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For the experts

Notes

As I said, I am a postdoc in theoretical physics, high-energy

theoretical physics to be more precise. My main interests are in supergravity

and string theory. Well, since not everybody is an expert (...), let me explain

a bit what that means. For the experts, I will give below a more precise

description of my research. So:

- What is string theory and why are we (physicists) interested in it?
- I will try to give a flavour of that in a few lines. OK, maybe not
- that few, but if you get bored skip this paragraph.

*

- String theory is, simply put, an attempt to unify all the fundamental
- particles in Nature. In other words, particles and forces which seem
- to us to be different (because of their different properties, and different
- theories needed to explain each one of them) are, in string theory,
- fundamentally the same.
- Why do we feel we need to find such a
- unified theory? Well, unification has been a rule that governed the
- history of
physics. Maybe the first one is the idea of the
*atom*, which - ancient Greeks had already. That is, that all the different substances
- we see are composed of a few different types of atoms, combined in
- various ways. But then we found that the atom is not fundamental,
- and is
composed of a dense
*nucleus*and*electrons*orbiting around it. - The nucleus
itself is made out of
*protons*and*neutrons*, and different - atoms are just composed of different numbers of protons, neutrons
- and electrons. In the 70's, we found that the protons and neutrons are
- not
fundamental either, but are each composed of 3 subunits called
*quarks.* - So: nowadays, we have a description of the known physics in terms of
- a theory of quarks, electrons, a few other exotic particles similar to the
- electron (called leptons), and the forces between them, described by particles
- called gauge bosons (photons, gluons, W and Z). All of these are described in
- the framework of what is generically called quantum field theory (QFT).
- In QFT, each force corresponds to a particle (for example, the electro-
- magnetic force corresponds to the photon).
- But we have also gravity, which cannot be described consistently within
- this framework. And that is considered by most theorists to be a problem.
- One of the
most important discoveries of Einstein was
**General Relativity**, - which
states that
*gravity is nothing else than the curvature of spacetime.* - In string theory, the framework of quantum field theory is slightly modified,
- and gravity is described together with the other particles and forces between them.

*

- So, what is the main message of string theory? That all the known
- fundamental building blocks of Nature (quarks, leptons and gauge bosons),
- together with lots of others not discovered yet, but predicted by the theory,
- are really not point particles, but very tiny string-like objects, oscillating
- very rapidly.The length scale of this strings is so unbelievably small
- that we might never be able to probe it (observe it directly in an experiment).
- And the fact that we see different kinds of particles is due to the fact that the
- strings vibrate differently (different modes of oscillation of a string corres-
- pond to different particles).
- A characteristic of string theory is that its consistency requires the
- presence of 7 extra dimensions, besides our 4 (3 space and one time).
- This extra dimensions are unobservable because they are also
- unbelievably tiny, in fact not much more than the size of the string itself.
- In the last few years, string theory has become not only a theory of strings, but
- rather also of membrane-like objects, or even objects extended in more than 2
- spatial dimensions (remember that we have a total of 11 dimensions), called
- p-branes (by a weird linguistical extension of the word mem-brane).

*

- And then there's supergravity. What is supergravity? Another attempt to unify
- gravity with the other interactions within QFT. It is a more conventional
- (conservative) approach, and is now generally believed to be inconsistent on its
- own. But it can be viewed as a special limit of string theory (it applies for
- distance scales which are not too small - bigger than the string theory length scale).

*

**My research: **

**The AdS-CFT correspondence **(started by Juan

Maldacena, 1997, in hep-th/9711200)

**SYM- pp waves correspondence**

(started by David Berenstein, Juan Maldacena and

myself in 2002, in hep-th/0202021)

The AdS-CFT correspondence relates really only supergravity (the low

energy limit of string theory) with field theory. The SYM-pp waves

correspondence relates the full string theory on pp waves with

the field theory on the boundary, but only for a subset of

observables.

PP waves (paralel plane waves) are gravitational waves, that is

disturbances in the gravitational field (i.e.curvature of spacetime)

propagating at the speed of light.

**Matrix theory
realization of M theory
**(started by Banks, Fischler, Shenker and Susskind

in 1996, in hep-th/9610043)

Matrix theory is a particular realization of M theory, which itself is an extension

of string theory, valid when the string theory approximation breaks down. I am

working on applying Matrix theory to the SYM-pp wave correspondence, to

cosmology (the origin and evolution of the Universe), among other things.

