my friends you are all invited to this seminar at AUB... read the abstract please
The Center for Advanced Mathematical Sciences (CAMS) invites you to a seminar entitled "Global Alpha-Symmetries in Superspace and GSO-free Superstrings," by Professor Dimitri Polyakov, AUB.
Abstract
We explore the hierarchy of hidden space-time symmetries of noncritical strings in RNS superstring theory, realized nonlinearly. Under these symmetry transformations the variation of the matter part of the RNS action is cancelled by that of the ghost part. These surprising global symmetries, referred to as the alpha-symmetries, are shown to originate from hidden space-time dimensions, implying the chain of holographic relations between noncritical strings and physical theories in higher dimensions. Using the alpha-symmetry generators, we modify the BRST operator of RNS superstring theory so that the tachyon is automatically excluded from the spectrum without any GSO-projection. We also argue that in the special d=4 case the physical operators of the modified BRST cohomology corresponds to those of the QCD string.
Abstract
We explore the hierarchy of hidden space-time symmetries of noncritical strings in RNS superstring theory, realized nonlinearly. Under these symmetry transformations the variation of the matter part of the RNS action is cancelled by that of the ghost part. These surprising global symmetries, referred to as the alpha-symmetries, are shown to originate from hidden space-time dimensions, implying the chain of holographic relations between noncritical strings and physical theories in higher dimensions. Using the alpha-symmetry generators, we modify the BRST operator of RNS superstring theory so that the tachyon is automatically excluded from the spectrum without any GSO-projection. We also argue that in the special d=4 case the physical operators of the modified BRST cohomology corresponds to those of the QCD string.
posted by nbr5 at 1/04/2008 01:56:00 AM
2 Comments:
are u sure this is how u spell tachyon?
(plsu u forgot to tell us the date)
I guess... because from a special relativity dynamics perspective a tachyon is a particle with space-like four-momentum. There are two equivalent approaches to handling their kinematics:
* Require that all the same formulae that apply to regular slower-than-light particles ("bradyons") also apply to tachyons. In particular the energy-momentum relation:
E^2 = p^2c^2 + m^2c^4 \;
where p is the relativistic momentum of the bradyon and m is its rest mass still holds, along with the formula for the total energy of a particle:
E = \frac{mc^2}{\sqrt{1 - \frac{v^2}{c^2}}}.
which is interpreted to mean that the total energy of a particle (bradyon or tachyon) contains a contribution from the rest mass (the "rest mass-energy") and a contribution from the body's motion, the kinetic energy.
However the energy equation has, when v is larger than c, an "imaginary" denominator, since the value inside the square root is negative. Since the total energy must be real then the numerator must also be imaginary, i.e. the rest mass m must be imaginary, since a pure imaginary number divided by another pure imaginary number is a real number.
* A simple substitution for the mass yields an equivalent way of describing tachyons with real masses. Define m = i*z (where i = \sqrt{-1}) and we get Einstein's energy-momentum relation to read:
E^2 + z^2c^4 = p^2c^2 \;
With this approach the energy equation becomes:
E = \frac{zc^2}{\sqrt{\frac{v^2}{c^2} -1}}.
And we avoid any necessity for imaginary masses, sidestepping the problem of interpreting exactly what a complex-valued mass may physically mean. Except, of course, when converting z back to m for interactions with non-tachyon particles
Both approaches are equivalent mathematically and have the same physical consequences. One curious effect is that, unlike ordinary particles, the speed of a tachyon increases as its energy decreases. (For ordinary bradyonic matter, E increases with increasing velocity, becoming arbitrarily large as v approaches c, the speed of light.) Therefore, just as bradyons are forbidden to break the light-speed barrier, so too are tachyons forbidden from slowing down to below c, since to reach the barrier from either above or below requires infinite energy.
Quantising tachyons shows that they must be spinless particles which obey Fermi-Dirac statistics, i,e. tachyons are scalar fermions, a combination which is not permitted for ordinary particles.[3] They also must be created and annihilated in pairs.
The existence of such particles would pose intriguing problems in modern physics. For example, taking the formalisms of electromagnetic radiation and supposing a tachyon had an electric charge—as there is no reason to suppose a priori that tachyons must be either neutral or charged—then a charged tachyon must lose energy as Cherenkov radiation—just as ordinary charged particles do when they exceed the local speed of light in a medium. A charged tachyon traveling in a vacuum therefore undergoes a constant proper time acceleration and, by necessity, its worldline forms a hyperbola in spacetime. However, as we have seen, reducing a tachyon's energy increases its speed, so that the single hyperbola formed is of two oppositely charged tachyons with opposite momenta (same magnitude, opposite sign) which annihilate each other when they simultaneously reach infinite velocity at the same place in space. (At infinite velocity the two tachyons have no energy each and finite momentum of opposite direction, so no conservation laws are violated in their mutual annihilation. The time of annihilation is frame dependent.) Even an electrically neutral tachyon would be expected to lose energy via gravitational Cherenkov radiation, since it has a gravitational mass, and therefore increase in velocity as it travels, as described above.
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