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Supersymmetric Gauge Field Theory and String Theory
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Designed as a sequel to the authors' "Introduction to Gauge Field Theory", "Supersymmetric Gauge Field Theory and String Theory" introduces first-year graduate students to supersymmetric theories, including supergravity and superstring theories. Starting with the necessary background in quantum field theory, the book covers the three key topics of high-energy physics. The emphasis is on practical calculations rather than abstract generalities or phenomenological results. Where possible, the authors show how to calculate, connecting the theoretical with the phenomenological. While the field continues to advance and grow, this book addresses the basic theory at the core and will likely remain relevant even if more advanced ideas change.
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Table of Contents

SUPERSYMMETRY ALGEBRA AND MULTIPLETS Introduction Dirac, Weyl and Mujorana Spinors Simple supersymmetry algebra Supersymmetry multiplets Supersymmetric free field theory Extended supersymmetry; References Exercises LAGRANGIANS FOR CHIRAL SUPERFIELDS Introduction Superfield representations of the supersymmetry algebra Expansion of chiral superfield in component fields Products of chiral superfields Renormalisable supersymmetric Lagrangians for chiral superfields Feynman rules for chiral supermultiplets Mass and coupling constant renormalisation Non-renormalisation theories Spontaneous supersymmetry breaking F-term supersymmetry breaking References Exercises LAGRANGIANS FOR VECTOR SUPERFIELDS Introduction The vector superfield Supersymmetric gauge invariance Spontaneously broken gauge invariance D-term supersymmetry breaking Supersymmetric non-Abeldian gauge theories Supersymmetric electroweak theory Renormalisation group equation References Exercises PURE SUPERGRAVITY Introduction Noether procedure Globally supersymmetric Lagrangian for the supergravity multiplet Locally supersymmetric Lagrangian for the supergravity multiplet References Exercises COUPLING OF SUPERGRAVITY TO MATTER Introduction Supergravity Lagrangian for the Wess-Zumino model General supergravity Lagrangian for chiral supermultiplets General supergravity Lagrangian including vector supermultiplets Spontaneous supersymmetry breaking in supergravity Super-Higgs mechanism and gravitino mass Hidden sector supersymmetry breaking Supersymmetry breaking by gaugino condensate Supersymmetry breaking effects in the observable sector No scale supergravity References Exercises SUPERGRAVITY GRAND UNIFIED THEORIES Hierarchy problem Minimal SU(5) supergravity GUT Renormalisation group equations Charginos and neutralinos Experimental signatures Proton decay References Exercises THE BOSONIC STRING Introduction The bosonic string action Equations of motion and covariant gauges Mode expansions and quantisation Virasoro algebra and masses of states for the closed string Virasoro algebra and masses of states for the open string Light cone gauge Low lying string states Path integral quantisation References Exercises THE SUPERSTRING Introduction The superstring action Equations of motion and covariant gauge Mode expansions and quantisation Super-virasoro algebra for the closed string Closed superstring ground states and superconformal anomalies Light cone gauge Superstring states, GSO projections and space-time supersymmetry Other formulations of the superstring References Exercises THE HETEROTIC STRING Introduction Mode expansions and quantisation Compactification of the bosonic string on a circle Compactification of the heterotic string on a torus Fermionisation and bosonisation Fermionic formulation of the compactified heterotic string References Exercises COMPACTIFICATION OF TEN DIMENSIONAL HETEROTIC STRING TO FOUR DIMENSIONS Introduction Toroidal compactifications Orbifold compactifications The untwisted sector of the Z^[3 orbifold The twisted sector of the Z^[3 orbifold Wilson lines Calabi-Yau manifolds DIRECT CONSTRUCTION OF FOUR DIMENSIONAL HETEROTIC STRING THEORIES Introduction Modular invariance and partition function Partition functions and GSO projections Four dimensional heterotic string theories Semi-realistic four dimensional models References Exercises SUPERSTRING INTERACTIONS Introduction Bosonic string vertex operators and conformal dimensions Bosonic open string scattering amplitudes Bosonic closed string amplitudes Superstring vertex operator Superstring scattering amplitudes Review of further developments References Exercises Appendices Index

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