mysteries of extra dimensions
Joseph Lykken
Fermi National Accelerator Laboratory
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a revolution in the making
 the physics of extra dimensions is a revolution
in the making
 like the quantum mechanics revolution of the 1920’s,
it is the result of many new ideas (from many people)
coming together to give a radically new picture of
physics and of the universe
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the universe: traditional view
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the universe: a bigger view
extra dimensions of space
everything we know about is on this slice
the rest is terra incognita
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questions for this talk
 why do physicists think that there
are extra dimensions of space?
 what is the physics that hides
extra dimensions?
 how can experiments discover and
explore extra dimensions?
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why do physicists think that there
are extra dimensions of space?
Reason #1: string theory
particle physicists developed string theory to
understand quantum gravity - to explain extreme
physics such as goes on inside black holes
supermassive black hole in
the center of galaxy M87
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string theory
in string theory, all the elementary particles
are merely different vibrations of a
single substance called strings.
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string theory
physicists have shown that quantum theory
only allows one unique theory of quantum
strings… but there is a catch:
quantum strings need 9 spatial dimensions to wiggle in!
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why do physicists think that there
are extra dimensions of space?
Reason #2: mysteries of particle physics
all ordinary matter is composed of just
three kinds of elementary particles.
but in particle accelerators we produce
many more!
why do these extra particles exist,
and why these particles but not others?
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in string theory the answer lies
in the shape of the extra dimensions
slice of a
6 dimensional CalabiYau space
determines how many ways the strings can vibrate,
and thus whether there are 3, 12, or 137 kinds of
elementary particles.
particle physics data already in our hands may be an
encrypted map of the geography of extra dimensions.
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why do physicists think that there
are extra dimensions of space?
Reason #3: the Big Bang
the three spatial dimensions that
we see are changing – expanding
we don’t understand what is the
dark energy driving the expansion
today
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why do physicists think that there
are extra dimensions of space?
Reason #3: the Big Bang
the three spatial dimensions that
we see are changing – expanding
we don’t understand what drove
cosmic inflation in the early
universe
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why do physicists think that there
are extra dimensions of space?
Reason #3: the Big Bang
the three spatial dimensions that
we see are changing – expanding
we don’t understand what
this was
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why do physicists think that there
are extra dimensions of space?
Reason #3: the Big Bang
the three spatial dimensions that
we see are changing – expanding
extra dimensions may be the
extra ingredient that explains
the history of the universe
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hidden dimensions
if extra spatial dimensions exist, they must be
(for some reason) difficult to probe
physicists have uncovered several possible
explanations:
e.g. the extra spatial dimensions
are compact and small
Nordstrom, Kaluza, and Klein, circa 1920
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compact extra dimensions
what do we look for experimentally?…
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Kaluza-Klein modes
if spatial dimension is compact
then momentum in that
dimension is quantized:
n
p
R
from our point of view we see new massive particles!
m 2  m02 
n2
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R
R2
3
R
KK momentum
tower of states
2
R
p
1
R
0
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how do we look for Kaluza-Klein particles?
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21st century particle physics
Fermilab’s Tevatron is the highest
energy accelerator in the world today.
protons collide with antiprotons at 2 TeV
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Kaluza-Klein dark matter
H-S Cheng, J. Feng, and K. Matchev
G. Servant and T. Tait
if we live in the “bulk” of compact extra dimensions,
then Kaluza-Klein parity (i.e. KK momentum)
is conserved.
so the lightest massive KK particle (LKP) is stable
could be a KK neutrino, bino, or photon
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how heavy is the LKP?
current data requires MLKP ~> 300 GeV
LKP as CDM wants MLKP ~ 600 – 1200 GeV
might be too heavy for the Tevatron, but the
LHC collider experiments will certainly see this
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furthermore, we could have signals from
direct searches in the next generation of
WIMP detectors
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hidden dimensions
recently, we have uncovered some more radical
explanations for hidden dimensions:
e.g. it may be that not all particles
(in a certain energy range)
move, probe, or see
the same number of spatial dimensions
a dramatic realization of this is called
the braneworld
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braneworlds
only gravitons and exotics
move in the “bulk” of the
extra dimensional universe
Standard Model particles are trapped on a brane and
can’t move in the extra dimensions
various kinds of braneworld scenarios
are quite natural in string theory
in the most extreme version of braneworld,
only gravity tells us about the extra dimensions
only the graviton (the force particle of gravity)
can move off the brane into extra dimensions
this hides the extra dimensions quite
efficiently, since gravity effects are hard to measure…
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gravitons
may be our only probe of extra dimensions
but gravity is so weak that we have never
even seen a graviton.
melectronmelectron
F=GN
r2
melectron
r
melectron
The gravitational attraction between two electrons is
about 1042 times smaller than the electromagnetic
repulsion.
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extra dimensions change gravity
gravity gets stronger at extremely high energies
MPlanck = 1019 GeV (or very short distances)
it gets stronger at not-so-high energies
(not-so-short distances) if there are extra dimensions….
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ADD braneworld models
Arkani-Hamed, Dimopoulos, Dvali
assume that only gravity sees n large extra
compact dimensions with common size R:
M
2
Planck
n
~R M
n 2
*
in ADD models M* ~ 1 TeV, in order to
eliminate the hierarchy problem of the
Standard Model. This energy scale is
perhaps in reach of the Fermilab Tevatron
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these are large extra dimensions
n 1