The basic idea of Matrix theory is that the notion of spacetime is not a fundamental

concept, but a derived one. The basic objects of Matrix theory are particle-like objects,

called "D0 branes", and when there are sufficiently many (N large) of them you can talk

about an approximate spacetime description in which the N D0 branes are almost

characterized by N positions, but in reality there are N^2 (N times N) position-like

variables ("N by N matrices").

We can get a image of this strange behaviour by mentally separating a few (in the drawing

below 3) D0 branes frome the N, and let the other N-3 create an approximate spacetime

background. Then, by including the relative separations of the particles (which normally

are not independent variables, only the absolute positions are), and also saying that, e.g.,

the distance between 1 and 2 is not the same as the distance between 2 and 1, we get

3^2=9 variables.

**Experimental consequences for string theory via AdS-CFT:
high energy QCD scattering and the RHIC fireball
**(with K. Kang and by myself, 2004-2005)

AdS-CFT relates general field theories (without gravity) in our 3+1 dimensions

to gravitational theories (string theory) in an abstract curved 10 dimensional space.

Most phenomena depend on the 10d space 4+1 dimensional part, which is of

Anti de Sitter (AdS) type. The field theory models for which the relation ("duality") is

well understood are highly symmetric (Conformal Field Theories, or CFT), and it was

not clear whether anything can be said for the dual of strong interactions (Quantum

ChromoDynamics, or QCD).

I have proposed that we can use a very simple model, AdS space that ends at a

"wall", as a dual of QCD. Then scattering (colliding) at high energies particles

that interact via strong interactions is mapped to collisions in the dual (abstract)

space, where particles are "spread out" over the 5th dimension, but the interaction

is concentrated in a small region near the wall. The strong force that governs the

real interactions is mapped to the gravitational force in the dual description

(abstract AdS space). Thus at high enough energies one produces black holes

(the ultimate effect of gravitational collisions) in AdS.

Initially, the created black holes are small enough, so they don't feel the curvature

of AdS. As one increases the collision energy, the black holes get bigger, and they

"feel" the curvature of AdS, and as they get even bigger they reach the "wall" at the

end of AdS, and get stuck there. Then the dual (AdS) description is effectively

4 dimensional (as the extra coordinates are "frozen"), and thus one describes

scattering in the real 4dimensional world, that is governed by strong interactions,

via scattering in an abstract 4d world (coming from the abstract AdS space),

governed by gravitational interactions.

A simple description of the 3+1 dimensional collision (in our real world) in terms

of an effective QCD field is given below. At high enough energies (for velocities

close to the speed of light), particles get "squashed" due to relativistic effects

("Lorentz contraction"), thus a spherical object will look as a pancake. If the

colliding particles are close enough, they will form a QCD analogue of a

black hole, i.e. the fireball that is observed at RHIC (Relativistic Heavy Ion Collider,

at Brookhaven).

The dual description of the collision is in terms of effectively 4 dimensional collisions

governed by gravity, in which black holes are formed and decay, by thermal emission

of particles. However this 4 dimensional gravity is not of the usual type, but the graviton

has a mass, which means that gravity travels slower than the speed of light and has a

finite range, governed by the graviton mass.

For completeness, a simple description of the usual 4 dimensional (Schwarzschild)

black holes: They are characterized by two objects: the singularity at its center

and the event horizon at some distance from it. An infalling observer notices nothing

at the horizon, but gravity (tidal forces pulling him apart) become infinitely strong

at the singularity in the center. From the point of view of an outside observer, the

"time dilation effect" increases (time passes slower near the black hole)and becomes

infinite at the horizon (objects are "frozen in time"), and the horizon is also the

place that emits particles thermally.

The dual black hole will still have an event horizon, but it is not clear that it will

have a singularity.

