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(here's more on SISSA if you want)
Here's Percacci's page:
http://people.sissa.it/~percacci/
Here's a sample:
==exerpt==
ASYMPTOTIC SAFETY
A quantum field theory that is perturbatively renormalizable and asymptotically free can be regarded as a fundamental theory, because it makes sense up to arbitrarily high energies, and is predictive because it fixes all but a finite number of couplings. This kind of requirement has played a decisive role in the construction and acceptance of the standard model of particle physics.
This notion can be generalized by relaxing the condition that the fixed point be the gaussian fixed point. More precisely one says that a theory is asymptotically safe if
(1) it has a FP and
(2) the set of theories that are attracted to this fixed point is finite dimensional.
...It has been proven that 4d Einstein gravity is perturbatively nonrenormalizable,... However, it could still be asymptotically safe at a nongaussian fixed point. In the last decade the availability of new nonperturbative tools has allowed significant progress on this issue...
In the last few years we have performed three different calculations that support this hypothesis.
* a calculation in the leading order of the 1/N expansion, where N is the number of minimally coupled matter fields. This shows that a FP exists for all couplings appearing in a derivative expansion of the action.
* a one loop calculation in pure gravity based on the most general action containing up to four derivatives of the metric. This makes a very clear connection to older work on this subject by many authors and sheds light on the origin of the fixed point.
* a calculation based on an action that is a polynomial in R of order up to eight, but is otherwise "exact". In this calculation it is found that operators of order R^3 and higher are irrelevant, so that for the first time one has direct evidence for point (2) above.
Research group: Roberto Percacci, Christoph Rahmede. External collaborators: Alessandro Codello.
==endquote==
What the recent paper of Percacci, Codello, Rahmede shows is that the critical hypersurface thru the fixed point has dimension 3. If you get three parameters right, the theory will take it from there. (The fixed point is an attractor on the critical hypersurface.)
Percacci has an interesting view of unification, indicated by this sample:
==exerpt==
UNIFIED THEORIES
...
...
In these theories the word "unification" is used in a very precise technical sense: one says that two gauge theories with gauge groups G_1 and G_2 are unified if one can construct a gauge theory with group G such that G_1 and G_2 can be identified as commuting subgroups of G. At the level of the action, the theory must be invariant under tranformations of the group G. The distinction between the two interactions must be due to the nature of the vacuum state, i.e. there must be a nonzero VEV of some order parameter that "breaks" G leaving G_1 and G_2 unbroken. On the other hand, modern attempts on the original problem of unifying gravity, starting from the early 1980's, have followed mostly the proposal made in the 1920 by Kaluza and Klein. This paved the way to the general acceptance of a higher dimensional world, which is a necessary ingredient of string theory. Much of the remaining work on unified theories has been forgotten, but it contains several ideas that could still be revived and lead to a unified theory of all the interactions, including gravity, in four dimensions.
The key to this issue is a proper understanding of the sense in which the gauge principle applies to gravity. It turns out that pure gravity is a "spontaneously broken" gauge theory, meaning that it contains some order parameter fields whose kinetic term, evaluated on the vacuum, generates a mass term for the gravitational connection. That the gravitational connection is massive is consistent with the fact that no such degrees of freedom are observed at low energies. The difference between gravity and other broken gauge theories such as the Glashow-Weinberg-Salam model, is that it contains not one but two Goldstone bosons. One of them disappears in giving mass to the gauge field and the other remains visible in the form of the metric or vierbein. At low energies the connection can therefore be written as a function of the surviving Goldstone boson.
With this understanding, it appears clearly that the unification of gravity with the other interactions, in the strict technical sense now used in particle physics, can be achieved if we enlarge the gauge group...
...
==endquote==
Here's Percacci's page:
http://people.sissa.it/~percacci/
Here's a sample:
==exerpt==
ASYMPTOTIC SAFETY
A quantum field theory that is perturbatively renormalizable and asymptotically free can be regarded as a fundamental theory, because it makes sense up to arbitrarily high energies, and is predictive because it fixes all but a finite number of couplings. This kind of requirement has played a decisive role in the construction and acceptance of the standard model of particle physics.
This notion can be generalized by relaxing the condition that the fixed point be the gaussian fixed point. More precisely one says that a theory is asymptotically safe if
(1) it has a FP and
(2) the set of theories that are attracted to this fixed point is finite dimensional.
...It has been proven that 4d Einstein gravity is perturbatively nonrenormalizable,... However, it could still be asymptotically safe at a nongaussian fixed point. In the last decade the availability of new nonperturbative tools has allowed significant progress on this issue...
In the last few years we have performed three different calculations that support this hypothesis.
* a calculation in the leading order of the 1/N expansion, where N is the number of minimally coupled matter fields. This shows that a FP exists for all couplings appearing in a derivative expansion of the action.
* a one loop calculation in pure gravity based on the most general action containing up to four derivatives of the metric. This makes a very clear connection to older work on this subject by many authors and sheds light on the origin of the fixed point.
* a calculation based on an action that is a polynomial in R of order up to eight, but is otherwise "exact". In this calculation it is found that operators of order R^3 and higher are irrelevant, so that for the first time one has direct evidence for point (2) above.
Research group: Roberto Percacci, Christoph Rahmede. External collaborators: Alessandro Codello.
==endquote==
What the recent paper of Percacci, Codello, Rahmede shows is that the critical hypersurface thru the fixed point has dimension 3. If you get three parameters right, the theory will take it from there. (The fixed point is an attractor on the critical hypersurface.)
Percacci has an interesting view of unification, indicated by this sample:
==exerpt==
UNIFIED THEORIES
...
...
In these theories the word "unification" is used in a very precise technical sense: one says that two gauge theories with gauge groups G_1 and G_2 are unified if one can construct a gauge theory with group G such that G_1 and G_2 can be identified as commuting subgroups of G. At the level of the action, the theory must be invariant under tranformations of the group G. The distinction between the two interactions must be due to the nature of the vacuum state, i.e. there must be a nonzero VEV of some order parameter that "breaks" G leaving G_1 and G_2 unbroken. On the other hand, modern attempts on the original problem of unifying gravity, starting from the early 1980's, have followed mostly the proposal made in the 1920 by Kaluza and Klein. This paved the way to the general acceptance of a higher dimensional world, which is a necessary ingredient of string theory. Much of the remaining work on unified theories has been forgotten, but it contains several ideas that could still be revived and lead to a unified theory of all the interactions, including gravity, in four dimensions.
The key to this issue is a proper understanding of the sense in which the gauge principle applies to gravity. It turns out that pure gravity is a "spontaneously broken" gauge theory, meaning that it contains some order parameter fields whose kinetic term, evaluated on the vacuum, generates a mass term for the gravitational connection. That the gravitational connection is massive is consistent with the fact that no such degrees of freedom are observed at low energies. The difference between gravity and other broken gauge theories such as the Glashow-Weinberg-Salam model, is that it contains not one but two Goldstone bosons. One of them disappears in giving mass to the gauge field and the other remains visible in the form of the metric or vierbein. At low energies the connection can therefore be written as a function of the surviving Goldstone boson.
With this understanding, it appears clearly that the unification of gravity with the other interactions, in the strict technical sense now used in particle physics, can be achieved if we enlarge the gauge group...
...
==endquote==
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