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Matteo Bertolini: Research
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Quantum Field Theory
Quantum field theory is the language in which all of
modern physics is formulated. It represents the
marriage of quantum mechanics with special
relativity and provides the mathematical framework
in which to describe particle physics. A particular
class of quantum field theories known as gauge
theories have the great virtue of being able to
describe interactions between different particles.
Interacting particles
In Nature we believe there are four fundamental
interactions which, eventually, are responsible for
the physical phenomena we observe: the
electromagnetic, weak, strong and gravitational
interactions. A (gauge) quantum field theory model,
known as the Standard Model, has proven to be the
correct way to describe, to an incredible high level of
precision against experiments, the first three of
them. Unfortunately, gravity seems to escape a
consistent quantum field theory description.
String Theory
Interacting Strings
String theory is an extension of ordinary quantum
field theory which, besides other things, has the
great virtue of being able to include also gravity into
the game. For this reason, string theory is believed
to be an all-encompassing theory of the Universe,
unifying all forces of Nature. The price to pay is quite
high, though. First, it is quite hard. Second, you must
believe a number of weird things: that fundamental
objects are not point-like but rather one-dimensional
strings, that we may live not in four but in ten or
eleven space-time dimensions, etc... This could
seem science fiction, at first sight. However, once
you start entering its misteries, you get convinced
string theory is not so exotic. In fact, I believe string
theory is a quite conservative (and reasonable) way
to extend ordinary quantum field theory, after all.
I now briefly sketch those aspects of string theory I
am interested in, these days. I am a son of the
so-called Second String Revolution and my research
interests have always being centered, in a way or
another, on D-branes, these being undoubtedly the
stars of this revolution.
D-branes - The Gauge/String
Correspondence
One of the biggest achievements of the second
string revolution was to realize that in string theory,
besides fundamental strings, there are also higher
dimensional defects, called D-branes. These objects
have a two-fold nature. On the one hand their
dynamics, at low energy, can be described in terms
of gauge theory degrees of freedom. On the other
hand, they are solitons in string theory and, as such,
they arise as classical solutions of the low-energy
effective theory and curve space-time. The above
complementarity of descriptions is the central
ingredient of the so-called gauge/string
correspondence.
The dual nature of D-branes
Its original version, the AdS/CFT duality, states the
equivalence between a string theory defined on
five-dimensional Anti-de Sitter space times a
five-sphere and a very peculiar four dimensional
gauge theory, N=4 supersymmetric Yang-Mills
theory. The AdS/CFT duality is a very deep and
successful conjecture, but also has some limitations.
In particular, it deals with a highly supersymmetric
and conformal gauge theory, thus very far from
describing the physical world. Soon after the
discovery of the AdS/CFT duality many efforts were
aimed trying to overcome the above limitations and
find new dual pairs where the gauge theories under
consideration were a) less supersymmetric and b)
non-conformal. For instance, it is now clear that
many information can be gained on the perturbative
and non-perturbative properties of N=1
supersymmetric gauge theories, with and without
matter, from suitable (super)gravity backgrounds.
Progress have also been made for the more
ambitious goal of describing N=0, i.e. non
supersymmetric gauge theories. Indeed, the final
(and very difficult) goal is to find a way to describe
QCD via a suitable string dual, being able to
understand qualitatively and quantitatively the strong
coupling dynamics of QCD via these new tools.
D-branes - Brane Worlds
Imagine our Universe is a ten dimensional string
world with D-branes. In this world, gauge degrees of
freedom are confined on the branes while gravity
degrees of freedom live in the full ten dimensional
space-time. Still, weak (as we like them to be)
gravity effects may be felt on the brane. In string
theory there are D-branes of different dimensions: a
Dp-brane is a p+1-dimensional defect whose world
volume is described in terms of p spatial dimensions
and one time dimension. This raises the crazy idea
to describe the Standard Model of fundamental
interactions on a 3-brane and understand four
dimensional gravity as "pulled-back" from the ten
dimensional world. This is often summarized saying
that we live on a brane.
Living on a brane
This idea has become very popular and different
lines of research are been developed. One of them
consists in trying to embed the Standard Model (or
supersymmetric extensions thereof) into string
theory via a bottom-up approach, engineering
suitable D-brane configurations living in some given
ten dimensional geometric background so to
reproduce the known particle spectrum and
interactions, at the most possible high level of
accuracy. Intersecting and magnetized brane worlds
are examples of these models. This also opened up
the possibility of addressing old but crucial issues in
string compactifications as the problem of moduli
stabilization, in a novel and controllable way. Indeed,
via complicated enough magnetized brane world
models (and some additional closed string
background fluxes) one can in principle achieve a
Standard Model-like Lagrangian, at low energy, with
all string moduli being fixed.