Susy, sugra, strings, branes, duality (6 pages)

Supersymmetry in 4d (14 pages)

Duality (21 pages)

Seiberg-Witten theory (12 pages)

Supergravity (37 pages)

Hamiltonian quantization and BRST (17 pages)

Integrable systems, application to N=4 SYM (42 pages)

-At

-PP waves (Mar
05, 2002)

-Black holes and
QCD (Feb 25, 2005)

-At Rutgers University:

-Black holes
and QCD (Mar 8, 2005)

-at
the Newton Institute in

-High
energy QCD collisions at RHIC and the LHC from dual black hole

My research covers a
wide range of subjects in string theory and supergravity:

Gauge-string theory
dualities, nonperturbative phenomena, matrix models,

noncommutative geometry,
particle phenomenology, cosmology, as well as the

nonperturbative
definition of string theory in various backgrounds (AdS, plane waves,

M theory
alternatives) and of supergravity compactifications.

Current interests
include experimental consequences of string theory for high

energy QCD
scattering via AdS-CFT, the definition of string interactions and holography in

plane waves, a possible
new M theory definition, braneworld phenomenology,

string cosmology,
Matrix models compactifications.

The main emphasis is on
the AdS-CFT correspondence and gauge-string theory

dualities. Recently, in
the paper

**Strings in flat space
and pp-waves from N=4 Super Yang-Mills**, with

David Berenstein and
Juan Maldacena, and then in the follow-ups

**Open strings on plane
waves and their Yang-Mills duals, **

with David Berenstein,
Edi Gava, Juan Maldacena and K.S. Narain and

**On lightcone string
field theory from Super Yang-Mills and holography,
** with David
Berenstein,

I have put the foundation of a relation between string theory and gauge

theory going beyond the usual AdS-CFT (which involves only gravity, not the full string

theory). It has generated significant amount of work since then (almost 700 papers to date).

My latest work tries to derive features of high energy scattering in QCD from AdS-CFT.

In the papers (with Kyungsik Kang)

Heisenberg saturation of the Froissart bound from AdS-CFT

The soft Pomeron from AdS-CFT

I showed that the "soft Pomeron" behaviour of the total QCD cross section can be

derived from AdS-CFT, and in

I have showed that one can describe the fireball observed at RHIC as a dual black hole,

in terms of an effective (KK reduced) massive gravity in 4d.

I have tried to bring AdS holography to the level of the Standard Model, and study possible

implications for phenomenology and string model building in

breaking in the context of gravity-gauge duality was realized in

with Juan Maldacena.

I am trying to define M theory as a Chern-Simons theory, by studying the possible

use of CS supergravity in phenomenology. The first step was taken in the paper

Matrix model compactifications and a link to noncommutative geometry was studied in

Massive IIA string theory and Matrix model compactification

with David Lowe and Sanjaye Ramgoolam.

I am also trying to prove nonperturbatively the AdS-CFT correspondence. In the paper

` A
new AdS-CFT correspondence, `with Warren Siegel,

I described a discretization of the string action in AdS space which provides a link

to Yang Mills theories in 4d.

An important part of my work was the study of consistent truncations, and the

proof that the AdS(7) times S(4) KK reduction admits a consistent truncation.

The ref. for that is

**Consistency
of the AdS(7) times S(4) reduction and the**

` origin
of self-duality in odd dimensions`, with Diana Vaman

and Peter van Nieuwenhuizen.

I also wrote a paper on the quantization of solitons. As a first step towards

understanding more difficult systems, like D-branes, I studied the simplest

solitons, namely in two dimensional field theories.

Ref (see the link below to the

**Topological
boundary conditions, the BPS bound,and**

**elimination
of ambiguities in the quantum mass of**

` solitons.`
, with Misha Stephanov, Peter van Nieuwenhuizen (my

advisor), and Anton Rebhan.

I co-authored one of the first papers to find concrete evidence for the

AdS-CFT correspondence, by a calculation of 3-point correlators

in SYM and in AdS space.

The Ref. is

**R-current
correlators in N=4 SuperYang-Mills theory from**

` Anti-de
Sitter supergravity, `with Gordon Chalmers, Ruud Siebelink

and Koenraad Schalm.

Here is a link to a complete list of my papers.

and a citation summary of my papers.

And here is my proffesional CV

So we now study *branes and strings*,
which gives a few unavoidable confusions:

if you go to a conference and are lost, and ask somebody about the place where

the conference on *branes and
strings *is, he will first think what is the connection

between the *brains* and
musical intruments? In fact, I don't know wether somebody

had a joking mind or it was a coincidence, but the Strings'98 conference in

conference in

other use of the term strings...

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