R ~ 109 Km
n2

R ~ 1mm
Pinhead
n3

R ~ 1nm
Gold atom

n  6,7 
Solar system
R ~ 10 fm
we can test these models in a variety
of experiments
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force laws
single photon exchange
single graviton exchange
both give 1/r potentials
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force laws
if extra dimensions appear at some length scale R,
exchange of massive graviton KK modes gives
additional Yukawa potentials
a e-r/l/r
look for these deviations in short-range gravity expts
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:
Eot-Wash
Group
no deviations seen at ~200 microns
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still possible to see something at ~ 10 microns
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lower bounds on M* , in TeV
astrophysics and cosmology constrain
ADD (or other) models with too many
low mass KK gravitons
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quantum gravity at colliders
if ADD is correct collider expts should see
effects of both real and virtual massive
KK gravitons
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quantum gravity at colliders
because we are on a brane, 2 SM particles
can collide to produce a single massive
graviton
quark
gluon (becomes
jet of hadrons)
antiquark
graviton
the graviton “escapes”
into the extra dimensions
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tree diagrams for qqbar
graviton + gluon
implemented
in PYTHIA
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these gravitons are heavy!
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CDF simulation courtesy M. Spiropulu
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Caveat:
while the monojet signature is
spectacular, it can be mimicked
by several Standard Model processes
now let’s look at real data
from the Tevatron:
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CDF preliminary
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CDF preliminary
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gravitons at the LHC
graviton has spin 2
M=1.5 TeV
100fb-1
Angular distributions
ATLAS can distinguish spin 2 vs 1 up to 1.72 TeV
B.C. Allanach, K. Odagiri, M.A. Parker, B.R. Weber (JHEP 09 (2000) 019 – ATL-PHYS-2000-029)
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virtual KK graviton exchanges will interfere
with SM diagrams in a variety of processes
theory treatment is slightly bogus because
sum of KK modes is sensitive to details of
the real UV theory
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Randall–Sundrum
warped space
G
mother brane
5th dimension
zero mode graviton likes to
be near mother, but Kaluza-Klein
graviton modes do not
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in warped space, it is
natural for gravity to be weak
• if we live anywhere but the “mother brane”,
gravity will seem weak
• gravity is weak because of small probability for
graviton to be near the weak brane
• on the weak brane the mass hierarchy of the
Standard Model becomes natural
• this scenario is testable at high energy colliders
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the warped braneworlds hide the
extra dimensions even more efficiently
than ADD braneworlds:
current experimental upper bounds
on the size of extra dimensions:
compactified space:
ADD braneworlds:
warped braneworld :
R <~ 10-16 cm
R <~ 200 microns
R <= infinity!
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collider signals can also be dramatically different
H. Davoudiasl, J. Hewett, T. Rizzo
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science fiction, science fact
although extra dimensions is
a pretty weird concept,
physics has already produced
many even weirder phenomena
the real leap of imagination
is designing experiments to
explore the extra dimensions - if they exist.
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new accelerators for new physics
Large Hadron Collider (CERN, 2007)
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new accelerators for new physics
Linear Collider
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emergent spacetime
long ago philosopher Immanuel Kant gave
a ~500 page proof that space and time are
a priori
however to make sense of quantum gravity,
not to mention the Big Bang singularity,
this cannot be true
in the real theory of everything,
spacetime should be emergent.
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emergent spacetime
a great theoretical challenge for the future
is to figure out where spacetime comes from
in the first place
spacetime must somehow arise “dynamically”,
but what does dynamics mean without spacetime?
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what is a dimension, anyway?
a good starting point is to realize that, operationally,
an extra dimension of space just means new degrees
of freedom of a certain type (Kaluza-Klein modes).
but we already have discovered examples in
string theory (e.g. AdS/CFT) where new degrees
of freedom can be interpreted either as an extra
dimension or as new dynamics without an
extra dimension!
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deconstructing dimensions
N. Arkani-Hamed, A. Cohen, H. Georgi
H-C Cheng, C. Hill, S. Pokorski, J. Wang
recently we have even discovered how to do
this in simple models that do not carry all
the heavy baggage of full-blown string theory
these “deconstruction models” are a first step
to a more dynamical understanding of
spacetime dimensions
particle theorists are learning to think differently…
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