiberg-Witten limit of string theories in the presence of an external B-field. General properties of these theories are studied as well as the phenomenological potential of noncommutative QED.Comment: 15 pages. Based on talks at the 9th Adriatic Meeting (Dubrovnik, Croatia) and at String Phenomenology 2003 (Durham, UK). v2 references adde

Remarks on Time-Space Noncommutative Field Theories

We propose a physical interpretation of the perturbative breakdown of unitarity in time-like noncommutative field theories in terms of production of tachyonic particles. These particles may be viewed as a remnant of a continuous spectrum of undecoupled closed-string modes. In this way, we give a unified view of the string-theoretical and the field-theoretical no-go arguments against time-like noncommutative theories. We also perform a quantitative study of various locality and causality properties of noncommutative field theories at the quantum level.Comment: 19 pages, LaTe

Direct T-violation measurements and T-odd effects in decay experiments

Motivated by the recent experimental announcements for direct measurements of time-reversal non-invariance in the neutral kaon system, we make a comparative discussion of the CPLEAR and KTeV measurements. The most suitable way to consistently incorporate the mixing, the time evolution and the decays of kaons, is to describe the neutral kaon system as a system with a non-Hermitean Hamiltonian. In this framework, the physical (decaying) incoming and outgoing states are distinct and belong to dual spaces. Moreover, since they are eigenstates of the full Hamiltonian, they never oscillate. This is directly manifest in the orthogonality conditions of the physical states, which entirely determine the evolution of the kaon system. Along these lines we conclude: CPLEAR studies K0-bar{K0} oscillations, a process where initial and final states can be reversed, the CPLEAR asymmetry being an effect directly related to the definition of time-reversal. Conclusively, CPLEAR provides a direct measurement of T-violation without any assumption either on unitarity or on CPT-invariance. The KTeV experiment studies in particular the process KL -> pi+ pi- e+ e- where they measure a T-odd effect. However, using unitarity together with estimates of the final state interactions, it should be possible to determine whether this effect can be identified with a genuine T-reversal violation.Comment: 11 pages, no figures. Presented at the 34th Rencontres de Moriond on Electroweak Interactions and Unified Theories, Les Arcs, 13-20 March, 199

Space-time noncommutativity and (1+1) Higgs Model

We compare the classical scattering of kinks in (1+1) Higgs model with its analogous noncommutative counterpart. While at a classical level we are able to solve the scattering at all orders finding a smooth solution, at a noncommutative level we present only perturbative results, suggesting the existence of a smooth solution also in this case.Comment: 18 pages, 2 figure

Large N Expansion and Softly Broken Supersymmetry

We examine the supersymmetric non-linear O(N) sigma model with a soft breaking term. In two dimensions, we found that the mass difference between supersymmetric partner fields vanishes accidentally. In three dimensions, the mass difference is observed but O(N) symmetry is always broken also in the strong coupling region.Comment: Plain Latex(8pages), No Figur

Feynman Path Integral on the Noncommutative Plane

We formulate Feynman path integral on a non commutative plane using coherent states. The propagator for a free particle exhibits UV cut-off induced by the parameter of non commutativity.Comment: 7pages, latex 2e, no figures. Accepted for publication on J.Phys.