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:
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
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.
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
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,
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)
the Newton Institute in
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)
High energy QCD from Planckian scattering in AdS and the Froissart bound and
Heisenberg saturation of the Froissart bound from AdS-CFT
I have showed that one can obtain the Froissart bound saturation from AdS-CFT, in
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
The RHIC fireball as a dual black hole
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
On Dp-Dp+4 systems, QCD dual and phenomenology.
The study of systems with lower (N=1 in n3d) supersymmetry and of dynamical supersymmetry
breaking in the context of gravity-gauge duality was realized in
The supergravity dual of a theory with dynamical supersymmetry breaking,
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
Towards a Chern-Simons M theory of OSp(1|32) X OSp(1|32)
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.
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
other use of the term strings...
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