Are photons open or closed strings?

Jon

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Jul 21, 2004, 12:09:54 AM7/21/04

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In one of his talks, Robert Dijkgraf said that closed strings behave as
gravitons at low energy, and that open strings manifest themselves as
photons or gluons. Half an hour later he said that Hawking radiation
appears when two open strings recombine on the brane to a closed one which
can escape into space-time.

This is contradictory -- but maybe I confuse something or misunderstood
the statement. Are photons open or closed strings? Does this depend on the
specific version of string theory? In fact, I'd like to have a sort of
mental image of a photon in string theory. Is there a way to picture
something that is precise enough to be helpful?

jon

Lubos Motl

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Jul 21, 2004, 12:17:21 AM7/21/04

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On Wed, 21 Jul 2004, Jon wrote:

> In one of his talks, Robert Dijkgraf said that closed strings behave as

> gravitons at low energy, and that open strings manifest themselves as...

Dear Jon,

in the conventional heterotic string models, all known particles are
closed strings. Moreover, gravitons are closed strings in all models -
because they are always responsible for the geometry of the whole
spacetime - i.e. they cannot be confined.

In the new brane world scenarios, all other particles except for gravitons
can be open strings stretched between the branes. This is helpful e.g. in
the "old large dimensions" models where it explains the weakness of
gravity - gravity is diluted in the large extra dimensions, but everything
else (such as photons) is concentrated on the brane.

There many other types of models where some particles arise from open
strings, some particles arise from singularities, and so on.

These different realizations of a photon are, of course, compatible with
Hawking radiation. Photons are always allowed to move anywhere in the 3+1
dimensions we know; the only ambiguity is whether they are allowed to
move in the additional dimensions. Because they can move anywhere in the
space we know, they can also be emitted by a radiating black hole.

If you would like to have one mental picture of a photon and other
particles - be sure that you're not the only one. I would also love to
have a unique model describing Nature correctly. Unfortunately, string
theory is too rich as of today and we have many potential realizations of
the known physics. Gravitons are always closed strings, as long as there
are any strings at all, but everything else can be both, depending on the
model.

Best wishes
Lubos
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pdkgpzn...@mailinator.com

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Jul 21, 2004, 3:04:28 PM7/21/04

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Dear Lubos,

to keep the discussion concrete, I'd like to focus on photons only.
Since there are many options, and all seem to have some truth, let us take one.
I am not interested (for the moment) in electrons or gravitons - just photons.

Let us take the version where photons are strings between branes, for example.
How do we have to imagine the motion of a photon? When a photon moves in a
light beam, how does the string (and the branes) move?

In simple terms, is the string perpendicular to the motion, or along it?

jon

Lubos Motl

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Jul 21, 2004, 10:34:04 PM7/21/04

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On Wed, 21 Jul 2004 pdkgpzn...@mailinator.com wrote:

> Let us take the version where photons are strings between branes, for example.
> How do we have to imagine the motion of a photon? When a photon moves in a
> light beam, how does the string (and the branes) move?
>
> In simple terms, is the string perpendicular to the motion, or along it?

Dear Jon, not only photons in braneworld scenarios, but *all* strings
everywhere in string theory always oscillate in all dimensions (which
usually means "all ten of dimensions") regardless of the motion of the
resulting photon. It would not be a critical string theory (critical means
"with the right number of spacetime dimensions, and therefore canceling
conformal anomaly") if the generic points on the string were moving in a
limited number of dimensions.

The only confined points can be the endpoints. In your case, the endpoints
are restrictd to oscillate within the worldvolume of the branes - which
includes the familiar 3+1 dimensions, and perhaps (but not necessarily)
a subset of the additional dimensions. But within the worldvolume of the
branes, again, even the endpoints are oscillating in *all* directions,
regardless of the motion of the center of mass (of your photon).

Another question is how the strings and their endpoints move in classical
string theory, which is essentially equivalent to the time evolution of
the "zero modes", especially in a particular classical solution. Yes, if
you consider a physical, transversely polarized photon (e.g.
x-polarization in a z-moving photon), the classical mode on the string
that is excited is the x-mode, which adds sinusoidal oscillations to the
string that are directed in the x-direction, and are therefore
perpendicular to the direction of motion. So the classical, average shape
of the string vibrates in this x-direction only - and this would be true
both for closed-string-photons and open-string-photons. But don't forget
that quantum mechanics implies that the string and everything else has
nonzero oscillations in all conceivable directions. Because of the
uncertainty principle, you cannot have a vanishing coordinate as well as
the same component of the velocity of a point along the string.

Urs Schreiber

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