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Outline

- Challenges
- Basics of String Theory
- The Gauge/Gravity Correspondence
- Black Holes in String Theory
- Experimental Signatures

Reviews

- SUPERSTRING THEORY. VOL.1 and 2

By Michael B. Green (Queen Mary, U. of London), J.H. Schwarz (Caltech), Edward Witten (Princeton U.),Cambridge, Uk: Univ. Pr. ( 1987).

- STRING THEORY. VOL. 1 and 2By J. Polchinski (Santa Barbara, KITP),. Cambridge, UK: Univ. Pr. (1998).
- WHAT IS STRING THEORY?By Joseph Polchinski (Santa Barbara, KITP),. e-Print Archive: hep-th/9411028.
- TARGET SPACE DUALITY IN STRING THEORY.By Amit Giveon (Hebrew U.), Massimo Porrati (New York U.), Eliezer Rabinovici (Hebrew U.),.Published in Phys.Rept.244:77-202,1994.
- STRING DUALITY: A COLLOQUIUM.By Joseph Polchinski (Santa Barbara, KITP),Published in Rev.Mod.Phys.68:1245-1258,1996.
- THE ORIGIN OF BLACK HOLE ENTROPY IN STRING THEORY.By Gary T. Horowitz (UC, Santa Barbara),. e-Print Archive: gr-qc/9604051.
- LECTURES ON STRINGS AND DUALITIES., By Cumrun Vafa (Harvard U.),e-Print Archive: hep-th/9702201.
- AN INTRODUCTION TO NONPERTURBATIVE STRING THEORY, By Ashoke Sen (Harish-Chandra Res. Inst.),. e-Print Archive:hep-th/9802051.
- LARGE N FIELD THEORIES, STRING THEORY AND GRAVITY.By Ofer Aharony (Rutgers U., Piscataway), Steven S. Gubser (Harvard U.), Juan M. Maldacena (Harvard U. & Princeton, Inst. Advanced Study), Hirosi Ooguri (UC, Berkeley & LBL, Berkeley), Yaron Oz (CERN),.

Published in Phys.Rept.323:183-386,2000.

- QUEST FOR UNIFICATION.By Edward Witten (Princeton, Inst. Advanced Study),. e-Print Archive: hep-ph/0207124.

Challenges

- The current description of nature is based on two amazingly successful theories: The Standard Model theory of particle interactions and General Relativity theory of gravity.
- The Standard Model is a quantum theory. General Relativity is a classical theory.

Quantum Gravity

- Performing an expansion in ħ in order to quantize General Relativity meets infinities that cannot be controlled.
- Where is quantum gravity relevant ?
- The gravitational coupling is

where is the Planck

length.

Energy Scale

- The corresponding energy scale is
- The effective gravity coupling is

. The effects of gravity

grow at high energies.

Quantum Gravity Scale

- At Planck scale energies gravity will

have a strength of the order of the

standard model interactions.

The traditional (natural) quantum gravity scale is the Planck energy:

Experiment?

- The Big Bang:

Fermi’s Theory

- Analogy: Fermi’s theory of weak interactions.

The effective coupling is .

At the energy scale of the

coupling is strong and we meet divergences in perturbation theory.

This signals new physics.

Challenges

- Construct a consistent theory of quantum gravity:

A theory that reduces to generalrelativity at low energies, and where quantum computations can be made to any required order.

The theory should explain fundamental

issues such as the black hole entropy.

Challenges

- A theory that incorporates the standard model, and contains at low energies gauge fields, chiral fermions etc.

Challenges

- A theory that will explain the big bang

singularity and its resolution.

A theory that will explain the standardmodel structure, gauge group and couplings, three generations and

the standard model parameters.

Strings: Status Report

- String theory is a consistent theory of quantum gravity.
- String theory incorporates the standard

model.

- String theory has not explained yet neither the big-bang singularity, nor the particular structure of the standard

model.

Basics of String Theory

- A point particle is replaced by a vibrating string.

String Mathematics

- The mathematics based on the concept of a point is very different from the mathematics based on the concept of a loop. Strings see the world in a different way than particles.

String Spectrum

- The strings oscillate and this gives

particles with mass being the energy

of the oscillations.

Massless particles: include gauge bosons, gravitons, fermions.

Massive particles: .

Strings and Quantization of Gravity

- Adding higher curvature corrections:
- String loops:

Resolution of Singularities

- Strings resolve (time-like) singularities of space-time.

FRW Model

- How the big-bang singularity is resolved is not yet understood.

Extra Dimensions

- Consistency of string theory implies

extra dimensions.

- However, the concept of dimension may not be a good one.

Scale of Extra Dimensions

- The traditional viewpoint:

Structure of Extra Dimensions

- The properties of the internal space determine the low energy data, such as the spectrum of particles and their interactions.

Supersymmetry

- A symmetry relating bosons to fermions: every fermion has a bosonic superpartner and vice versa.

quarks squarks

gluons gluinos

Higgs Higgsino

Why Supersymmetry ?

(Riccardo Rattazzi’s talk)

- The gauge hierarchy: why the characteristic energy scale of the standard model is much smaller than the characteristic scale of gravity ?

Unification

- Unification of couplings:

Superstrings

- The way we understand string (M) theory, it requires supersymmetry (at least in some high energy scale) for

consistency.

Strings + Supersymmetry = Superstrings

Compactification

- In ten dimensions string theory has

one parameter: the string scale .

The string coupling is a modulus: the VEV of the dilaton field.

Compactification Moduli

- Compacification to four dimensionsintroduces other parameters (moduli)describing the volume and shape of theinternal space.

Lifting the Moduli

- The moduli appear in four dimensions

as massless scalars.

- Much work in done on building mechanisms to lift the moduli (give mass to the scalars).
- The introduction of fluxes is one such working framework.

Scales

- At weak string coupling ,

the string scale and the compactification scale lie

just below the Planck scale at energies

of order , far beyond experiment.

This is modified when string theory

is strongly coupled.

Model Building at

- Compactification on six dimensional spaces (Calabi-Yau) provides a rich class of supersymmetric models in four dimensions.
- One gets naturally GUT gauge groups (SU(5),SO(10),E6) and three generations of chiral fermions.
- There is a large number of scalar fields.

String Dualities

- How many different consistent string theories we have?
- There is one theory. The various string theories are related by dualities.
- S-duality:

It exchanges elementary particles with

solitons (magnetic monopoles).

Strings at Strong Coupling

R=gSlS

- String Theory in ten dimensions is

S-dual to an elevendimensional theory.

At strong coupling a new dimension

is opened up !

Type IIA

M-theory

- The eleven-dimensional theory is called M-theory. At low energies it is described by eleven-dimensional supergravity.
- Compactification on seven-dimensional manifolds, such as CY times a line segment or G2 holonomy manifolds allows model building at

D-branes

- Objects on which open strings can end.

Brane-world Scenarios

- Open string massless excitations include gauge fields.
- Closed string massless excitations include the graviton.

Compact Dimensions Scale

- The brane-world scenarios allow large extra dimensions, which are probed by the closed string modes such as the graviton. The standard model particles are confined to the brane.

The String Scale

- The brane-world scenarios allow low string scales:
- Main obstacle to quantitative realistic scenarios is the supersymmetry breaking mechanism.

Supersymmetry Breaking

- The world that we see is not supersymmetric. How is supersymmetry broken?
- Generic choice of compactification withfluxes breaks supersymmetry on the worldvolume of the D-branes. The soft terms are computable.

Branes - Antibranes systems

- Generic Branes-antibranes systems break supersymmetry. What is required is a controlled computational scheme.

Unification

- Gravity can unify with the other forces by introducing extra dimensions and changing the running of its coupling with energy.

The Landscape

- The string equations have a large

number of solutions describing different worlds. How ours is picked?

Gauge/Gravity Correspondence

- String theory on certain curved spaces

is dual to gauge theories in one lower dimension (on the boundary).

Holography (‘t Hooft)

- The number of degrees of freedom of a quantum theory of gravity in a region of space increases with the area enclosing it (and not with the volume as local quantum field theories).

The AdS/CFT Correspondence

- String theory on asymptotically anti-de-Sitter (AdS) space, with RR flux of units, is dual to four-dimensional (conformal) gauge theory (Maldacena).
- Unification: Space-time+RG scale

Map of Parameters

- On the string side there are two dimensionless expansion parameters:
- On the gauge theory side there are also

two dimensionless expansion parameters:

Large

- The curvature expansion is a strong coupling expansion on the gauge theory

side:

- String expansion is the large

expansion:

How to calculate?

- To each operator of the gauge theorycorresponds a string excitation.
- The generating functional of the ofthe correlation functions of the fieldtheory is the string partition function(with given boundary conditions).

The QCD String

- Various QCD-like backgrounds have been constructed. They exhibit confinement and mass gap.

Glueball Scattering

- Although string scattering at high energy is soft due to their extended nature, in the warped space geometry one gets the hard scattering(power law ) behaviour of glueballs at high energy.

QCD at High Temperature

- The confinement-deconfinement phase transition corresponds to two five-

dimensional geometries.

One dominates the string (gravity) action at low temperature and the other at high temperature.

Perturbative QCD

(see Lance Dixon’s talk)

- Perturbative gluon amplitudes can be computed via a dual description of topological string theory on twistor space (Witten).
- This provides simplified computational schemes and recursion relations.

Black Holes

- In classical General Relativity black holes have horizon. It is a surface in

space-time, which when crossed does not allow a return.

Due to quantum effects, black holes emit thermal radiation:

Black Hole Microstates

- What are the internal constituents of the black holes that explain the temperature? What is the microscopic origin of the Bekenstein-Hawking entropy

From D-branes to Black Holes

- For certain black holes, D-brane states are the internal constituents.

Higher Curvature Corrections

- Recently progress has been made in the study of higher curvature corrections to the black holes entropy:
- The challenge: non-supersymmetric black holes.

Non-Critical Strings

- Strings that propagate in less than tendimensions. They can provide alternative to compactification, as well as dual descriptions of gauge theories

(Polyakov).

- Geometries of the form:

The Status of Non-Critical Strings

- Tachyon free superstrings can be constructed in even dimensions.
- The curved background geometries have typically string scale curvature:

Experimental Signatures

- Supersymmetry and the mechanism of supersymmetry breaking.
- Detection of string scalar fields.
- Magnetic monopoles.
- Strings in the sky.
- Extra dimensions.
- Low scale quantum gravity.

Theoretical Signature

- Construct a string model that reproduces the low energy (standard model) data.

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